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

Physical Review B

This is a review of Collected Works of John Tate. Parts I, II, edited by Barry Mazur and Jean-Pierre Serre. American Mathematical Society, Providence, Rhode Island, 2016. For several decades it has been clear to the friends and colleagues of John Tate that a “Collected Works” was merited. The award of the Abel Prize to Tate in 2010 added impetus, and finally, in Tate’s ninety-second year we have these two magnificent volumes, edited by Barry Mazur and Jean-Pierre Serre. Beyond Tate’s published articles, they include five unpublished articles and a selection of his letters, most accompanied by Tate’s comments, and a collection of photographs of Tate. For an overview of Tate’s work, the editors refer the reader to [4]. Before discussing the volumes, I describe some of Tate’s work. 1. Hecke L-series and Tate’s thesis Like many budding number theorists, Tate’s favorite theorem when young was Gauss’s law of quadratic reciprocity. When he arrived at Princeton as a graduate student in 1946, he was fortunate to find there the person, Emil Artin, who had discovered the most general reciprocity law, so solving Hilbert’s ninth problem. By 1920, the German school of algebraic number theorists (Hilbert, Weber, . . .) together with its brilliant student Takagi had succeeded in classifying the abelian extensions of a number field K: to each group I of ideal classes in K, there is attached an extension L of K (the class field of I); the group I determines the arithmetic of the extension L/K, and the Galois group of L/K is isomorphic to I. Artin’s contribution was to prove (in 1927) that there is a natural isomorphism from I to the Galois group of L/K. When the base field contains an appropriate root of 1, Artin’s isomorphism gives a reciprocity law, and all possible reciprocity laws arise this way. In the 1930s, Chevalley reworked abelian class field theory. In particular, he replaced “ideals” with his “idèles” which greatly clarified the relation between the local and global aspects of the theory. For his thesis, Artin suggested that Tate do the same for Hecke L-series. When Hecke proved that the abelian L-functions of number fields (generalizations of Dirichlet’s L-functions) have an analytic continuation throughout the plane with a functional equation of the expected type, he saw that his methods applied even to a new kind of L-function, now named after him. Once Tate had developed his harmonic analysis of local fields and of the idèle group, he was able prove analytic continuation and functional equations for all the relevant L-series without Hecke’s complicated theta-formulas. Received by the editors September 5, 2016. 2010 Mathematics Subject Classification. Primary 01A75, 11-06, 14-06. c ©2017 American Mathematical Society

The collected works

The electron-phonon interaction in solids is important for many interesting properties of solids, among them the critical temperature of phonon-mediated superconductors, the effective electron mass in metals and semiconductors, and the carrier dynamics in semiconductors. Modern density-functional techniques have made it possible to perform $a\phantom{\rule{0}{0ex}}b$ $i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o$ calculations of the electron-phonon interaction. This review explains these techniques and discusses their applications.

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Electron-phonon interactions from first principles

The long-standing popularity of thermoelectric materials has contributed to the creation of various thermoelectric devices and stimulated the development of strategies to improve their thermoelectric performance. In this review, we aim to comprehensively summarize the state-of-the-art strategies for the realization of high-performance thermoelectric materials and devices by establishing the links between synthesis, structural characteristics, properties, underlying chemistry and physics, including structural design (point defects, dislocations, interfaces, inclusions, and pores), multidimensional design (quantum dots/wires, nanoparticles, nanowires, nano- or microbelts, few-layered nanosheets, nano- or microplates, thin films, single crystals, and polycrystalline bulks), and advanced device design (thermoelectric modules, miniature generators and coolers, and flexible thermoelectric generators). The outline of each strategy starts with a concise presentation of their fundamentals and carefully selected examples. In the end, we point out the controversies, challenges, and outlooks toward the future development of thermoelectric materials and devices. Overall, this review will serve to help materials scientists, chemists, and physicists, particularly students and young researchers, in selecting suitable strategies for the improvement of thermoelectrics and potentially other relevant energy conversion technologies.

Advanced Thermoelectric Design: From Materials and Structures to Devices

In the search of clean and efficient energy sources intermediate temperature solid oxide fuel cells are among the prime candidates. What sets the limit of their efficiency is the solid electrolyte. A promising material for the electrolyte is ceria. This thesis aims to improve the characteristics of these electrolytes and help provide thorough physical understanding of the processes involved. This is realised using first principles calculations. The class of methods based on density functional theory generally ignores temperature effects. To accurately describe the intermediate temperature characteristics I have made adjustments to existing frameworks and developed a qualitatively new method. The new technique, the high temperature effective potential method, is a general theory. The validity is proven on a number of model systems. Other subprojects include low-dimensional segregation effects, adjustments to defect concentration formalism and optimisations of ionic conductivity.

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Lattice dynamics of anharmonic solids from first principles

We have developed a thorough and accurate method of determining anharmonic free energies. The technique is based in ab initio molecular dynamics and map a model Hamiltonian to the fully anharmonic ...

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Temperature dependent effective potential method for accurate free energy calculations of solids

The temperature-dependent effective potential (TDEP) method is generalized beyond pair interactions The second- and third-order force constants are determined consistently from ab initio molecular 

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Temperature-dependent effective third-order interatomic force constants from first principles

We present first-principles calculations of the thermal and thermal transport properties of ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ that combine an ab initio molecular dynamics (AIMD) approach to calculate interatomic force constants (IFCs) along with a full iterative solution of the Peierls-Boltzmann transport equation for phonons. The newly developed AIMD approach allows determination of harmonic and anharmonic interatomic forces at each temperature, which is particularly appropriate for highly anharmonic materials such as ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$. The calculated phonon dispersions, heat capacity, and thermal expansion coefficient are found to be in good agreement with measured data. The lattice thermal conductivity, ${\ensuremath{\kappa}}_{l}$, calculated using the AIMD approach nicely matches measured values, showing better agreement than the ${\ensuremath{\kappa}}_{l}$ obtained using temperature-independent IFCs. A significant contribution to ${\ensuremath{\kappa}}_{l}$ from optic phonon modes is found. Already at room temperature, the phonon line shapes show a notable broadening and onset of satellite peaks reflecting the underlying strong anharmonicity.

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Phonon thermal transport in Bi 2 Te 3 from first principles

The anharmonic lattice dynamics of rock-salt thermoelectric compounds SnTe and PbTe are investigated with inelastic neutron scattering (INS) and first-principles calculations. The experiments show that, surprisingly, although SnTe is closer to the ferroelectric instability, phonon spectra in PbTe exhibit a more anharmonic character. This behavior is reproduced in first-principles calculations of the temperature-dependent phonon self-energy. Our simulations reveal how the nesting of phonon dispersions induces prominent features in the self-energy, which account for the measured INS spectra and their temperature dependence. We establish that the phase space for three-phonon scattering processes, combined with the proximity to the lattice instability, is the mechanism determining the complex spectrum of the transverse-optic ferroelectric mode.

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Olle Hellman

Papers

Lattice dynamics of anharmonic solids from first principles

Temperature dependent effective potential method for accurate free energy calculations of solids

Temperature-dependent effective third-order interatomic force constants from first principles

Phonon thermal transport in Bi 2 Te 3 from first principles

Phonon self-energy and origin of anomalous neutron scattering spectra in SnTe and PbTe thermoelectrics