Radiative Condensation Research Articles

Thermal and Turbulent Properties of the Warm Neutral Medium in the Solar Neighborhood

Abstract The transition from the diffuse warm neutral medium (WNM) to the dense cold neutral medium (CNM) is what set the initial conditions to the formation of molecular clouds. The properties of the turbulent cascade in the WNM, essential to describe this radiative condensation process, have remained elusive in part due to the difficulty in mapping out the structure and kinematics of each H i thermal phase. Here we present an analysis of a 21 cm hyper-spectral data cube from the GHIGLS H i survey where the contribution of the WNM is extracted using ROHSA, a Gaussian decomposition tool that includes spatial regularization. The distance and volume of the WNM emission is estimated using 3D dust extinction map information. The thermal and turbulent contributions to the Doppler line width of the WNM were disentangled using two techniques, one based on the statistical properties of the column density and centroid velocity fields, and the other on the relative motions of CNM structures as a probe of turbulent motions. We found that the volume of WNM sampled here (5.2 × 105 pc3), located at the outer edge of the Local Bubble, shows thermal properties in accordance with expected values for heating and cooling processes typical of the solar neighborhood: P th/k B = (4.4 ± 2.6) × 103 K cm−3, n = 0.74 ± 0.41 cm−3, and T k = (6.0 ± 1.3) × 103 K. The WNM has the properties of sub/trans-sonic turbulence, with a turbulent Mach number at the largest scale probed here (l = 130 pc) of , a density contrast of , and velocity and density power spectra compatible with k −11/3. The low Mach number of the WNM provides dynamical conditions that allow the condensation mode of thermal instability to grow freely and form CNM structures, as predicted by theory.

Influence of ionization and ion loss on radiative and gravitational instabilities of inhomogeneous plasma with dust polarization force

In the present work, the radiative condensation and gravitational instabilities of inhomogeneous self-gravitating partially ionized dusty plasma have been studied with dust polarization force, ionization and recombination. The basic equations are constructed using four fluid model. The full dynamics of charged dust grains, ions and neutral species are employed considering the electrons as inertialess which have finite thermal conductivity and radiative cooling. The general dispersion relation is derived and discussed for different dusty plasma situations. It is found that the instability conditions are greatly affected due to the polarization force and recombination. Specifically, it is pointed out that the polarization force enhances the growth rate of both the radiative and gravitational instability while the recombination frequency decreases it. Both the parameters have influencing role in short wavelength regime. The e-folding times are calculated for maximum growth rates of gravitational and radiative condensation instabilities. The present work is applicable for study of interstellar molecular clouds and therefore the corresponding free fall time of molecular clouds is also presented.

Micromechanics modeling and homogenization of glass fiber reinforced polymer composites subject to synergistic deterioration

Composites have been successfully adopted in manufacturing and aerospace applications and are rapidly expanding into civil infrastructure. This paper develops an experimentally-validated 3D multi-physics finite element model for predicting the synergistic effects of combined physical/chemical degradation processes of UV radiation and water condensation at elevated temperatures in representative volume elements of glass fiber reinforced polymeric matrix composites subjected to environmental exposure and mechanical loading. Validation studies are conducted by comparing the results of multi-physics FEM simulations with accelerated exposure experiments. Sensitivity analyses are conducted to investigate the effect of mesh density on the accuracy of results. The effects of woven structure, diffusive parameters, and matter loss flux on the evolution of deterioration are analyzed on both a local and global scale.

Mechanical properties of pultruded GFRP profiles under seawater sea sand concrete environment coupled with UV radiation and moisture

In this research, the mechanical properties of various glass fibre reinforced polymer (GFRP) pultruded profiles exposed to seawater sea sand concrete (SWSSC) and its combination with UV radiation and water vapour condensation were studied. The effect of different conditions, duration of conditioning, and the profile cross-section configuration on the mechanical properties were investigated. Three-point bending, tension, and compression tests were carried out to obtain the mechanical properties, including flexural, tensile and compressive strengths and tensile elastic modulus. Furthermore, in order to scrutiny the mechanisms and extent of damage, scanning electron microscopy (SEM) was carried out on the test samples before and after the exposures. Finally, regression models were derived according to the experimental data to describe the mechanical properties of profiles after exposure to the aggressive environments used in this study. The maximum reductions of about 30%, 33% and 46% were observed in three-point bending, tensile and compressive tests, respectively amongst all samples when exposed for 90 days to simulated SWSSC. These reductions increased for the same sections to 52%, 47%, and 50% when the GFRP profiles were pre-exposed for 3000 h to UV radiation and moisture before exposing for 90 days to simulated SWSSC.

