Electron Density Model Research Articles

An Electron Density Model of the D‐ and E‐Region Ionosphere for Transionospheric VLF Propagation

AbstractTerrestrial Very‐Low‐Frequency (VLF) energy from both lightning discharges and radio transmitters has a role in affecting the energetic electrons in the Van Allen radiation belts, but quantification of these effects is particularly difficult, largely due to the collisional damping experienced in the highly variable electron density in the D‐ and E‐region ionosphere. The Faraday International Reference Ionosphere (FIRI) model was specifically developed by combining lower‐ionosphere chemistry modeling with in situ rocket measurements, and represents to date the most reliable source of electron density profiles for the lower ionosphere. As a full‐resolution empirical model, FIRI is not well suited to D‐ and E‐region ionosphere inversion, and its applicability in transionospheric VLF simulation and in remote sensing of the lower ionosphere is limited. Motivated by how subionospheric VLF remote sensing has been aided by the Wait and Spies (WS) profile (Wait & Spies, 1964), in this study, we parameterize the FIRI profiles and extend the WS profile to the E‐region ionosphere by introducing two new parameters: the knee altitude hk and the sharpness parameter for the E‐region ionosphere βE. Using this modified WS profile, we calculate the expected signals at different receiver locations from the NAA, NPM, and NWC transmitters under the full range of possible ionospheric conditions. We also describe and validate a method about how these results can be readily used to translate VLF measurements into estimates of the lower ionosphere electron density. Moreover, we use this method to evaluate the sensitivity of different ground receiver locations in lower‐ionosphere remote sensing.

Measuring Density Functional Parameters from Electron Diffraction Patterns.

We integrate density functional theory (DFT) into quantitative convergent-beam electron diffraction (QCBED) to create a synergy between experiment and theory called QCBED-DFT. This synergy resides entirely in the electron density which, in real materials, gives rise to the experimental CBED patterns used by QCBED-DFT to refine DFT model parameters. We use it to measure the Hubbard energy U for two strongly correlated electron systems, NiO and CeB_{6} (U=7.4±0.6 eV for d orbitals in NiO and U=3.0±0.6 eV for f orbitals in CeB_{6}), and the boron position parameter x for CeB_{6} (x=0.1992±0.0003). In verifying our measurements, we demonstrate an accuracy test for any modeled electron density.

Quantification of Ionospheric Perturbations From Lightning Using Overlapping Paths of VLF Signal Propagation

AbstractLightning induced perturbations of the lower ionosphere are investigated with very low frequency (VLF) remote sensing on a unique overlapping propagation path geometry. The signals from two VLF transmitters (at different frequencies) are observed at a single receiver after propagation through a common channel in the Earth‐ionosphere waveguide. This measurement diversity allows for greater certainty in quantification of perturbations to the ionospheric D region. Changes in amplitude and phase are modeled with the Long Wave Propagation Capability (LWPC) software package to quantify changes in reference height and steepness of the two parameter D region electron density model. Since the nighttime D region profile prior to the perturbation is found to strongly affect the resulting quantification, and is highly variable and generally unknown at nighttime, an error minimization method for identifying the most likely ionospheric disturbance independent of the ambient profile is used. Analysis of 12 large lightning perturbations resulting from discharges with peak currents greater than 160 kA shows that the ionospheric reference height can change by 2–8 km. We investigate both early/fast events (direct ionization and heating from lightning) and lightning‐induced electron precipitation (LEP) events, induced by lightning hundreds of kilometer away. LEP events increase D region electron density while early/fast events can lead to a increase or decrease in electron density. Multi‐point observations along a VLF propagation path are needed to further improve ionospheric perturbation quantification with VLF remote sensing.

Echo occurrence in the southern polar ionosphere for the SuperDARN Dome C East and Dome C North radars

In this paper, echo occurrence rates for the Dome C East (DCE) and the new Dome C North (DCN) radars are studied. We report the ionospheric and ground scatter echo occurrence rates for selected periods around equinoxes and solstices in the final part of the solar cycle XXIV. The occurrence maps built in Altitude Adjusted Corrected Geomagnetic latitude and Magnetic Local Time coordinates show peculiar patterns highly variable with season. The comparisons of the radar observations with the International Reference Ionosphere model electron density and with ray tracing simulations allow us to explain the major features of observed patterns in terms of electron density variations. The study shows the great potential of the DCE and DCN radar combination to the Super Dual Auroral Radar Network (SuperDARN) convection mapping in terms of monitoring key regions of the high-latitude ionosphere critical for understanding of the magnetospheric dynamics.

