The XSophe-Sophe-XeprView computer simulation software suite enables scientists to easily determine spin Hamiltonian parameters from isotropic, randomly oriented and single crystal continuous wave electron paramagnetic resonance (CW EPR) spectra from radicals and isolated paramagnetic metal ion centers or clusters found in metalloproteins, chemical systems and materials science. XSophe provides an X-windows graphical user interface to the Sophe programme and allows: creation of multiple input files, local and remote execution of Sophe, the display of sophelog (output from Sophe) and input parameters/files. Sophe is a sophisticated computer simulation software programme employing a number of innovative technologies including; the Sydney OPera HousE (SOPHE) partition and interpolation schemes, a field segmentation algorithm, the mosaic misorientation linewidth model, parallelization and spectral optimisation. In conjunction with the SOPHE partition scheme and the field segmentation algorithm, the SOPHE interpolation scheme and the mosaic misorientation linewidth model greatly increase the speed of simulations for most spin systems. Employing brute force matrix diagonalization in the simulation of an EPR spectrum from a high spin Cr(III) complex with the spin Hamiltonian parameters g(e) = 2.00, D=0.10 cm(-1), E/D = 0.25, A(x) = 120.0, A(y) = 120.0, A(z) = 240.0 x 10 (-4) cm(-1) requires a SOPHE grid size of N = 400 (to produce a good signal to noise ratio) and takes 229.47 s. In contrast the use of either the SOPHE interpolation scheme or the mosaic misorientation linewidth model requires a SOPHE grid size of only N = 18 and takes 44.08 and 0.79 s, respectively. Results from Sophe are transferred via the Common Object Request Broker Architecture (CORBA) to XSophe and subsequently to XeprView where the simulated CW EPR spectra (1D and 2D) can be compared to the experimental spectra. Energy level diagrams, transition roadmaps and transition surfaces aid the interpretation of complicated randomly oriented CW EPR spectra and can be viewed with a web browser and an OpenInventor scene graph viewer.

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.

This paper demonstrates that standard algorithms for training support vector machines generally produce solutions with a greater number of support vectors than are strictly necessary. An algorithm is presented that allows unnecessary support vectors to be recognized and eliminated while leaving the solution otherwise unchanged. The algorithm is applied to a variety of benchmark data sets (for both classification and regression) and in most cases the procedure leads to a reduction in the number of support vectors. In some cases the reduction is substantial.

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A reversible linear master equation model is presented for pressure- and temperature-dependent bimolecular reactions proceeding via multiple long-lived intermediates. This kinetic treatment, which applies when the reactions are measured under pseudo-first-order conditions, facilitates accurate and efficient simulation of the time dependence of the populations of reactants, intermediate species and products. Detailed exploratory calculations have been carried out to demonstrate the capabilities of the approach, with applications to the bimolecular association reaction C3H6 + H reversible arrow C3H7 and the bimolecular chemical activation reaction C2H2 +(CH2)-C-1--> C3H3+H. The efficiency of the method can be dramatically enhanced through use of a diffusion approximation to the master equation, and a methodology for exploiting the sparse structure of the resulting rate matrix is established.

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 discrete variable representation (DVR) which facilitates the action of the potential energy operator. The angular DVR is optimized in relation to the reference Hamiltonian by standard procedures. In addition, a scheme which exploits the full sparsity of the kinetic energy operator in the Wigner representation has been devised which avoids having to construct full-length vectors in the Wigner representation. As a demonstration of the power and efficiency of this algorithm, all transitional mode eigenstates lying between the potential minimum and 100 cm−1 above threshold have been computed for a center-of-mass separation of 3 Å in the ketene system. The performance attributes of the earlier primitive algorithm and the new optimized algorithm are compared.

The large deflection theory circular cross–section elastic rods is used to consider the writhing of long straight rods subjected to tension and torque, such as undersea cables, and to closed loops with inserted twist, such as DNA supercoils.The writhed shape of the long straight rod under tension and torque is easily generated by twisting a piece of string with the fingers and consists of three separate parts: a balanced ply region, a free end loop, and two tail regions. The solution for the rod shape in each of the regions is found. The results are then joined together to ensure continuity of the position and tangent vectors of the strand centre line through the introduction of point forces and moments at the points where the strands enter and exit the balanced ply. The results of the model are consistent with simple experiments on long braided rope.The writhed shape of the closed loop with twist inserted between the ends prior to closure is modelled as a balanced ply joined to two end loops. The analysis combines the mechanics solution with the conservation of topological link to provide a simple formula which quantitatively predicts the approximate shape and helix angle of the supercoil. The results are in good agreement with simple experiments on rope and with available data on DNA supercoils.

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.

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. © 1997 John Wiley & Sons, Inc. J Comput Chem 18:1004–1010, 1997

An RRKM/master equation model is constructed for the isomerization of cyclopropene. It is shown how the dense matrix of the master equation operator can be reduced to a banded form by a combination of diffusion equation approximation and equation rearrangement. The lowest eigenvalues and eigenvectors of the master equation, which are sufficient for simulation purposes, are rapidly found using shift and invert Lanczos based methods.

The application of the Nesbet algorithm to the full iterative solution of the two-dimensional master equation for thermal unimolecular reactions is presented. This leads to an efficient algorithm for computing thermal rate coefficients in the falloff regime for reactions such as simple fission dissociations, radical-radical recombinations, and ion-molecule reactions wherein microcanonical dissociation rate coefficients are sensitive to both the vibrational energy and the angular momentum of the excited species.