Hydrophilic radiative cooler for direct water condensation in humid weather

Sub-ambient radiative cooling has been achieved recently by applying advanced nanofabrication technologies, which attracts extensive research attention due to its passive cooling characteristic. Water condensation is an important application of radiative cooling, which is also an unconventional technology for gaining fresh water without consuming energy. However, limited efforts have been devoted to improving the water harvesting using the state-of-the-art radiative cooling materials. To efficiently accomplish dew condensation by radiative cooling, we first take a theoretical approach to analyze the weather conditions for effective dew condensation. Then, we propose the durable enhance specular reflector-metal by 3 M Company (DESR-M) as an efficient material for dew condensation and further improve its dew condensation performance through a simple hydrophilic coating. The dew condensation performance shows significant enhancement over the previously used polytetrafluororoethylene (PTFE) radiative condenser. On-site experiment result shows that the hydrophilic DESR-M can achieve lowest cooling temperature among all the three samples. The dew yield improves by 72.7% and 88.1% compared to DESR-M and PTFE, respectively.

Radiative and gravitating modes in the partially ionized magnetized dusty plasma

In the present study, fluid theory is used to investigate the gravitational and radiative condensation instabilities of a partially ionized magnetized dusty plasma system. The effects of ion and electron capture by dust grains, the charge variation of dust grains, and the radiative effects of electron species are also taken into account. The dynamics of all four species are considered to derive modified densities that further lead to a general dispersion relation. The general dispersion relation describes the propagation of low frequency electrostatic dust acoustic waves in magnetized self-gravitating partially ionized dusty plasma with ionization-recombination, dust charge variations, and radiative effects. Gravitational modes of propagation and radiative modes of propagation are illustrated separately for both parallel and perpendicular cases. Conditions for instabilities are also derived to explain the gravitational collapse and radiative condensation of the system. The numerical results are presented to signify the role of dust neutral collision frequency, dust charge fluctuation, magnetic field, and recombination ionization effects on both the radiative condensation and gravitational instabilities. The relevance of the present study to interstellar molecular clouds is also discussed and the effect of considered parameters on the critical wavelength, critical wave number, luminosity, etc., has been investigated.

Processing effects on the kinetics morphology and properties of hybrid sol-gel superhydrophobic coatings

Hybrid superhydrophobic sol-gel coatings were synthesized and applied on glass substrates. Low surface energy was obtained by using hydrophobic organo-functionalized silanes and roughness was formed by alkyl modified silica nanoparticles (NPs). However, these superhydrophobic coating (SHCs) are known to exhibit lack of interfacial adhesion of the NPs and limited interfacial adhesion with the underlying substrates, as demonstrated by their ease of removal in harsh environments. In this study, hybrid hydrophobic sol-gel and hydrophobic silica NPs based SHCs were prepared with the objective to obtain enhanced interfacial adhesion both between the silica NPs and the sol-gel matrix and between the sol gel matrix and glass substrates. Consequently, three curing processes were studied: Thermal, radiation, and dual curing. Dual-cured SHC presented the highest mechanical and environmental durability. It retained its superhydrophobicity (SH) for 17 tape peels and for 1000 h under accelerated weathering conditions. Failure analysis indicated that strong interfacial bonding was formed at the interface between the alkyl modified silica NPs and the hybrid hydrophobic sol gel matrix due to the interfacial free radical chemistry as well as between the sol gel coating and the glass substrate due to condensation chemistry. Moreover, the dual-cured hybrid sol-gel demonstrated transparent SHCs with over 90 % optical transmittance, water contact angle (CA) of 160˚ and a correspondingly sliding angle (SA) of ∼0˚. Morphological and roughness analyses revealed a uniform, hierarchic structure consisting of micro- and nano-sized asperities with Gaussian peak density distribution, like the Lotus leaf surface. According to ATR-IR analysis, dual curing process combines the mechanisms of chain polymerization of functional vinyl silane by radiation and thermal condensation polymerization of fluoro-silane to form a siloxane network. Hence, only chain or only condensation mechanisms lead to partial crosslinked network and low interfacial adhesion of the NPs to the sol-gel system. The dual-cured coating's failure appeared to be more ductile, compared to the brittle fracture and the delamination that were observed for thermal or radiation-cured coatings, respectively.

