Dyadic Greens function for a topological insulator stratified sphere

We construct the dyadic Greens functions (DGFs) for a topological insulator (TI) stratified sphere within the framework of axion electrodynamics. For these DGFs, the additional expansion coefficients are included to account for the axion coupling effect. With the application of these DGFs, we derive the formulation of light scattering from a dipole near a TI stratified sphere. In our numerical studies, we give three types of configurations (a metal-coated TI sphere, a metal-TI-metal-coated TI sphere and an alternating metal-TI stratified sphere) to investigate how the topological magneto-electric (TME) response of the TI sphere (shells) influences on the multipolar plasmonic resonance of the metal shells. For these types, the results show that the TME effect causes some modifications of the decay rate spectrum for an emitting dipole near a TI stratified sphere. For the multipolar resonances of the metal shells, it is observed that the TME-induced red-shifts for the bonding and lower order antibonding modes are found but those for the higher order antibonding modes are insignificant. In addition, for a metal-coated TI sphere, we take into account the effects of losses in the TI core of which the dielectric function is chosen to be the form of the bulk or five quintuple layers (5QL) slab and then the some modifications of the TME-induced decay rate spectrum are obviously suppressed. These phenomenological characteristics provide useful guidance to probing the TME effect via molecular fluorescence experiments

SLT-Resolution for the Well-Founded Semantics

Global SLS-resolution and SLG-resolution are two representative mechanisms for top-down evaluation of the well-founded semantics of general logic programs. Global SLS-resolution is linear for query evaluation but suffers from infinite loops and redundant computations. In contrast, SLG-resolution resolves infinite loops and redundant computations by means of tabling, but it is not linear. The principal disadvantage of a non-linear approach is that it cannot be implemented using a simple, efficient stack-based memory structure nor can it be easily extended to handle some strictly sequential operators such as cuts in Prolog. In this paper, we present a linear tabling method, called SLT-resolution, for top-down evaluation of the well-founded semantics. SLT-resolution is a substantial extension of SLDNF-resolution with tabling. Its main features include: (1) It resolves infinite loops and redundant computations while preserving the linearity. (2) It is terminating, and sound and complete w.r.t. the well-founded semantics for programs with the bounded-term-size property with non-floundering queries. Its time complexity is comparable with SLG-resolution and polynomial for function-free logic programs. (3) Because of its linearity for query evaluation, SLT-resolution bridges the gap between the well-founded semantics and standard Prolog implementation techniques. It can be implemented by an extension to any existing Prolog abstract machines such as WAM or ATOAM.Comment: Slight modificatio

Linear Tabulated Resolution Based on Prolog Control Strategy

Infinite loops and redundant computations are long recognized open problems in Prolog. Two ways have been explored to resolve these problems: loop checking and tabling. Loop checking can cut infinite loops, but it cannot be both sound and complete even for function-free logic programs. Tabling seems to be an effective way to resolve infinite loops and redundant computations. However, existing tabulated resolutions, such as OLDT-resolution, SLG- resolution, and Tabulated SLS-resolution, are non-linear because they rely on the solution-lookup mode in formulating tabling. The principal disadvantage of non-linear resolutions is that they cannot be implemented using a simple stack-based memory structure like that in Prolog. Moreover, some strictly sequential operators such as cuts may not be handled as easily as in Prolog. In this paper, we propose a hybrid method to resolve infinite loops and redundant computations. We combine the ideas of loop checking and tabling to establish a linear tabulated resolution called TP-resolution. TP-resolution has two distinctive features: (1) It makes linear tabulated derivations in the same way as Prolog except that infinite loops are broken and redundant computations are reduced. It handles cuts as effectively as Prolog. (2) It is sound and complete for positive logic programs with the bounded-term-size property. The underlying algorithm can be implemented by an extension to any existing Prolog abstract machines such as WAM or ATOAM.Comment: To appear as the first accepted paper in Theory and Practice of Logic Programming (http://www.cwi.nl/projects/alp/TPLP

ReaxFF-lg: Correction of the ReaxFF Reactive Force Field for London Dispersion, with Applications to the Equations of State for Energetic Materials

The practical levels of density functional theory (DFT) for solids (LDA, PBE, PW91, B3LYP) are well-known not to account adequately for the London dispersion (van der Waals attraction) so important in molecular solids, leading to equilibrium volumes for molecular crystals ∼10-15% too high. The ReaxFF reactive force field is based on fitting such DFT calculations and suffers from the same problem. In the paper we extend ReaxFF by adding a London dispersion term with a form such that it has low gradients (lg) at valence distances leaving the already optimized valence interactions intact but behaves as 1/R^6 for large distances. We derive here these lg corrections to ReaxFF based on the experimental crystal structure data for graphite, polyethylene (PE), carbon dioxide, and nitrogen and for energetic materials: hexahydro-1,3,5-trinitro- 1,3,5-s-triazine (RDX), pentaerythritol tetranitrate (PETN), 1,3,5-triamino-2,4,6-trinitrobenzene (TATB), and nitromethane (NM). After this dispersion correction the average error of predicted equilibrium volumes decreases from 18.5 to 4.2% for the above systems. We find that the calculated crystal structures and equation of state with ReaxFF-lg are in good agreement with experimental results. In particular, we examined the phase transition between α-RDX and γ-RDX, finding that ReaxFF-lg leads to excellent agreement for both the pressure and volume of this transition occurring at ∼4.8 GPa and ∼2.18 g/cm^3 density from ReaxFF-lg vs 3.9 GPa and ∼2.21 g/cm^3 from experiment. We expect ReaxFF-lg to improve the descriptions of the phase diagrams for other energetic materials