Effect of Hydrostatic Pressure and Temperature on Quantum Confinement of AlGaN/GaN HEMTs

In this paper, an analytical model for quantum confinement electron density in two-dimensional quantum well, has been investigated. In order to obtain the exact AlGaN/GaN HEMTs parameters such as electron density, the wave function, band gap, polarization charge, effective mass and dielectric constant, the hydrostatic pressure and temperature effects are taken into account. It has been found that the electron density decreases with increasing temperature and increases with increasing hydrostatic pressure. With increasing hydrostatic pressure, the effective mass decreases and the quantum confinement electrons are increased in the quantum well. Also with increasing hydrostatic pressure, the height of wave functions increase and decreases electron wave functions to penetrate the quantum barrier but increasing the temperature behaves the opposite of increasing the pressure. However, with increasing temperature, the effective mass is increased and the quantum confinement electrons are reduced. The calculated results for electron density are in good agreement with existing experimental data.

A Global Empirical Model of Electron Density Profile in the F Region Ionosphere Basing on COSMIC Measurements

AbstractThe topside ionosphere accounts for a dominant part of the ionospheric total electron content, whereas accurate global modeling of topside ionospheric electron density (Ne) profile has not been fully achieved. In this study, a high precision Ne profile model, named α‐Chapman Based Electron Density Profile Model (α‐Chapman‐Based‐EDP), was built by using ∼4.5 million Ne profiles from the Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC‐1) radio occultations. We first describe each of the profiles using five parameters of the α‐Chapman function, that is, peak density (NmF2) and height (hmF2) of F2 layer, scale height (Hm) as well as its altitude change rates, and then built a model for each of the parameters as a function of latitude, longitude, month, local time, and solar activity, through Empirical orthogonal function (EOF) analysis and Fourier expansion. Combining all the five models, we construct the α‐Chapman‐Based‐EDP. Compared with observations from COSMIC‐1 and ‐2, the model captures the ionospheric climatology well, such as solar activity dependence, seasonal variation, and spatial pattern, including the equatorial ionization anomaly and midlatitude trough as well as their variabilities. Our model can describe nearly 80% variability of Ne in F region. In contrast, the IRI2016 cannot well reproduce these characteristics, with errors higher than our model. The potential applications of our model were also discussed. A dense matrix data calculated by the model will be released in https://www.researchgate.net/profile/Qiaoling_Li5 with the permissions of COSMIC organizations.

Application of a Multi‐Layer Artificial Neural Network in a 3‐D Global Electron Density Model Using the Long‐Term Observations of COSMIC, Fengyun‐3C, and Digisonde

AbstractThe ionosphere plays an important role in satellite navigation, radio communication, and space weather prediction. However, it is still a challenging mission to develop a model with high predictability that captures the horizontal‐vertical features of ionospheric electrodynamics. In this study, multiple observations during 2005–2019 from space‐borne global navigation satellite system (GNSS) radio occultation (RO) systems (COSMIC and FY‐3C) and the Digisonde Global Ionosphere Radio Observatory are utilized to develop a completely global ionospheric three‐dimensional electron density model based on an artificial neural network, namely ANN‐TDD. The correlation coefficients of the predicted profiles all exceed 0.96 for the training, validation and test datasets, and the minimum root‐mean‐square error of the predicted residuals is 7.8 × 104 el/cm3. Under quiet space weather, the predicted accuracy of the ANN‐TDD is 30%–60% higher than the IRI‐2016 at the Millstone Hill and Jicamarca incoherent scatter radars. However, the ANN‐TDD is less capable of predicting ionospheric dynamic evolution under severe geomagnetic storms compared to the IRI‐2016 with the STORM option activated. Additionally, the ANN‐TDD successfully reproduces the large‐scale horizontal‐vertical ionospheric electrodynamic features, including seasonal variation and hemispheric asymmetries. These features agree well with the structure revealed by the RO profiles derived from the FORMOSAT/COSMIC‐2 mission. Furthermore, the ANN‐TDD successfully captures the prominent regional ionospheric patterns, including the equatorial ionization anomaly, Weddell Sea anomaly and mid‐latitude summer nighttime anomaly. The new model is expected to play an important role in the application of GNSS navigation and in the explanation of the physical mechanisms involved.