Effects of UV radiation, moisture and elevated temperature on mechanical properties of GFRP pultruded profiles

The present research examines the effects of UV radiation, moisture and elevated temperature on the mechanical properties of GFRP pultruded profiles. Flexural, compressive and tensile properties of different GFRP sections were studied after they were exposed for 1000, 1500, 2000 and 3000 h to UV radiation and water vapour condensation cycles. Mechanical tests, including three-point bending, compression and tension tests, SEM analyses, and statistical studies were conducted to gather comprehensive results. The results showed that the mechanical properties of various GFRP sections generally decreased with the duration of conditioning: however, the rate of the decrease that was only slight up to 1000 h, increased rapidly during 1000–2000 h, and again it was slow during 2000–3000 h. The maximum reductions were 34%, 28% and 23% after exposure to 3000 h cycles for bending, tensile and compression tests, respectively. In the bending tests, where inter-laminar shear failure controls ultimate strength, the degradation was greater compared to the situation where fibres fracture controls the failure. Further, regarding the cross-section parameter, it was concluded that the thickness and perimeter are the effective factors; the thinner the sample and the larger the perimeter, the greater is the reduction. However, the maximum effect of the cross section in terms of thickness and perimeter did not exceed 13% among all sections.

Effect of Fibers Configuration and Thickness on Tensile Behavior of GFRP Laminates Exposed to Harsh Environment.

The present study indicates the importance of using glass fiber reinforced polymer (GFRP) laminates with appropriate thickness and fibers orientation when exposed to harsh environmental conditions. The effect of different environmental conditions on tensile properties of different GFRP laminates is investigated. Laminates were exposed to three environmental conditions: (1) Freeze/thaw cycles without the presence of moisture, (2) freeze/thaw cycles with the presence of moisture and (3) UV radiation and water vapor condensation cycles. The effect of fiber configuration and laminate thickness were investigated by considering three types of fiber arrangement: (1) Continuous unidirectional, (2) continuous woven and (3) chopped strand mat and two thicknesses (2 and 5 mm). Microstructure and tensile properties of the laminates after exposure to different periods of conditioning (0, 750, 1250 and 2000 h) were studied using SEM and tensile tests. Statistical analyses were used to quantify the obtained results and propose prediction models. The results showed that the condition comprising UV radiation and moisture condition was the most aggressive, while dry freeze/thaw environment was the least. Furthermore, the laminates with chopped strand mat and continuous unidirectional fibers respectively experienced the highest and the lowest reductions properties in all environmental conditions. The maximum reductions in tensile strength for chopped strand mat laminates were about 7%, 32%, and 42% in the dry freeze/thaw, wet freeze/thaw and UV with moisture environments, respectively. The corresponding decreases in the tensile strength for unidirectional laminates were negligible, 17% and 23%, whereas those for the woven laminates were and 7%, 24%, and 34%.

Analysis of radiative gravitational modes in magnetized dusty plasma with non-thermal ion distribution

The characteristics of radiative gravitational modes in non-thermal magnetized dusty plasma with charge fluctuation and the polarization force of dust particles are investigated. The electron species are assumed to be radiative and the ions are assumed to be non-thermal. A normal mode analysis is applied to derive the general dispersion relation for radiative magnetized self-gravitating dusty plasma. Modified radiative condensation and self-gravitational instability criteria for both perpendicular and parallel modes of propagation are obtained. Analytically, it is found that the presence of a non-thermal ion population significantly modified the usual radiative condensation instability criterion, and damped the growth rate of the radiative mode. The obtained analytical results are further discussed in the numerical result section. We investigate the fact that the non-thermal ion population acts as a stabilizing source for radiative condensation instability in magnetized self-gravitating dusty plasma fluid, including the dust polarization force and charge fluctuation. The thermal conductivity with non-thermal ion distribution quickly moves the system towards stability. The implications of the results in the region of the interstellar medium (ISM) are discussed.

