The restricted two-body problem in constant curvature spaces

We perform the bifurcation analysis of the Kepler problem on $S^3$ and $L^3$. An analogue of the Delaunay variables is introduced. We investigate the motion of a point mass in the field of the Newtonian center moving along a geodesic on $S^2$ and $L^2$ (the restricted two-body problem). When the curvature is small, the pericenter shift is computed using the perturbation theory. We also present the results of the numerical analysis based on the analogy with the motion of rigid body.Comment: 29 pages, 7 figure

Nanoscale engineering of hybrid magnetite–carbon nanofibre materials for magnetic resonance imaging contrast agents

Magnetic nanomaterials show significant promise as contrast agents for magnetic resonance imaging (MRI). We have developed a new highly efficient one-step procedure for the synthesis of magnetically- functionalised hollow carbon nanofibres, where (i) the carbon nanofibres act as both a template and a support for the nucleation and growth of magnetite nanoparticles and (ii) the structural (size, dispersity and morphology) and functional (magnetisation and coercivity) properties of the magnetic nanoparticles formed on nanofibres are strictly controlled by the mass ratio of the magnetite precursor to the nanofibres and the solvent employed during synthesis. We have shown that our magnetite-nanofibre materials are effectively solubilised in water resulting in a stable suspension that has been employed as a ‘‘negative’’ MRI contrast agent with an excellent transverse relaxivity (r2) of (268 13) mM s 1, surpassing current commercial materials and state-of-the-art magnetic nanoscale platforms in performance for MRI contrast at high magnetic fields. The preparation and evaluation of this unique hybrid nanomaterial represents a critical step towards the realisation of a highly efficient ‘‘smart’’ MRI theranostic agent – a material that allows for the combined diagnosis (with MRI), treatment (with magnetic targeting) and follow-up of a disease (with MRI) – currently in high demand for various clinical applications, including stratified nanomedicine

Size-selected Fe3O4–Au hybrid nanoparticles for improved magnetism-based theranostics

Size-selected Fe3O4–Au hybrid nanoparticles with diameters of 6–44 nm (Fe3O4) and 3–11 nm (Au) were prepared by high temperature, wet chemical synthesis. High-quality Fe3O4 nanocrystals with bulk-like magnetic behavior were obtained as confirmed by the presence of the Verwey transition. The 25 nm diameter Fe3O4–Au hybrid nanomaterial sample (in aqueous and agarose phantom systems) showed the best characteristics for application as contrast agents in magnetic resonance imaging and for local heating using magnetic particle hyperthermia. Due to the octahedral shape and the large saturation magnetization of the magnetite particles, we obtained an extraordinarily high r2-relaxivity of 495 mM−1·s−1 along with a specific loss power of 617 W·gFe−1 and 327 W·gFe−1 for hyperthermia in aqueous and agarose systems, respectively. The functional in vitro hyperthermia test for the 4T1 mouse breast cancer cell line demonstrated 80% and 100% cell death for immediate exposure and after precultivation of the cells for 6 h with 25 nm Fe3O4–Au hybrid nanomaterials, respectively. This confirms that the improved magnetic properties of the bifunctional particles present a next step in magnetic-particle-based theranostics