An Electron Density Model of the D- and E-region Ionosphere for Transionospheric VLF Propagation

An Electron Density Model of the D- and E-region Ionosphere for Transionospheric VLF Propagation

A Novel Method for Deriving the Vary‐Chap Scale Height Profile in the Topside Ionosphere

AbstractThe modeling of topside ionospheric electron density using height‐varying scale height methods have received increasing attention. The modified Chapman function with a variable scale height, known as Vary‐Chap function, can well represent the topside electron density profiles, and is considered as a promising direction to improve the International Reference Ionosphere model. In order to facilitate modeling, a new formula with four unknown coefficients is proposed to fit the Vary‐Chap scale height, and these unknowns can be determined by the least squares technique. The approximated electron density profile is reconstructed by using the fitted scale height, and its average percentage error relative to the measured electron density profile is quantitatively analyzed by using the Alouette/ISIS topside sounder data sets and COSMIC radio occultation databases, and the accuracies of five other approaches (i.e., Nava et al., 2008, https://doi.org/10.1016/j.jastp.2008.01.015; Nusmei et al., 2012, https://doi.org/10.1029/2012RS004989; Porl et al., 2019, https://doi.org/10.1007/s10712-019-09521-3; Reinisch et al., 2007, https://doi.org/10.1016/j.asr.2006.05.032; Wu et al., 2020, https://doi.org/10.1029/2019JA027637) to approximate the topside electron density profiles are also compared. From the perspective of average percentage error, our formula performs well to reconstruct the topside electron density profiles, especially at the altitudes between hmF2 and hmF2 + 1,200 km.

Multipole electron densities and structural parameters from synchrotron powder X-ray diffraction data obtained with a MYTHEN detector system (OHGI).

Powder X-ray diffraction has some inherent advantages over traditional single-crystal X-ray diffraction in accurately determining electron densities and structural parameters due to the lower requirements for sample crystallinity, simpler corrections and measurement simultaneity. For some simple inorganic materials, it has been shown that these advantages can compensate for disadvantages such as peak overlap and error-prone background subtraction. Although it is challenging to extend powder X-ray diffraction-based electron-density studies to organic materials with significant peak overlap, previous results using a dedicated vacuum diffractometer with a large image-plate camera (AVID) demonstrated that it can be done. However, the vacuum setup with the off-line detector system was found to prohibit a widespread use. Fast microstrip detectors, which have been employed at a number of powder diffraction beamlines, have the potential to facilitate electron-density studies. Nevertheless, no electron-density studies even for materials with slight peak overlap have been performed with microstrip detectors. One of the most critical problems has been a difference in sensitivity between microstrip channels, which substantially defines the dynamic range of a detector. Recently, a robust approach to this problem has been developed and applied to a total scattering measurement system (OHGI) with 15 MYTHEN microstrip modules. In the present study, synchrotron powder X-ray diffraction data obtained with OHGI are evaulated in terms of multipole electron densities and structural parameters (atomic positions and displacement parameters). These results show that, even without a dedicated setup and perfect samples, electron-density modelling can be carried out on high-quality powder X-ray diffraction data. However, it was also found that the required prior information about the sample prohibits widespread use of the method. With the presently obtainable data quality, electron densities of molecular crystals in general are not reliably obtained from powder data, but it is an excellent, possibly superior, alternative to single-crystal measurements for small-unit-cell inorganic solids. If aspherical atomic scattering factors can be obtained from other means (multipole databases, theoretical calculations), then atomic positions (including for hydrogen) and anisotropic atomic displacement parameters (non-hydrogen atoms) of excellent accuracy can be refined from synchrotron powder X-ray diffraction data on organic crystals.

Unveiling the high regioselectivity and stereoselectivity within the synthesis of spirooxindolenitropyrrolidine: A molecular electron density theory perspective

AbstractA molecular electron density theory (MEDT) study for the [3 + 2] cycloaddition (32CA) reaction of indoledione and N‐methyl glycine with (E)‐1‐bromonitrostyrene leading to the spirooxindole‐pyrrolidine adduct is presented. Electron localisation function (ELF) study of the in situ generated azomethine ylide classifies a pseudodiradical electronic structure associated with low activation energies. This 32CA reaction is a polar process with electronic flux from the strongly nucleophilic azomethine ylide to the strongly electrophilic nitrostyrene, confirmed from the global electron density transfer (GEDT) above 0.20 e at the transition states (TSs). Parr function analysis predicts the correct regioselectivity from the two‐centre interactions. The reaction is kinetically controlled with negative free energy of reaction which makes it irreversible. The activation enthalpy of the favoured TS is lowered by 3.4, 6.3 and 9.3 kcal mol−1 in methanol relative to the other feasible reaction paths, consistent with the experimentally observed complete regioselectivity and stereoselectivity. ELF topological characterisation along the reaction path predicts a two‐stage one‐step molecular mechanism, and bond formation is controlled by the nucleophilic character of the azomethine ylide. ELF study, Laplacian of electron density and independent gradient model (IGM) analysis predict non‐covalent interactions at the TSs, where the new C–C bond formation has not been started.