Comparative Analysis of Hygrothermal Behaviour of the Exterior Walls in Transient Regime

Energy conservation and an intelligent use of resources are among primary objectives in the contemporary society. The decrease of energy consumption in buildings has many benefits both on operating costs and environment preservation too. During the buildings life-cycle, the energy consumption for operation, in winter through heating and in summer through ventilation, is more important than the energy used in the construction phase, requiring passive measures from the design stage. The paper presents the results of a study of the behaviour, in a variable regime, of the external wall with different structures, to the mass transfer and temperature variations. The influence of the placement of interior or exterior thermal insulation layers on the hygrothermal behaviour of the envelope element was determined by means of WUFI® Pro software, which takes into account the built-in moisture, driving rain, solar radiation, long-wave radiation, capillary transport, and summer condensation.

ROHSA: Regularized Optimization for Hyper-Spectral Analysis

Context. Extracting the multiphase structure of the neutral interstellar medium is key to understanding star formation in galaxies. The radiative condensation of the diffuse warm neutral medium producing a thermally unstable lukewarm medium and a dense cold medium is closely related to the initial step leading the atomic-to-molecular (HI-to-H2) transition and the formation of molecular clouds. Up to now, the mapping of these phases out of 21 cm emission hyper-spectral cubes has remained elusive mostly due to the velocity blending of individual cold structures present on a given line of sight. As a result, most of the current knowledge about the HI phases rests on a small number of absorption measurements on lines of sight crossing radio sources. Aims. The goal of this work is to develop a new algorithm to perform separation of diffuse sources in hyper-spectral data. Specifically the algorithm was designed in order to address the velocity blending problem by taking advantage of the spatial coherence of the individual sources. The main scientific driver of this effort was to extract the multiphase structure of the HI from 21 cm line emission only, providing a means to map each phase separately, but the algorithm developed here should be generic enough to extract diffuse structures in any hyper-spectral cube. Methods. We developed a new Gaussian decomposition algorithm named ROHSA based on a multi-resolution process from coarse to fine grid. ROHSA uses a regularized nonlinear least-square criterion to take into account the spatial coherence of the emission and the multiphase nature of the gas simultaneously. In order to obtain a solution with spatially smooth parameters, the optimization is performed on the whole data cube at once. The performances of ROHSA were tested on a synthetic observation computed from numerical simulations of thermally bi-stable turbulence. We apply ROHSA to a 21 cm observation of a region of high Galactic latitude from the GHIGLS survey and present our findings. Results. The evaluation of ROHSA on synthetic 21 cm observations shows that it is able to recover the multiphase nature of the HI. For each phase, the power spectra of the column density and centroid velocity are well recovered. More generally, this test reveals that a Gaussian decomposition of HI emission is able to recover physically meaningful information about the underlying three-dimensional fields (density, velocity, and temperature). The application on a real 21 cm observation of a field of high Galactic latitude produces a picture of the multiphase HI, with isolated, filamentary, and narrow (σ ~ 1−2 km s−1) structures, and broader (σ ~ 4−10 km s−1), diffuse, and space-filling components. The test-case field used here contains significant intermediate-velocity clouds that were well mapped out by the algorithm. As ROHSA is designed to extract spatially coherent components, it performs well at projecting out the noise. Conclusions. In this paper we introduce ROHSA, a new algorithm that performs a separation of diffuse sources in hyper-spectral data on the basis of a Gaussian decomposition. The algorithm makes no assumption about the nature of the sources, except that each one has a similar line width. The tests we made shows that ROHSA is well suited to decomposing complex 21 cm line emission of regions of high Galactic latitude, but its design is general enough that it could be applied to any hyper-spectral data type for which a Gaussian model is relevant.

Multiscale Applications of Two Online-Coupled Meteorology-Chemistry Models during Recent Field Campaigns in Australia, Part I: Model Description and WRF/Chem-ROMS Evaluation Using Surface and Satellite Data and Sensitivity to Spatial Grid Resolutions

