Accurate and efficient algorithm for Bader charge integration

We propose an efficient, accurate method to integrate the basins of attraction of a smooth function defined on a general discrete grid, and apply it to the Bader charge partitioning for the electron charge density. Starting with the evolution of trajectories in space following the gradient of charge density, we derive an expression for the fraction of space neighboring each grid point that flows to its neighbors. This serves as the basis to compute the fraction of each grid volume that belongs to a basin (Bader volume), and as a weight for the discrete integration of functions over the Bader volume. Compared with other grid-based algorithms, our approach is robust, more computationally efficient with linear computational effort, accurate, and has quadratic convergence. Moreover, it is straightforward to extend to non-uniform grids, such as from a mesh-refinement approach, and can be used to both identify basins of attraction of fixed points and integrate functions over the basins.Comment: 19 pages, 8 figure

Design studies on the effects of orientation, lunation, and location on the performance of lunar radiators

Effects of orientation, lunation, and location on performance of lunar radiator - design studie

A Predictive Analytics Algorithm (Red Team) of Analytics’ Predictors (Blue Team): World Forensic Social Science Supercolliders

Mathematical and theoretical biologists recognize the inherent ambiguity in simulacra computation of living processes. An aspect of cultural distinction is theological beliefs. A micro case study of the Chinese and Hebrew development of mathematics is shown to be predictable. The Fokker-Planck, Kolmogorov, and Langevin equations are applied to addressing the TA1, TA2, and TA3 goals for the RFI regarding forensic social science supercolliders. The solution of an evolving parametric algorithm for forward (deductive) and backward (inductive) computation of v and phi variables is presented. Redundant validation for the calibration of parametrics concludes the discussion

Electroweak Theory Without Higgs Bosons

A perturbative SU(2)_L X U(1)_Y electroweak theory containing W, Z, photon, ghost, lepton and quark fields, but no Higgs or other fields, gives masses to W, Z and the non-neutrino fermions by means of an unconventional choice for the unperturbed Lagrangian and a novel method of renormalisation. The renormalisation extends to all orders. The masses emerge on renormalisation to one loop. To one loop the neutrinos are massless, the A -> Z transition drops out of the theory, the d quark is unstable and S-matrix elements are independent of the gauge parameter xi.Comment: 27 pages, LaTex, no figures; revised for publication; accepted by Int. J. Mod. Phys. A; includes biographical note on A. F. Nicholso

Prediction of water temperature metrics using spatial modelling in the Eastern and Western Cape, South Africa

Key aspects of a river's temperature regime are described by magnitudes, timing and durations of thermal events, and frequencies of extreme exceedance events. To understand alterations to thermal regimes, it is necessary to describe thermal time series based on these statistics. Classification of sites based on their thermal metrics, and understanding of spatial patterns of these thermal statistics, provides a powerful approach for comparing study sites against reference sites. Water temperature regime dynamics should be viewed regionally, where regional divisions have an inherent underpinning by an understanding of natural thermal variability. The aim of this research was to link key water temperature metrics to readily-mapped environmental surrogates, and to produce spatial images of temperature metrics: 37 temperature metrics were derived for 12 months of sub-daily water temperatures at 90 sites in the Eastern Cape and Western Cape provinces, South Africa. These metrics were correlated with 16 environmental variables. Correlations enabled development of multiple regression models which facilitated mapping of temperature metrics over the study area. This approach has the potential to be applied at a national scale as more thermal time series are collected nationally. It is argued that the appropriateness of management decisions in rivers can be improved by including guidelines for thermal metrics at a regional scale. Such maps could facilitate incorporation of a temperature component into management guidelines for water resources