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

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

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.

Point defects and impurities strongly affect the physical properties of materials and have a decisive impact on their performance in applications. First-principles calculations have emerged as a powerful approach that complements experiments and can serve as a predictive tool in the identification and characterization of defects. The theoretical modeling of point defects in crystalline materials by means of electronic-structure calculations, with an emphasis on approaches based on density functional theory (DFT), is reviewed. A general thermodynamic formalism is laid down to investigate the physical properties of point defects independent of the materials class (semiconductors, insulators, and metals), indicating how the relevant thermodynamic quantities, such as formation energy, entropy, and excess volume, can be obtained from electronic structure calculations. Practical aspects such as the supercell approach and efficient strategies to extrapolate to the isolated-defect or dilute limit are discussed. Recent advances in tractable approximations to the exchange-correlation functional ($\mathrm{DFT}+U$, hybrid functionals) and approaches beyond DFT are highlighted. These advances have largely removed the long-standing uncertainty of defect formation energies in semiconductors and insulators due to the failure of standard DFT to reproduce band gaps. Two case studies illustrate how such calculations provide new insight into the physics and role of point defects in real materials.

First-principles calculations for point defects in solids

Phase-change materials are widely used as non-volatile memories, for example in optical data storage, but the search for improved phase-change materials has proved difficult. Based on a fundamental understanding of their bonding characteristics, a systematic prediction of phase-change properties has now become possible.

A map for phase-change materials.

Revealing the strain-hardening behavior of twinning-induced plasticity steels: Theory, simulations, experiments

We propose a fully ab initio based integrated approach to determine the volume and temperature dependent free-energy surface of nonmagnetic crystalline solids up to the melting point The approach is based on density-functional theory calculations with a controlled numerical accuracy of better than 1 meV/atom It accounts for all relevant excitation mechanisms entering the free energy including electronic, quasiharmonic, anharmonic, and structural excitations such as vacancies To achieve the desired accuracy of $l1\text{ }\text{meV}/\text{atom}$ for the anharmonic free-energy contribution without losing the ability to perform these calculations on standard present-day computer platforms, we develop a numerically highly efficient technique: we propose a hierarchical scheme---called upsampled thermodynamic integration using Langevin dynamics---which allows for a significant reduction in the number of computationally expensive ab initio configurations compared to a standard molecular dynamics scheme As for the vacancy contribution, concentration-dependent pressure effects had to be included to achieve the desired accuracy Applying the integrated approach gives us direct access to the free-energy surface $F(V,T)$ for aluminum and derived quantities such as the thermal expansion coefficient or the isobaric heat capacity and allows a direct comparison with experiment A detailed analysis enables us to tackle the long-standing debate over which excitation mechanism (anharmonicity vs vacancies) is dominant close to the melting point

https://physics.aps.org/featured-article-pdf/10.1103/PhysRevB.79.134106

Ab initio up to the melting point: Anharmonicity and vacancies in aluminum

Thermal properties of an extensive set of fcc metals (Al, Pb, Cu, Ag, Au, Pd, Pt, Rh, and Ir) have been studied using density-functional theory in combination with the quasiharmonic approximation. Systematic convergence checks have been performed to ensure an accuracy greater than $1\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$/atom in the free energies. Phonon dispersion relations, Gr\"uneisen parameters, free energies, thermal expansions, and heat capacities have been calculated for the two popular exchange-correlation functionals: Local density approximation and Perdew-Burke-Ernzerhof generalized gradient approximation [Phys. Rev. Lett. 77, 3865 (1996)]. The results are found to be in excellent agreement with both experimental and CALPHAD data.

Tilmann Hickel

Papers

First-principles calculations for point defects in solids

A map for phase-change materials.

Revealing the strain-hardening behavior of twinning-induced plasticity steels: Theory, simulations, experiments

Ab initio up to the melting point: Anharmonicity and vacancies in aluminum

Ab initio study of the thermodynamic properties of nonmagnetic elementary fcc metals: Exchange-correlation-related error bars and chemical trends