Air pollution and associated human exposure are important research areas in Greater Sydney, Australia. Several field campaigns were conducted to characterize the pollution sources and their impacts on ambient air quality including the Sydney Particle Study Stages 1 and 2 (SPS1 and SPS2), and the Measurements of Urban, Marine, and Biogenic Air (MUMBA). In this work, the Weather Research and Forecasting model with chemistry (WRF/Chem) and the coupled WRF/Chem with the Regional Ocean Model System (ROMS) (WRF/Chem-ROMS) are applied during these field campaigns to assess the models’ capability in reproducing atmospheric observations. The model simulations are performed over quadruple-nested domains at grid resolutions of 81-, 27-, 9-, and 3-km over Australia, an area in southeastern Australia, an area in New South Wales, and the Greater Sydney area, respectively. A comprehensive model evaluation is conducted using surface observations from these field campaigns, satellite retrievals, and other data. This paper evaluates the performance of WRF/Chem-ROMS and its sensitivity to spatial grid resolutions. The model generally performs well at 3-, 9-, and 27-km resolutions for sea-surface temperature and boundary layer meteorology in terms of performance statistics, seasonality, and daily variation. Moderate biases occur for temperature at 2-m and wind speed at 10-m in the mornings and evenings due to the inaccurate representation of the nocturnal boundary layer and surface heat fluxes. Larger underpredictions occur for total precipitation due to the limitations of the cloud microphysics scheme or cumulus parameterization. The model performs well at 3-, 9-, and 27-km resolutions for surface O3 in terms of statistics, spatial distributions, and diurnal and daily variations. The model underpredicts PM2.5 and PM10 during SPS1 and MUMBA but overpredicts PM2.5 and underpredicts PM10 during SPS2. These biases are attributed to inaccurate meteorology, precursor emissions, insufficient SO2 conversion to sulfate, inadequate dispersion at finer grid resolutions, and underprediction in secondary organic aerosol. The model gives moderate biases for net shortwave radiation and cloud condensation nuclei but large biases for other radiative and cloud variables. The performance of aerosol optical depth and latent/sensible heat flux varies for different simulation periods. Among all variables evaluated, wind speed at 10-m, precipitation, surface concentrations of CO, NO, NO2, SO2, O3, PM2.5, and PM10, aerosol optical depth, cloud optical thickness, cloud condensation nuclei, and column NO2 show moderate-to-strong sensitivity to spatial grid resolutions. The use of finer grid resolutions (3- or 9-km) can generally improve the performance for those variables. While the performance for most of these variables is consistent with that over the U.S. and East Asia, several differences along with future work are identified to pinpoint reasons for such differences.

Impact of Dynamic State on the Mass Condensation Rate of Solar Prominences

Abstract The interiors of quiescent prominences are filled with turbulent flows. The evolution of upflow plumes, descending pillars, and vortex motions has been clearly detected in high-resolution observations. The Rayleigh–Taylor instability is thought to be a driver of such internal flows. Descending pillars are related to the mass budgets of prominences. There is a hypothesis of dynamic equilibrium where the mass drainage via descending pillars and the mass supply via radiative condensation are balanced to maintain the prominence mass; however, the background physics connecting the two different processes is poorly understood. In this study, we reproduced the dynamic interior of a prominence via radiative condensation and the mechanism similar to the Rayleigh–Taylor instability using a three-dimensional magnetohydrodynamic simulation including optically thin radiative cooling and nonlinear anisotropic thermal conduction. The process to prominence formation in the simulation follows the reconnection–condensation model, where topological change in the magnetic field caused by reconnection leads to radiative condensation. Reconnection is driven by converging motion at the footpoints of the coronal arcade fields. In contrast to the previous model, by randomly changing the speed of the footpoint motion along a polarity inversion line, the dynamic interior of prominence is successfully reproduced. We find that the mass condensation rate of the prominence is enhanced in the case with dynamic state. Our results support the observational hypothesis that the condensation rate is balanced with the mass drainage rate and suggest that a self-induced mass maintenance mechanism exists.

Modified Jeans instability of collisional dusty magnetoplasma in presence of radiative cooling and dust charge fluctuation

We have investigated the modifications in the self-gravitational instability of magnetized collisional dusty plasma, arising from the radiative effects of electrons and ions, and charge fluctuation of dust. The electron and ion dynamics are described by their radiative effects and considering the full dynamics of dust and neutrals, the general dispersion relation is derived. The properties of the general dispersion relation are discussed in the absence and presence of dust charge fluctuation. The results of these two cases are further reduced for parallel and perpendicular modes of propagation. The consequences of magnetic field, collisions, dust charge fluctuation, and radiative condensation on the growth rate of self-gravitational instability are discussed analytically and graphically. We found that the radiative effects and dust charge variation increase the growth rate of self-gravitational instability while the presence of magnetic field and collisions shows the stabilizing behavior. The findings are discussed in context of the structure formation in interstellar clouds.

