We compute the survival probability of an electron neutrino in its flight through the solar core experiencing the Mikheyev-Smirnov-Wolfenstein effect with all three neutrino species considered. We adopted a hybrid method that uses an accurate approximation formula in the non-resonance region and numerical integration in the non-adiabatic resonance region. The key of our algorithm is to use the importance sampling method for sampling the neutrino creation energy and position and to find the optimum radii to start and stop numerical integration. We further developed a parallel algorithm for a message passing parallel computer. By using an idea of job token, we have developed a dynamical load balancing mechanism which is effective under any irregular load distributions.
Monte Carlo Search of Orbit Space
We present a Monte Carlo optimization algorithm to search for the boundary points of the orbit space which is important in determining the symmetry breaking directions in the Higgs potential and the Landau potential. Our algorithm is robust and generally applicable. For large problems we have also developed a parallel version. We apply the method to the Landau potential of the d-wave abnormal superconductor, He-3 and a SU(5) Higgs potential.
Invariant functions on the Brillouin zone
We show explicitly how to linearize the action of crystallographic space groups on the Brillouin zone. For two-dimensional crystallography it yields eight four-dimensional representations and five six-dimensional representations. For the 73 arithmetic classes in dimension three, it yields, respectively, 33, 24, 16 linear representations of dimension 6, 8, 12. We give the corresponding Molien functions. For the representations of dimensions four and six, we compute the invariants (up to 96 numerator invariants for for R lattices). We can even extend the results to the 16 hexagonal arithmetic classes. All obtained results are presented in the form of short tables. Using the possibility to make plots of invariant function for the two-dimensional crystallography we exploit our corresponding results and also study the orbit spaces.
Topology of Energy Bands
There have been recent predictions of topologically unavoidable branch crossing in the energy band structure of solids. Calculations of energy dispersion relations are carried out in a number of crystals with orthorhombic space group (SG) symmetry. Our numerical calculations by WIEN97 verify the topological crossings and are in good agreement with the predictions based on representations of SGs.
Yang-Lee zero in Ising model
We show that the singularity of the free energy of Ising models in the absence of a magnetic field on the triangular, square, and honeycomb lattices is related to zeros of the pseudopartition function on an elementary cycle. Using the Griffiths' smoothness postulate, we extend these results to the case in a magnetic field and derive a formula of the critical line of an Ising antiferromagnet, which is in good agreement with the numerical results.