HAR, TAAM and BODD refinements of model crystal structures using Cu Kα and Mo Kα X-ray diffraction data

The Independent Atom Model (IAM) of electron density is used in routine X-ray data analysis. However, this model does not give a quantitative description of the electron-density distribution. A better model that allows for modelling of aspherical charge density deformations is introduced by the Hansen–Coppens variant of the multipole model of electron density. However, the application of this model requires crystals of excellent quality and high-resolution XRD data which are quite often difficult criteria to fulfil. Therefore, Mo Kα and Cu Kα data of three model compounds (tricyclic imide, xylitol and methyluracil) were refined using IAM and new methods which enabled the refinement and reconstruction of charge density based on the Cu Kα data. These methods were the Bond-Oriented Deformation Density (BODD) model, Hirshfeld Atom Refinement (HAR) and the Transferable Aspherical Atom Model (TAAM). The final results were compared to the model obtained from neutron diffraction experiments. Our results demonstrated not only that Cu Kα data may be refined using BODD, HAR and TAAM methods, but also revealed systematic errors arising from the use of Cu Kα data. These errors were a result of the limited information in the low-resolution data set that manifested as higher values for the anisotropic displacement parameters (ADPs) and smaller maxima and minima of the residual electron density for the Cu Kα data compared to the Mo Kα data. Notably, these systematic errors were much less significant than those found for the IAM. Therefore, the application of BODD, HAR and TAAM on Cu Kα data has a more significant influence on the final results of refinement than for the Mo Kα data.

Thickness parameters in the empirical modeling of bottomside electron density profiles

All empirical models of the ionosphere electron density profile rely, among other parameters, on the efficient description of the thickness of the F2 layer that controls the profile shape. Considering the trend towards data assimilation in such models to give near real time 3D specification of the electron density, the efficiency of such description becomes particularly important. This paper discusses the thickness parameters of the International Reference Ionosphere (IRI) and NeQuick2 empirical models and their effects on the modeled electron density profiles by comparing them with experimentally derived profiles. A simple technique to optimize the use of experimental data to forecast electron density specifications is proposed. It is based on the previous output of the assimilation of NmF2, hmF2, with the addition of the experimentally computed thickness parameters of the IRI and NeQuick models. This technique appears to be able to forecast reasonably well the electron density profile at least 30 min ahead of a given epoch. The possible use of such electron density profile forecast, for applications in HF radio waves propagation is suggested.

Global Comparison of F2-Layer Peak Parameters Estimated by IRI-2016 With Ionospheric Radio Occultation Data During Solar Minimum

The F2-layer peak parameters of the International Reference Ionosphere (IRI) model are critical to its subsequent applications because of the vital role of the peak parameters in determining other IRI model outputs. Therefore, we analyzed the statistical deviation and ionospheric climatology of NmF2/hmF2 between the most current version of the IRI model, namely IRI-2016, and ionospheric radio occultation (IRO) data, including Constellation Observing System for Meteorology Ionosphere and Climate (COSMIC) and FengYun-3C (FY3C), during the recent solar minimum in 2017-2019. The International Union of Radio Science (URSI) model for F2-layer peak electron density (NmF2) and the Bilitza-Sheikh-Eyfrig (BSE), Altadill-Magdaleno-Torta-Blanch (AMTB), and SHUbin (SHU) models for maximum ionization height (hmF2) in IRI-2016 are compared with the IRO dataset. A statistical analysis shows a systematic offset of less than 10% in NmF2 between IRI-2016 URSI and IRO data, and the SHU option for hmF2 shows a better fit to IRO data than BSE and AMTB. A climatology comparison shows that NmF2 estimated by IRI-2016 URSI is consistent with that of the IRO dataset in terms of the general trend in the typical ionospheric characteristics; except for some discrepancies in the marine area, the IRO data may provide a feasible reference for IRI estimation in marine regions. The hmF2 options of BSE/AMTB/SHU show hemispheric asymmetry like the IRO dataset. Moreover, hmF2 of BSE/AMTB and IRO/SHU show some discrepancies in fine structures, such as the day-night reversal phenomenon.

