The Grad-Shafranov Reconstruction of Toroidal Magnetic Flux Ropes: Method Development and Benchmark Studies

We develop an approach of Grad-Shafranov (GS) reconstruction for toroidal structures in space plasmas, based on in-situ spacecraft measurements. The underlying theory is the GS equation that describes two-dimensional magnetohydrostatic equilibrium as widely applied in fusion plasmas. The geometry is such that the arbitrary cross section of the torus has rotational symmetry about the rotation axis $Z$, with a major radius $r_0$. The magnetic field configuration is thus determined by a scalar flux function $\Psi$ and a functional $F$ that is a single-variable function of $\Psi$. The algorithm is implemented through a two-step approach: i) a trial-and-error process by minimizing the residue of the functional $F(\Psi)$ to determine an optimal $Z$ axis orientation, and ii) for the chosen $Z$, a $\chi^2$ minimization process resulting in the range of $r_0$. Benchmark studies of known analytic solutions to the toroidal GS equation with noise additions are presented to illustrate the two-step procedures and to demonstrate the performance of the numerical GS solver, separately. For the cases presented, the errors in $Z$ and $r_0$ are 9$^\circ$ and 22\%, respectively, and the relative percent error in the numerical GS solutions is less than 10\%. We also make public the computer codes for these implementations and benchmark studies.Comment: submitted to Sol. Phys. late Dec 2016; under review; code will be made public once review is ove

Green's function method for single-particle resonant states in relativistic mean field theory

Relativistic mean field theory is formulated with the Green's function method in coordinate space to investigate the single-particle bound states and resonant states on the same footing. Taking the density of states for free particle as a reference, the energies and widths of single-particle resonant states are extracted from the density of states without any ambiguity. As an example, the energies and widths for single-neutron resonant states in $^{120}$Sn are compared with those obtained by the scattering phase-shift method, the analytic continuation in the coupling constant approach, the real stabilization method and the complex scaling method. Excellent agreements are found for the energies and widths of single-neutron resonant states.Comment: 20 pages, 7 figure

Ternary Hom-Nambu-Lie algebras induced by Hom-Lie algebras

The purpose of this paper is to investigate ternary multiplications constructed from a binary multiplication, linear twisting maps and a trace function. We provide a construction of ternary Hom-Nambu and Hom-Nambu-Lie algebras starting from a binary multiplication of a Hom-Lie algebra and a trace function satisfying certain compatibility conditions involving twisting maps. We show that mutual position of kernels of twisting maps and the trace play important role in this context, and provide examples of Hom-Nambu-Lie algebras obtained using this construction

Investigation of Solid Dispersion of Atorvastatin Calcium in Polyethylene Glycol 6000 and Polyvinylpyrrolidone

Purpose: To improve the solubility and bioavailability of atorvastatin calcium (ATC), a poorly watersoluble 3-hydroxy 3-methyl glutaryl CoA (HMG-CoA) reductase inhibitor, by a solid dispersion technique using polyethylene glycol 6000 (PEG 6000) or polyvinylpyrrolidone k30 (PVP K30).Methods: The solid dispersions were characterised by differential scanning calorimetry (DSC), powder x-ray diffraction (PXRD) and Fourier transformed infrared (FT-IR) spectroscopy. The dissolution characteristics of the formulations were determined in vitro, while the bioavailability of the solid dispersion and suspension was evaluated in rats.Results: DSC, PXRD and FT-IR data confirmed the formation of solid dispersion. The dissolution results showed that almost 95 % of ATC in ATC- PVP K30 solid dispersion dissolved in 5 min. The amount of ATC in ATC-PVP K30 SD, ATC-PEG 6000 SD and pure ATC that dissolved in 60 min was 103, 85 and 93 %, respectively. In addition, in vivo bioavailability studies in rats showed that area under concentration-time curve (AUC) and peak concentration (Cmax) of ATC-PVP K30 solid dispersion was 3.5-fold and 4.9-fold higher than that of the drug in suspension. Time to attain peak concentration (Tmax) of ATC-PVP K30 solid dispersion was 0.25 ± 0.00 h, which is shorter than 0.83 ± 0.26 h for suspension.Conclusion: The results obtained indicates that solid dispersions of ATC made with polyethylene glycol 6000 and polyvinylpyrrolidone K30 are an effective new approach to designing formulations of poorly soluble ATC for greatly enhanced solubility and bioavailability.Keywords: Solid dispersion, Atorvastatin, Polyethylene glycol, Polyvinypyrrolidone K30, Bioavailability, Dissolutio

A numerical study on ice failure process and ice-ship interactions by Smoothed Particle Hydrodynamics

In this paper, a Smoothed Particle Hydrodynamics (SPH) method is extended to simulate the ice failure process and ice-ship interactions. The softening elastoplastic model integrating Drucker-Prager yield criterion is embedded into the SPH method to simulate the failure progress of ice. To verify the accuracy of the proposed SPH method, two benchmarks are presented, which include the elastic vibration of a cantilever beam and three-point bending failure of the ice beam. The good agreement between the obtained numerical results and experimental data indicates that the presented SPH method can give the reliable and accurate results for simulating the ice failure progress. On this basis, the extended SPH method is employed to simulate level ice interacting with sloping structure and three-dimensional ice- ship interaction in level ice, and the numerical data is validated through comparing with experimental results of a 1:20 scaled Araon icebreaker model. It is shown the proposed SPH model can satisfactorily predict the ice breaking process and ice breaking resistance on ships in ice-ship interaction

Emergence of intrinsic superconductivity below 1.178 K in the topologically non-trivial semimetal state of CaSn3

Topological materials which are also superconducting are of great current interest, since they may exhibit a non-trivial topologically-mediated superconducting phase. Although there have been many reports of pressure-tuned or chemical-doping-induced superconductivity in a variety of topological materials, there have been few examples of intrinsic, ambient pressure superconductivity in a topological system having a stoichiometric composition. Here, we report that the pure intermetallic CaSn3 not only exhibits topological fermion properties but also has a superconducting phase at 1.178 K under ambient pressure. The topological fermion properties, including the nearly zero quasi-particle mass and the non-trivial Berry phase accumulated in cyclotron motions, were revealed from the de Haas-van Alphen (dHvA) quantum oscillation studies of this material. Although CaSn3 was previously reported to be superconducting at 4.2K, our studies show that the superconductivity at 4.2K is extrinsic and caused by Sn on the degraded surface, whereas its intrinsic bulk superconducting transition occurs at 1.178 K. These findings make CaSn3 a promising candidate for exploring new exotic states arising from the interplay between non-trivial band topology and superconductivity, e.g. topological superconductivityComment: 20 pages,4 figure