We compute the survival probability of an electron neutrino in its flight through the solar core experiencing the MikheyevSmirnovWolfenstein effect with all three neutrino species considered. We adopted a hybrid method that uses an accurate approximation formula in the nonresonance region and numerical integration in the nonadiabatic 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.
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 dwave abnormal superconductor, He3 and a SU(5) Higgs potential.
We show explicitly how to linearize the action of crystallographic space groups on the Brillouin zone. For twodimensional crystallography it yields eight fourdimensional representations and five sixdimensional 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 twodimensional crystallography we exploit our corresponding results and also study the orbit spaces.
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.
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.
We are constructings phase diagrams in the PT plane for various ferromagnetic & ferroelectric materials.
FerroelasticFerroelectric correlations with ordering as a nature of irreversible phase transitions PZNPT (Pb(Zn_{1/3}N_{2/3})O_{3}xPbTiO_{3}) single crystals undergoes a diffuse ferroelectric phase transition for low value of x ant at Tc which is strongly frequency dependent. The last properties are common for all the family of relaxors. Another property which is common for many Pbbased relaxors with perovskite structure are weak diffuse superstructure reflections in Xray diffraction pattern which was not reported for PZNPT. On the contrary it was found proper ferroelectric structure in wide interval of x value variation. At x<8% the polar axe of PZNPT coincides with [111] direction of perovskite primitive cell (parent phase) structure providing rhombohedral symmetry of crystal (Rphase). Electric field applied along [001] direction and exceeding 15 KV/cm influence the polar axe rotates to [UOV] plane inducing monoclinic symmetry of crystal (Mcphase). Mphase continues to be the ground state of PZNPt even after external field removing. The nature of irreversible phase transition RM was the subject of our research.
The reason for stoichiometric ordering in Babased complex perovskites Ba(Me^{2+}_{1/3}Me^{5+}_{2/3})O_{3} is remarkable material for microwave wireless communication it sufferes stoichiometric 1:2 ordering at relative high temperature (T³1800^{0}C). Here we present the theory, which display the correlation between the type of ordering and energy of effective pairs interactions between cation in perovskite lattice. The conditions of stability of 1:1 ordering are the result of calculation the energy pair interactions related to G,R,M and X points of Brilluen zone (BZ). It is easy to present quadratic part of Landau potential dependence on the prder parameters R_{4}, M_{7}, X_{6} and Г_{1}: (1) where (2) and W_{i }is the sums of effective ordering energy of pair coupling, which includes the interactions between the ions situated in ith coordinated sphere in respect to eachother. To stabilize 1:2 ordered state in perovskite structure we have considered the effective interactions in the first eight coordinated spheres. Using notation analigical to (1) –(2), we may present (3) (4) Using (2), (3) and selfconsistent approximation we defined the temperature of the second order phase transition in the ordered state. Then W_{i} was calculated with screening LienardJones potential of ionic interactions. Using this approximation we had estimated the stability of 1:1 and 1:2 types of orderings in respect to additional agents.
Parallel Computing
We have developed a parallel computer system (ParCom) for various physics simulations. Its connection topology is 2D tours. The computing engine of a processing element is a DSP processor TMS320C30 which is capable of 33 milion floating point operations at Mhz and features a 1 channel DMA. processing elements are physically connected by dual port rams which can transfer dataat 16.66 Mbytes per second aling a selected channel. An overlapped packet switching algorithm is adopted for message routing. Message passing is handledby DMA independently from CPU. The DMA of PE1 writes data to the DPM in a given channel and the DMA of PE1 writes data to th e DPM in a given channel and the DMA of PE2 reads data from that DPM. The host is a PC running under Linux which hs 4 communication channels with the array of PEs. It allows 4 simutaneous independent jobs. Our preliminary test results confirm that the hardware is working s designed. However, further software developments are needed.
Parallel WIEN 97 The problem is to parallelize solving an eigenvalue problem such as Hz=lSz, where H is the Hamiltonian matrix, S is the overlap matrix, l is the eigenvalue, and z is the eigenvector. We used the MPI and the SCALAPACK library. Figure : Lines with symbols are the decrease of memory size with changing processor grid (m´m) for the matrix size, N=1008,2027,3012,4021. Dotted lines indicates the expected decrease of memory size which behaves as 8(12/m2)N2 . The degree of the decrease is slightly smaller than the expected one Figure : Cputime with respect to several process grid, serial, (2´2), (2´3), (3´3), (3´4), (4´4). Dotted lines indicate ideal graphs for 3012 and 4021 cases.
The electronic and structual properties for TiMe (Me = Fe, Co, Ni, Ru, Rh, Pd , Os, Ir, Pt) alloys are studied using the full potential linearized augmented plane wave (FLAPW) method.
The electronic structure of the (001) and (100) surfaces for B2 Tibased transition metal alloys were investigated using the fullpotential linearized augmented planewave method in the localdensity approximation.
We investigate the interaction of hydrogen with the B2 TiFe (001) and (110) surfaces using the full  potential linearized augmented plane wave(FLAPW) method.
Electronic structure calculations of the ordered ferromagnetic and paramagnetic transition metal alloys FeCo, Ni_{3 }Fe and Ni_{3}Mn are performed using the fullpotential linearized augmented plane wave method.
We studied the optical absorption spectra of CdSe quantum well structures confined by ZnSe and ZnS epilayer to see the effect of quantum confinement on the optical properties. The result is that proper passivation reduces surface states of CdSe and may enhance luminescence efficiency.
We have studied structural stability of cubic (Fm3m) and tetragonal (P42_{1}c) phases of NaBH_{4} in the PT plane. NaBH_{4} is one of practical candidates for the hydrogen storage in the fuel cell technology.
We^{ }have studied the stability of a thallium nanocluster of various^{ }numbers of atoms (N=1,2,…,10) on a Si(111)7×7 substrate using density^{ }functional theory total energy calculations. We have compared it with^{ }clusters of other group III elements (Al, Ga, and In).^{ }Thallium is found to be unstable with the triangular cluster,^{ }which has been known to be stable for other group^{ }III elements. Instead, a slightly different structure, in which Si^{ }atop atoms are lower than thallium atoms in height by^{ }2.56 Å, was found to be quite stable. Such an abnormal^{ }structure originates from the inert pair of 6s^{2} electrons due^{ }to the significant spinorbit interaction. The initial relaxed N=6 Tl^{ }cluster continues to grow with increasing N up to N=9^{ }in the faultedhalf unit cell, which is consistent with experimental^{ }observations.
