number22_red1.gif   Neutrino Astro Physics

    Solar neutrino   

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.


1. J.S. Kim , Y.S Chae and J.D. Kim, "Numerical computation of solar neutrino flux attenuated by MSW mechanism" , Comp. Phys. Comm.  120 (1999), 41-56 

2. J.S. Kim and K.S Lee, "Earth regeneration effect  of  solar neutrinos: a numerical treatment with three active neutrino flavors" Comp.  Phys. Comm. 135 (2001), 176-189

     number22_red2.gif    Symmetry Related Problem

    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. 


1. J.S. Kim , J-C Toledano and P.Toledano, "Monte Carlo optimization applied to Symmetry Breaking", Comp. Phys. Comm. 109 (1998), 207-226                                                                                                                                                                                 


  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.


1. J. S. Kim , L. Michel, B. I. Zhilinskii ," The ring of invariant real functions on the Brillouin zone"Phys. Rep. 341(2001) , 337-376


 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.


1. Geunsik Lee, Jai  Sam  Kim and  J. Zak , " Numerical verification of topologycal crossings in band structure of solids " J. Phys. : Condes. Matter 15 (2003) ,2005-2016


      number22_red3.gif  Phase Transition

 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.


1.  X. Z. Wang and J. S. Kim, " The critical nature of  ideal Bose - Einstein condensation : similarity sith Yang-Lee theory  of  phase transition", Phys. Rev. E 59 (1999), 1242-1245

2. X. Z. Wang and J. S. Kim , "The Critical Line of  an Anisotropic Ising Antiferromagnet on Square and Honycomb Lattices" Phys. Rev. E 56(1997), 2793-2804

3. X. Z. Wang and J. S. Kim , "The Critical Line of an Ising Antiferromagnet on Square and Honycomb Lattices" Phys.  Rev.  Lett. 78(1997), 413-416



Phase transitions of ferromagnetic-ferroelectric materials       


We are constructings phase diagrams in the P-T plane for various ferromagnetic & ferroelectric materials.


Ferroelastic-Ferroelectric correlations with ordering as a nature of irreversible phase transitions

PZN-PT (Pb(Zn1/3N2/3)O3-xPbTiO3) 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 Pb-based relaxors with perovskite structure are weak diffuse superstructure reflections in X-ray diffraction pattern which was not reported for PZN-PT. On the contrary it was found proper ferroelectric structure in wide interval of x value variation. At x<8% the polar axe of PZN-PT coincides with [111] direction of perovskite primitive cell (parent phase) structure providing rhombohedral symmetry of crystal (R-phase). Electric field applied along [001] direction and exceeding 15 KV/cm influence the polar axe rotates to [UOV] plane inducing monoclinic symmetry of crystal (Mc-phase). M-phase continues to be the ground state of PZN-Pt even after external field removing. The nature of irreversible phase transition R-M was the subject of our research.


The reason for stoichiometric ordering in Ba-based complex perovskites

Ba(Me2+1/3Me5+2/3)O3 is remarkable material for microwave wireless  communication it sufferes stoichiometric 1:2 ordering at relative high temperature (T³18000C). 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 R4, M7, X6 and Г1:




and Wi is the sums of effective ordering energy of pair coupling, which includes the interactions between the ions situated in i-th coordinated sphere in respect to each-other. 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)


Using (2), (3) and self-consistent approximation we defined the temperature of the second order phase transition in the ordered state. Then Wi was calculated with screening Lienard-Jones 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(1-2/m2)N2 . The degree of the decrease is slightly smaller than the expected one


Figure : Cpu-time 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.



         Solid State Physics

 Electronic strcture of Ti-based transition metal alloys

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.


1.  S. E. Kulkova, D. V. Valujsky, Jai Sam Kim, Geunsik Lee and Y. M. Koo, "Optical properties of TiNi, TiCo and TiFe thin films, Physica B",Condensed Matter, 304 (2001), 186-192

2.  S. E. Kulkova, D. V. Valujsky, Jai Sam Kim, Geunsik Lee and Y. M. Koo, " Electronic structure of binary and ternary Ti-based shape-memory alloys", Solid State Communications, 119 ( 2001) , 619-623

The electronic structure of the (001) and (100) surfaces for B2 Ti-based transition metal alloys were investigated using the full-potential linearized augmented plane-wave method in the local-density approximation.


1. Lee, G.; Kim, J.S.; Koo, Y.M.; Kulkova, S.E.; Smolin, I.Yu.; Valujsky, D.V. "The investigation in bonding of hydrogen on the B2 TiFe (001) and (110) surfaces", Physics of Low-Dimensional Structures,11( 2001),89-103  

2. S. E. Kulkova, D. V. Valujsky,Jai Sam Kim, G. Lee, Y.M. Koo," Surface electronic structure of Ti-based transition metal alloys", Physical Review B (Condensed Matter and Materials Physics), 65 (2002), 085410/1-7

We investigate the interaction of hydrogen with the B2 TiFe (001) and (110) surfaces using the full - potential linearized augmented plane wave(FLAPW) method.


1.  Lee, G.; Kim, J.S.; Koo, Y.M.; Kulkova, S.E.; Smolin, I.Yu.; Valujsky, D.V. ,"The investigation in bonding of hydrogen on the B2 TiFe (001) and (110) surfaces, Physics of Low-Dimensional Structures", 11( 2001), 89-103

2. G. Lee, J. S. Kim, Y. M. Koo and S. E. Kulkova," The adsorption of hydrogen on B2 TiFe surfaces", International Journal of Hydrogen Energy, 27 (2002), 403-412

3. S.E. Kulkova , S.V. Eremeev, V.E. Egorushkin, J.S. Kim, S. Y. Oh,"Hydrogen adsorption on Pd/TiFe (110) sruface",  Solid State Communications, 126 (2003), 405-408

Electronic structure calculations of the ordered ferromagnetic and paramagnetic transition metal alloys FeCo, Ni3 Fe and Ni3Mn are performed using the full-potential linearized augmented plane wave method.


1.  S. E. Kulkova, D. V. Valujsky,Jai Sam Kim, Geunsik Lee and Y. M. Koo The electronic properties of FeCo, Ni3Mn and Ni3Fe at the orderdisorder transition, Physica B: Condensed Matter, 322 (2002), 236-247


  Optical property of CdSe quantum dot   

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.


1.   S.J. Yun, G. Lee, J.S. Kim, S.K. Shin, and Y-G Yoon, Electronic structure and optical absorption spectra of CdSe covered with ZnSe and ZnS epilayers, Solid State Commun. 137 (2006) 332


   Ab initio phase diagram on the pressure-temperature plane   

We have studied structural stability of cubic (Fm3m) and tetragonal (P421c) phases of NaBH4 in the P-T plane. NaBH4 is one of practical candidates for the hydrogen storage in the fuel cell technology.


1.   G. Lee, J.Y. Lee, and J.S. Kim, Ab initio P-T phase diagram of NaBH4, Solid State Commun. 139 (2006) 516


   Ab initio study of thallium nanoclusters on Si(111)-7×7

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 6s2 electrons due to the significant spin-orbit interaction. The initial relaxed N=6 Tl cluster continues to grow with increasing N up to N=9 in the faulted-half unit cell, which is consistent with experimental observations.


1.   G. Lee, C. G. Hwang, N. D. Kim, J. Chung, J. S. Kim, and S. Lee, Ab initio study of thallium nanoclusters on Si(111)-7×7, Physical Review B 76 (2007) 245409