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

This paper reviews recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases. It focuses on effects beyond standard weak-coupling descriptions, such as the Mott-Hubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or lowest-Landau-level physics in quasi-two-dimensional gases in fast rotation. Strong correlations in fermionic gases are discussed in optical lattices or near-Feshbach resonances in the BCS-BEC crossover.

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Many-Body Physics with Ultracold Gases

日本物理学会誌及びJournal of the Physical Society of Japanの月刊について

The electronic ground state of a periodic system is usually described in terms of extended Bloch orbitals, but an alternative representation in terms of localized "Wannier functions" was introduced by Gregory Wannier in 1937. The connection between the Bloch and Wannier representations is realized by families of transformations in a continuous space of unitary matrices, carrying a large degree of arbitrariness. Since 1997, methods have been developed that allow one to iteratively transform the extended Bloch orbitals of a first-principles calculation into a unique set of maximally localized Wannier functions, accomplishing the solid-state equivalent of constructing localized molecular orbitals, or "Boys orbitals" as previously known from the chemistry literature. These developments are reviewed here, and a survey of the applications of these methods is presented. This latter includes a description of their use in analyzing the nature of chemical bonding, or as a local probe of phenomena related to electric polarization and orbital magnetization. Wannier interpolation schemes are also reviewed, by which quantities computed on a coarse reciprocal-space mesh can be used to interpolate onto much finer meshes at low cost, and applications in which Wannier functions are used as efficient basis functions are discussed. Finally the construction and use of Wannier functions outside the context of electronic-structure theory is presented, for cases that include phonon excitations, photonic crystals, and cold-atom optical lattices.

Maximally-localized Wannier Functions: Theory and Applications

The large, temperature-independent, low-frequency dielectric constant recently observed in single-crystal CaCu3Ti4O12 is most plausibly interpreted as arising from spatial inhomogenities of its local dielectric response Probable sources of inhomogeneity are the various domain boundaries endemic in such materials: twin, Ca ordering, and antiphase boundaries The material in, and neighboring, such boundaries can be insulating or conducting We construct a decision tree for the resulting six possible morphologies, and derive or present expressions for the dielectric constant for models of each morphology We conclude that all six morphologies can yield dielectric behavior consistent with observations Thus, present experimental findings are insufficient to establish the internal morphology responsible for the remarkable properties of CaCu3Ti4O12, and we suggest further experiments to distinguish among them

Extrinsic models for the dielectric response of CaCu3Ti4O12

Structural and electronic properties of ${\mathrm{CaCu}}_{3}{\mathrm{Ti}}_{4}{\mathrm{O}}_{12}$ are calculated using density-functional theory within the local spin-density approximation. After an analysis of structural stability, zone-center optical phonon frequencies are evaluated using the frozen-phonon method and mode effective charges are determined from computed Berry-phase polarizations. Excellent agreement between calculated and measured phonon frequencies is obtained. The calculated mode effective charges are in poorer agreement with experiment, although they are of the correct order of magnitude and the lattice contribution to the static dielectric constant is calculated to be $\ensuremath{\sim}40.$ On the basis of these results, various mechanisms are considered for the enormous dielectric response reported in recent experiments. No direct evidence is found for intrinsic lattice or electronic mechanisms, suggesting that increased attention should be given to extrinsic effects.

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First-principles study of the structure and lattice dielectric response of CaCu 3 Ti 4 O 12

The large, temperature-independent, low-frequency dielectric constant recently observed in single-crystal CaCu{3}Ti{4}O{12} is most plausibly interpreted as arising from spatial inhomogenities of its local dielectric response. Probable sources of inhomogeneity are the various domain boundaries endemic in such materials: twin, Ca-ordering, and antiphase boundaries. The material in and neighboring such boundaries can be insulating or conducting. We construct a decision tree for the resulting six possible morphologies, and derive or present expressions for the dielectric constant for models of each morphology. We conclude that all six morphologies can yield dielectric behavior consistent with observations and suggest further experiments to distinguish among them.

Extrinsic models for the dielectric response of CaCu{3}Ti{4}O{12}

We have investigated the interaction of oxygen vacancies and $180\ifmmode^\circ\else\textdegree\fi{}$ domain walls in tetragonal ${\mathrm{PbTiO}}_{3}$ using density-functional theory. Our calculations indicate that the vacancies do have a lower formation energy in the domain wall than in the bulk, thereby confirming the tendency of these defects to migrate to, and pin, the domain walls. The pinning energies are reported for each of the three possible orientations of the original Ti-O-Ti bonds, and attempts to model the results with simple continuum models are discussed.

First-principles study of oxygen-vacancy pinning of domain walls in PbTiO 3

The spatial decay properties of Wannier functions and related quantities have been investigated using analytical and numerical methods. We find that the form of the decay is a power law times an exponential, with a particular power-law exponent that is universal for each kind of quantity. In one dimension we find an exponent of $\ensuremath{-}3/4$ for Wannier functions, $\ensuremath{-}1/2$ for the density matrix and for energy matrix elements, and $\ensuremath{-}1/2$ or $\ensuremath{-}3/2$ for different constructions of nonorthonormal Wannier-like functions.

/pdf/exponential-decay-properties-of-wannier-functions-and-2u66vme3oe.pdf

Lixin He

Papers

Extrinsic models for the dielectric response of CaCu3Ti4O12

First-principles study of the structure and lattice dielectric response of CaCu 3 Ti 4 O 12

Extrinsic models for the dielectric response of CaCu{3}Ti{4}O{12}

First-principles study of oxygen-vacancy pinning of domain walls in PbTiO 3

Exponential Decay Properties of Wannier Functions and Related Quantities