A quantum crystallographic approach to short hydrogen bonds.

In this work we use high-resolution synchrotron X-ray diffraction for electron density mapping, in conjunction with ab initio modelling, to study short O—H⋯O and O+—H⋯O− hydrogen bonds whose behaviour is known to be tuneable by temperature. The short hydrogen bonds have donor–acceptor distances in the region of 2.45 Å and are formed in substituted urea and organic acid molecular complexes of N,N′-dimethylurea oxalic acid 2 : 1 (1), N,N-dimethylurea 2,4-dinitrobenzoate 1 : 1 (2) and N,N-dimethylurea 3,5-dinitrobenzoic acid 2 : 2 (3). From the combined analyses, these complexes are found to fall within the salt-cocrystal continuum and exhibit short hydrogen bonds that can be characterised as both strong and electrostatic (1, 3) or very strong with a significant covalent contribution (2). An additional charge assisted component is found to be important in distinguishing the relatively uncommon O—H⋯O pseudo-covalent interaction from a typical strong hydrogen bond. The electron density is found to be sensitive to the extent of static proton transfer, presenting it as a useful parameter in the study of the salt–cocrystal continuum. From complementary calculated hydrogen atom potentials, we attribute changes in proton position to the molecular environment. Calculated potentials also show zero barrier to proton migration, forming an ‘energy slide’ between the donor and acceptor atoms. The better fundamental understanding of the short hydrogen bond in the ‘zone of fluctuation’ presented in a salt-cocrystal continuum, enabled by studies like this, provide greater insight into their related properties and can have implications in the regulation of pharmaceutical materials.

A comparison of Galactic electron density models using PyGEDM

AbstractGalactic electron density distribution models are crucial tools for estimating the impact of the ionised interstellar medium on the impulsive signals from radio pulsars and fast radio bursts. The two prevailing Galactic electron density models (GEDMs) are YMW16 (Yao et al. 2017, ApJ, 835, 29) and NE2001 (Cordes & Lazio 2002, arXiv e-prints, pp astro–ph/0207156). Here, we introduce a software packagePyGEDMwhich provides a unified application programming interface for these models and the YT20 (Yamasaki & Totani 2020, ApJ, 888, 105) model of the Galactic halo. We usePyGEDMto compute all-sky maps of Galactic dispersion measure (DM) for YMW16 and NE2001 and compare the large-scale differences between the two. In general, YMW16 predicts higher DM values towards the Galactic anticentre. YMW16 predicts higher DMs at low Galactic latitudes, but NE2001 predicts higher DMs in most other directions. We identify lines of sight for which the models are most discrepant, using pulsars with independent distance measurements. YMW16 performs better on average than NE2001, but both models show significant outliers. We suggest that future campaigns to determine pulsar distances should focus on targets where the models show large discrepancies, so future models can use those measurements to better estimate distances along those line of sight. We also suggest that the Galactic halo should be considered as a component in future GEDMs, to avoid overestimating the Galactic DM contribution for extragalactic sources such as FRBs.

Investigation of the ionosphere over Antarctica under quiet space weather conditions: results of vertical sounding of the ionosphere September 14–24, 2020

