K. E. Gates

Computer simulation of magnetic resonance spectra employing homotopy

Multidimensional homotopy provides an efficient method for accurately tracing energy levels and hence transitions in the presence of energy level anticrossings and looping transitions. Herein we describe the application and implementation of homotopy to the analysis of continuous wave electron paramagnetic resonance spectra. The method can also be applied to electron nuclear double resonance, electron spin echo envelope modulation, solid-state nuclear magnetic resonance, and nuclear quadrupole resonance spectra.

XSophe — Sophe — XeprView

The XSophe-Sophe-XeprView computer simulation software suite provides scientists with an easy-to-use research tool for the analysis of isotropic, randomly orientated and single crystal continuous wave electron paramagnetic resonance (CW EPR) spectra. XSophe provides an X Windows graphical user interface to the Sophe programme allowing; the creation of multiple input files, the local and remote execution of Sophe and display of Sophelog (output from Sophe) and input parameters/files. Sophe is a sophisticated computer simulation software programme with a number of innovative technologies including; the Sophe partition and interpolation schemes, a field segmentation algorithm, the mosaic misorientation line width model, parallelisation (OpcnMP — for SGI computers running the lrix operating system) and spectral optimisation. In conjunction with the SOPHE partition scheme and the field segmentation algorithm, the SOPHE interpolation scheme and mosaic misorientation linewidth model greatly increase the speed of simulations for most spin systems. The output of CW EPR spectra (1D and 2D) from the Sophe programme can be visualised in conjunction with the experimental spectrum in XeprView or Xepr. Energy level diagrams, transition roadmaps and transition surfaces aid the interpretation of complicated randomly orientated EPR spectra and can he viewed with a netscape browser and an OpenInventor scene graph viewer.

Application of inverse iteration to 2-dimensional master equations

Recent developments in unimolecular theory have placed great emphasis on the role played by angular momentum in determining the details of the dependence of the rate coefficient on pressure and temperature. The natural way to investigate these dependencies is through the master equation formulation, where the rate coefficient is recovered as the eigenvalue of the smallest magnitude of the spatial operator. Except for very simple cases, the master equation must be solved with numerical methods. For the 2‐dimensional master equation this leads to large sparse matrices and correspondingly lengthy computational times in order to determine the eigenvalue of the least magnitude. A reformulation of the problem in terms of a diffusion equation approximates the final matrix with a narrow banded matrix that can easily be factored using a variation of Gaussian elimination. The 2‐dimensional master equation can then be solved with inverse iteration, which rapidly converges to the desired eigenpair. This method can be up to 10 times faster than conventional iterative algorithms for finding the desired eigenpair.

A pseudospectral algorithm for the computation of transitional-mode eigenfunctions in loose transition states. II. Optimized primary and grid representations

A highly optimized pseudospectral algorithm is presented for effecting the exact action of a transitional-mode Hamiltonian on a state vector within the context of iterative quantum dynamical calculations (propagation, diagonalization, etc.). The method is implemented for the benchmark case of singlet dissociation of ketene. Following our earlier work [Chem. Phys. Lett. 243, 359 (1995)] the action of the kinetic energy operator is performed in a basis consisting of a direct product of Wigner functions. We show how one can compute an optimized (k,Ω) resolved spectral basis by diagonalizing a reference Hamiltonian (adapted from the potential surface at the given center-of-mass separation) in a basis of Wigner functions. This optimized spectral basis then forms the working basis for all iterative computations. Two independent transformations from the working basis are implemented: the first to the Wigner representation which facilitates the action of the kinetic energy operator and the second to an angular di...

Discovery of emergent natural laws by hierarchical multi-agent systems

This paper defines an approach to simulation of natural systems, inspired by complex systems theory. A complex natural system is modeled as a multi-agent simulation system, agents representing living organisms, physical entities or environmental processes. Agents and their interactions can be aggregated to higher-level group agents. The properties and behavior of these group agents are determined by, or emerge from, the properties and behavior of the individual agents composing the group. Group agents discover macro-level natural laws implied by the properties and behavior of individual agents modeling micro-level natural entities. Such a system can be implemented in a distributed programming environment, exploiting emergence, hierarchy, and concurrency to perform large-scale simulations.