Total Electron Content (TEC) estimation over Pakistan from local GPS network using spherical harmonics

Many organizations allow GNSS users to access Global Ionosphere Maps (GIMS). However, the TEC estimates derived from GIMs are of insufficient quality to describe small-scale TEC variations over Pakistan. In this paper, the first local TEC map over Pakistan for the year 2019, derived from a regional GPS network, is presented. Spherical harmonics expansion is employed to estimate TEC with the spatial resolution of latitude 0.2° x longitude 0.2° and temporal resolution of 5 minutes. The impact of changing the degree/order of harmonics is assessed and it is determined that harmonic expansion up to 6 degrees is sufficient for estimating accurate TEC map for the region of interest. We have demonstrated that the TEC maps of Pakistan generated by local model conform better to the GIM by Center of Orbit Determination (CODE) (RMS = 5.83) as compared to International Reference Ionosphere (IRI-2016) (RMS = 7.18). We found that the TEC estimated by the local model shows a better correlation to measured TEC; CODE-GIM overestimated TEC, while IRI-2016 underestimates it. Moreover, it was observed that TEC peaks during noon (1100-0100 LT) and Equinox (April). The residuals of local TEC estimates with respect to TEC obtained from CODE- GIM indicate the inaccuracy of CODE-GIM over the region of Pakistan: highest deviation of TEC from local model with respect to CODE –GIM was observed in April (RMS = 8.73) and minimum in October (RMS = 2.78). We have also analyzed the performance of our maps in geomagnetically disturbed days. The research presented in this paper will contribute towards the ionosphere study over Pakistan, where limited research is available currently.

Unusual Structures of Interpolyelectrolyte Complexes: Vesicles and Perforated Vesicles

By means of computer simulation and analytical theory, we first demonstrated that the interpolyelectrolyte complexes in dilute solution can spontaneously form hollow spherical particles with thin continuous shells (vesicles) or with porous shells (perforated vesicles) if the polyions forming the complex differ in their affinity for the solvent. The solvent was considered good for the nonionic groups of one macroion and its quality was varied for the nonionic groups of the other macroion. It was found that if the electrostatic interactions are weak compared to the attraction induced by the hydrophobicity of the monomer units, the complex in poor solvent tends to form “dense core–loose shell” structures of different shapes. The strong electrostatic interactions favor the formation of the layered, the hollow, and the filled structured morphologies with the strongly segregated macroions. Vesicles with perforated walls were distinguished as the intermediate between the vesicular and the structured solid morphologies. The order parameter based on the spherical harmonics expansion was introduced to calculate the pore distribution in the perforated vesicles depending on the solvent quality. The conditions of the core–shell and hollow vesicular-like morphologies formation were determined theoretically via the calculations of their free energy. The results of the simulation and theoretical approaches are in good agreement.

Simulating the diffraction line profile from nanocrystalline powders using a spherical harmonics expansion

An accurate description of the diffraction line profile from nanocrystalline powders can be obtained by a spherical harmonics expansion of the profile function. The procedure outlined in this work is found to be computationally efficient and applicable to the line profile for any crystallite shape and size. Practical examples of the diffraction pattern peak profiles resulting from cubic crystallites between 1 and 100 nm in size are shown.

Homogenization of a spherical harmonics expansion model

This paper deals with the analysis of the behavior of a Spherical Harmonics Expansion (SHE) model associated with an oscillating electrostatic potential.

The Application of Improved Spherical Harmonics Expansion-Based Multilevel Fast Multipole Algorithm in the Solution of Volume-Surface Integral Equation

During the solution of volume-surface integral equation (VSIE), to reduce the core memory requirement of the radiation patterns (RPs) of the basis functions, an improved spherical harmonics expansion-based multilevel fast multipole algorithm (SE-MLFMA) using the mixed-potential representation and the triangle-/tetrahedron-based grouping scheme is applied. Numerical results show that accompanying with a faster speed, the memory requirement of the RPs in the improved SE-MLFMA is several times less than that in the conventional MLFMA without compromising accuracy. A result employing the OpenMP parallelization and vector arithmetic logic unit (VALU) hardware acceleration technique is also shown to illustrate the robustness and scalability of the improved SE-MLFMA method.