There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

https://repository.kulib.kyoto-u.ac.jp/dspace/bitstream/2433/202086/1/j.scriptamat.2015.07.021.pdf

First principles phonon calculations in materials science

The tetragonal to orthorhombic ferroelastic phase transition between rutile- and ${\text{CaCl}}_{2}$-type ${\text{SiO}}_{2}$ at high pressures is studied using first-principles calculations and the Landau free-energy expansion. The phase transition is systematically investigated in terms of characteristic phonon modes with ${\text{B}}_{1g}$ and ${\text{A}}_{g}$ symmetries, shear moduli, transverse-acoustic mode, rotation angle of the ${\text{SiO}}_{6}$ octahedra, spontaneous symmetry-breaking and volume strains, and enthalpy. The results show that these physical behaviors at the transition are well described using the Landau free-energy expansion parametrized by the first-principles calculations.

/pdf/first-principles-calculations-of-the-ferroelastic-transition-4b3qx4ec16.pdf

First-principles calculations of the ferroelastic transition between rutile-type and CaCl2-type SiO2 at high pressures

Phonon plays essential roles in dynamical behaviors and thermal properties, which are central topics in fundamental issues of materials science. The importance of first principles phonon calculations cannot be overly emphasized. Phonopy is an open source code for such calculations launched by the present authors, which has been world-widely used. Here we demonstrate phonon properties with fundamental equations and show examples how the phonon calculations are applied in materials science.

First-principles calculations based on hybrid Hartree-Fock density functionals provide a clear picture of the defect energetics and electronic structure in ZnO. Among the donorlike defects, the oxygen vacancy and hydrogen impurity, which are deep and shallow donors, respectively, are likely to form with a substantial concentration in $n$-type ZnO. The zinc interstitial and zinc antisite, which are both shallow donors, are energetically much less favorable. A strong preference for the oxygen vacancy and hydrogen impurity over the acceptorlike zinc vacancy is found under oxygen-poor conditions, suggesting that the oxygen vacancy contributes to nonstoichiometry and that hydrogen acts as a donor, both of which are without significant compensation by the zinc vacancy. The present results show consistency with the relevant experimental observations.

/pdf/defect-energetics-in-zno-a-hybrid-hartree-fock-density-3fpzny1883.pdf

Defect energetics in ZnO: A hybrid Hartree-Fock density functional study

The electronic structure of ${\mathrm{InGaZnO}}_{4},$ which has a layered structure with alternating laminated layers of ${\mathrm{InO}}_{2}$ and ${\mathrm{GaZnO}}_{2},$ was calculated in order to investigate the mechanism of electrical conductivity. In the crystal structure obtained through relaxation calculations using classical two-center potentials, the Ga ion in the ${\mathrm{GaZnO}}_{2}$ layer has pentagonal coordination forming a bipyramid with five oxygen ions, while the Zn ion in the same layer has tetrahedral coordination, losing a bond with the oxygen at the top of one pyramid. The molecular orbitals of model clusters for the relaxed structure, which were calculated by the discrete variational $X\ensuremath{\alpha}$ method using a model cluster, show strong two-dimensional structures. The electronic states at the edge of the conduction band are the result of overlapping between In $5s$ orbitals, and delocalize in the ${\mathrm{InO}}_{2}$ layer. The energy in the Ga $4s$ and Zn $4s$ states in the ${\mathrm{GaZnO}}_{2}$ layer was too large to be doped with electrons. The In $5s$ states are considered to be conduction paths for carrier electrons. A very high conductivity can be expected in the case where dopant ions are introduced into the ${\mathrm{GaZnO}}_{2}$ layers.

/pdf/mechanism-of-electrical-conductivity-of-transparent-ingazno-3fp41h068c.pdf

Isao Tanaka

Papers

First principles phonon calculations in materials science

First-principles calculations of the ferroelastic transition between rutile-type and CaCl2-type SiO2 at high pressures

First principles phonon calculations in materials science

Defect energetics in ZnO: A hybrid Hartree-Fock density functional study

Mechanism of electrical conductivity of transparent InGaZnO 4