We present observational results of variations in the ionospheric parameters hmF2 and NmF2 over the Ukrainian Antarctic station “Akademik Vernadsky” for magnetically quiet conditions. The results of comparative analysis of observational data and the International Reference Ionosphere-2016 model predictions are presented. The main objective of this study is to investigate the temporal variations of two key ionospheric parameters – the F2 layer peak height and electron density – during very quiet space weather conditions using data of vertical sounding of the ionosphere obtained over the Ukrainian Antarctic station “Akademik Vernadsky” and comparison the observation results with model values. Methods: The temporal variations of the F2 layer peak height and electron density were calculated from ionograms obtained with ionosonde installed at the Ukrainian Antarctic station “Akademik Vernadsky” with subsequent electron density profile inversion. Diurnal variations of hmF2 and NmF2 were calculated using a set of sub-models of the IRI-2016 model for comparison with results of observational studies. Results: We found that for the Antarctic region option of IRI-2016 model for the F2 layer peak height SHU-2015 provides a better fit for hmF2 through the investigated period compare to the AMTB-2013 model predictions. Electron density models (URSI, CCIR) generally well reproduce the observed variations of NmF2 during periods of absence non-standard manifestations of space weather, which are possible for quiet conditions too. Hypotheses regarding the possible reasons for experimental and model differences in variations of NmF2 are discussed. The analysis of effect of geomagnetic storm on September 24, 2020 on NmF2 variations was carried out. Conclusions: The obtained results demonstrate peculiarities of the state of the ionosphere-plasmasphere system over Antarctica under very quiet space weather conditions and provide evaluation of predictive capabilities of modern international reference ionosphere models. New knowledge about the features of electron density variations in the ionosphere for magnetically quiet conditions over the Antarctic region has practical value for specialists which are engaged in the study of the near-Earth space environment, in particular, at high latitudes, and also work on correction of global ionospheric models. Keywords: electron density, F2 layer peak height, ionosonde, quiet space weather, models of the ionosphere, downward plasma flux

Estimating foF2 from GPS TEC over Islamabad and Darwin using NeQuick2 during 2011–2014

This paper describes statistical attempts of estimating the critical frequency of the F2 layer (foF2) using Global Positioning System (GPS) Total Electron Content (TEC), with the help of electron density model NeQuick2, for monthly hourly median conditions. The stations under study are Islamabad (geog. lat: 33.66° N, long: 73.23° E, geomag. lat: 25.21° N) and Darwin (geog. lat: 12.46° S, long: 130.85° E, geomag. lat: 21.96° S) for the years 2011 to 2014. As first approximation, a linear regression analysis between ionosonde foF2 values and GPS TEC produced a regression coefficient that lies between 77% to 83% at Darwin and between 81% and 87% at Islamabad. Two methods were used for the same purpose - First, using GPS TEC and NeQuick2 slab thickness, which produced the Root Mean Square Error (RMSE) of less than 1 MHz at Islamabad, but greater than 1 MHz for Darwin. Second, using an iteration process by ingesting GPS TEC in NeQuick2 to improve foF2 such that optimum foF2 obtained by iteration process has corresponding NeQuick2 TEC, which is close to GPS one within ±5%. This provides foF2 estimation with 84% confidence over Islamabad. The results show that the attempts are inspiring for obtaining reliable foF2 from GPS TEC over Islamabad.

Adaptation of the NeQuick2 model for GNSS wide-area ionospheric delay correction in China and the surrounding areas

As an empirical three-dimensional ionospheric electron density model, NeQuick2 can generally represent the temporal and spatial characterization of ionospheric Total Electron Content (TEC) at a global scale. However, mismodeling errors usually exist between NeQuick2 representation and actual state of short-term ionospheric variation in small scales. In this contribution, an adaptation method is proposed for the NeQuick2 model based on data ingestion with GNSS-derived ionospheric TEC data. The relationship between the background NeQuick2 Slant TEC (STEC) estimations and real STEC measurements can be properly modelled with a ‘scaling factor’ in a highly efficient manner. In order to verify the feasibility and usefulness of the algorithm, validation experiments are carried out with GNSS tracking stations in China and the surrounding areas under different levels of solar activity. The results show that the bias of NeQuick2 corrections after adaptation are mostly within 1.0 TECu, suggesting that the systematic bias of the original NeQuick2 model can be significantly reduced. In comparison with about 50%-70% STEC RMS errors corrected by the original NeQuick2 model, the NeQuick2 model after adaptation can generally correct about 80% − 90% STEC RMS errors, which is also better than the CODE final GIM product as it has smaller residual bias and uses fewer reference stations. Therefore, the proposed algorithm can be satisfactorily applied in wide area GNSS ionospheric corrections.

Structure and stoichiometry of CTAB-DNA complexes.

We have studied the structure of cetyltrimethylammonium bromide-DNA complexes using small angle x-ray diffraction and elemental analysis. These complexes exhibit a two-dimensional hexagonal phase. The diffraction data have been analyzed using electron density models based on two different structures of these complexes proposed in the literature, which differ in the micelle to DNA stoichiometry. The structure with a 1:2 micelle-DNA stoichiometry is found to be more consistent with the diffraction data. Furthermore, this structure is also supported by the stoichiometry deduced from elemental analysis. Madelung energies of the two structures, calculated from the electrostatic interaction between their cylindrical constituents, give insight into their relative stability.