The Simplified Spherical Harmonic (SPN) approximation was first introduced as a three-dimensional (3-D) extension of the plane-geometry Spherical Harmonic (PN) equations. A third order SPN (SP3) solver, recently implemented in the Nodal Expansion Method (NEM), has shown promising performance in the reactor core neutronics simulations. This work is focused on the development and implementation of the transport corrected interface and boundary conditions in NEM SP3 solver, following recent published work on the rigorous SPN theory for piecewise homogeneous regions. A streamlined procedure has been developed to generate the flux zero and second order/moment discontinuity factors (DFs) of the generalized equivalence theory to eliminate the error introduced by pin-wise homogenization. Moreover, several color set models with varying size and configuration are later explored for their capability of generating DFs that can produce results equivalent to that using the whole-core homogenization model for more practical implementations. The new developments are tested and demonstrated on the C5G7 benchmark. The results show that the transport corrected SP3 solver shows general improvements to power distribution prediction compared to the basic SP3 solver with no DFs or only zero order/moment DFs. The complete equivalent calculations using the DFs can almost reproduce transport solutions with high accuracy. The use of equivalent parameters from larger size color set models show better prediction in the whole-core calculations. By coupling different color set models DFs can offer the best accuracy at both eigenvalues and power distributions.

The accurate quantification of $\frac{F{e}^{3+}}{\Sigma Fe}$ ratios for Mössbauer spectroscopic room temperature measurements involves many steps and, when shown in a composite Mössbaur data table, does not allow enough space for more Mössbauer parameters to be presented in the composite table. So a simple formula is derived, (presented as a short communication) which users will find helpful when they have to determine corrected $\frac{F{e}^{3+}}{\Sigma Fe}$ ratios in their room temperature Mössbauer experiments.

Nanoparticles of platinum-group metals (PGM) on carbon supports are widely used as catalysts for a number of chemical and electrochemical conversions on laboratory and industrial scale. The newly emerging field of single atom catalysis focuses on the ultimate level of metal dispersion, i.e. atomically dispersed metal species anchored on the substrate surface. However, the presence of single atoms in traditional nanoparticle-based catalysts remains largely overlooked. In this work we use aberration-corrected scanning transmission electron microscope to investigate four commercially available nanoparticle-based PGM/C catalysts (PGM = Ru, Rh, Pd, Pt). We show that in addition to nanoparticles, single atoms are also present on the surface of carbon substrates. These observations raise questions about the role that single atoms play in conventional nanoparticle PGM/C catalysts. We critically discuss the observations with regard to the quickly developing field of single atom catalysis.

There is no formal difference between particles and black holes. This formal similarity lies in the intersection of gravity and quantum theory; quantum gravity. Motivated by this similarity, `wave-black hole duality' is proposed, which requires having a proper energy-momentum tensor of spacetime itself. Such a tensor is then found as a consequence of `principle of minimum gravitational potential'; a principle that corrects the Schwarzschild metric and predicts extra periods in orbits of the planets. In search of the equation that governs changes of observables of spacetime, a novel Hamiltonian dynamics of a Pseudo-Riemannian manifold based on a vector Hamiltonian is adumbrated. The new Hamiltonian dynamics is then seen to be characterized by a new `tensor bracket' which enables one to finally find the analogue of Heisenberg equation for a `tensor observable' of spacetime.