Observation of Marfes in the Wendelstein 7-X stellarator with inboard limiters

In the first operational campaign of the Wendelstein 7-X (W7-X) stellarator we observed Marfe-like radiation belts at the plasma edge. We describe and analyze the behaviour of these radiation belts, especially with respect to the high density inside the belt, with a set of suitable diagnostics. We present evidence suggesting that these Marfe-like radiation belts are triggered by a drop of the edge temperature below 30 eV. From this observation we draw the conclusion that the physical cause of Marfes in tokamaks and Marfe-like radiation belts in W7-X is the same, namely radiative condensation. Furthermore, both exhibit the device symmetry, i.e. axisymmetry in a tokamak and the fivefold stellarator symmetry in W7-X.

Water harvesting from fog using building envelopes: part I

AbstractNew sources of clean water are currently being researched and implemented, to face global water shortage. Techniques such as desalination or cloud seeding can have a high yield but present problems such as excessive energy consumption or consistent environmental impacts. Fog harvesting stands out for being considerably simpler and inexpensive compared to the previous. In the last decades researchers have developed detailed studies and numerical models, supported by a number of successful examples located mainly in arid or seasonally arid climates. This study surveys existing methods to collect water from fog, such as drop coalescence on vertically placed meshes, chemical absorption and desorption and radiative condensers. Yields from different collectors are compared and some considerations on influencing climatic factors are discussed, suggesting that radiative systems may be applied on building envelopes as collection devices. A follow‐up paper will present experimental results on applying radiative collection systems in buildings.

Water harvesting from fog using building envelopes: part II

AbstractFog harvesting stands out as a simple and inexpensive form to produce drinkable water from alternative sources, when compared to other available techniques. This paper presents results from a set of experiments performed on radiative condensers, deemed as a promising system to be integrated in building envelopes, following a literature review on fog condensers presented in a previous work. An analysis of condensation potential obtained using high emissivity substrates and titanium dioxide nanocoatings is presented, as well as the influence of sample position and orientation, and impact of climatic variables. Finally, the role of nanotechnology in overcoming limitations of radiative systems is discussed as a means to increase harvesting efficiency with functionalized, engineered nano‐patterns on collector surface. Based on biomimicry principles, nanocoatings including nanoscale 3D optimal geometries are discussed, and the use of nanoimprint technology (NIL) is proposed to massively produce nano‐patterned panels with biomimetic fog capturing features.

Effect of Sequential Exposure to UV Radiation and Water Vapor Condensation and Extreme Temperatures on the Mechanical Properties of GFRP Bars

AbstractThis paper presents test results carried out to investigate the mechanical properties of E-glass fiber-reinforced polymer (E-GFRP) bars with four different diameters (6, 8, 10, and 14 mm) a...

Particle removal mechanisms in synergistic aging of polymers and glass reinforced polymer composites under combined UV and water

Complex degradation processes occur during synergistic aging of polymers and Polymer Matrix Composites (PMCs) by UV radiation and water condensation at elevated temperatures. The damage is associated with the formation of surface micro-particles and their subsequent removal by slowly moving water. The particle removal significantly accelerates the overall degradation process of the materials [1]. In this research, hydrodynamic effects have been analyzed to explain removals of micro-particles from polymeric materials affected by synergistic aging by UV and water. Viscous shear stresses generated by slowly moving water were determined on polymer surfaces as a function of surface morphology, flow rates, and volumetric forces. Subsequently, a new micro-particle removal mechanism was suggested by comparing the adhesion forces calculated using the Johnson-Kendall-Roberts (JKR) model and the Hamaker approach with the drag forces created by slow water flows. In the experimental part, the particle removal mechanism has been verified on an inclined unidirectional glass/epoxy surface with randomly distributed epoxy particles subjected to a gravitational flow of water. It has been shown that the movement of polymer particles on polymer/composite surfaces depends very strongly on particle sizes, water velocity and surface morphology. The research presented in this study clearly explains why polymer and GRP degradation by UV in the presence of occasional slow water flows is much faster than just by the individual exposure to UV radiation reported in Ref. 1.