Hans-Rainer Trebin

IMD: A SOFTWARE PACKAGE FOR MOLECULAR DYNAMICS STUDIES ON PARALLEL COMPUTERS

We report on implementation and performance of the program IMD, designed for short range molecular dynamics simulations on massively parallel computers. After a short explanation of the cell-based algorithm, its extension to parallel computers as well as two variants of the communication scheme are discussed. We provide performance numbers for simulations of different sizes and compare them with values found in the literature. Finally we describe two applications, namely a very large scale simulation with more than 1.23×109 atoms, to our knowledge the largest published MD simulation up to this day and a simulation of a crack propagating in a two-dimensional quasicrystal.

The topology of non-uniform media in condensed matter physics

Abstract Methods of algebraic topology have been employed recently to classify defects and non-singular textures of condensed matter systems, and to describe two-defect processes. In this article a systematic review is presented of these methods and their applications. The non-uniform media are characterized by fields valued in a space of degeneracy, whose topological properties are investigated. Ways to represent such a space are reported. An introduction is given to the necessary mathematical tools, viz. the homotopy groups and exact sequences thereof. Combinations, entanglements and transformations of singularities are discussed. The connection between the homotopic defect classification and the description of many-defect systems is elaborated. The limitations and necessary modifications of the method for systems of broken translational symmetry are examined.

Quasicrystals : structure and physical properties

1. Synthesis, Metallurgy and Characterization. 2. Structure and Mathematical Modelling. 3. Electronic and Magnetic Properties. 4. Thermal and Dynamic Properties. 5. Mechanical Properties. 6. Surfaces and Thin Films.This review revolves around the question which general distribution of scatterers (in a Euclidean space) results in a pure point diffraction spectrum. Firstly, we treat mathematical diffration theory and state conditions under which such a distribution has pure point diffraction. We explain how a cut and project scheme naturally appears in this context and then turn our attention to the special situation of model sets and lattice substitution systems. As an example, we analyse the paperfolding sequence. In the last part, we summarize some aspects of stochastic point sets, with focus both on structure and diffraction.

Self-assembly of monatomic complex crystals and quasicrystals with a double-well interaction potential.

For the study of crystal formation and dynamics, we introduce a simple two-dimensional monatomic model system with a parametrized interaction potential. We find in molecular dynamics simulations that a surprising variety of crystals, a decagonal, and a dodecagonal quasicrystal are self-assembled. In the case of the quasicrystals, the particles reorder by phason flips at elevated temperatures. During annealing, the entropically stabilized decagonal quasicrystal undergoes a reversible phase transition at 65% of the melting temperature into an approximant, which is monitored by the rotation of the de Bruijn surface in hyperspace.

An extension of the Landau-Ginzburg-de Gennes theory for liquid crystals

Abstract Using angular momentum representation a method is proposed that allows the systematic construction of a generalized Landau-de Gennes elastic free energy of liquid crystals, in powers of a symmetric and traceless tensor order parameter, polarization field, of external fields and all respective derivatives. By this method all linearly independent elastic invariants and surface terms are constructed for nematics and cholesterics up to fourth order terms. In particular it is shown that up to fourth order in the tensor order parameter there are nineteen bulk elastic constants and four surface terms in the free energy of a general, biaxial nematic. In addition, the stability of this expansion is studied in detail. Some special cases of the elastic free energy of liquid crystals, already discussed in the literature, are reexamined and discrepancies with our results are emphasized. Finally, a thermo-dynamically correct way of establishing contact between the generalized de Gennes elastic free energy and ...

Crack propagation in quasicrystals

Crack propagation is studied in a two dimensional decagonal model quasicrystal. The simulations reveal the dominating role of highly coordinated atomic environments as structure intrinsic obstacles for both dislocation motion and crack propagation. For certain overloads, these obstacles and the quasiperiodic nature of the crystal result in a specific crack propagation mechanism: The crack tip emits a dislocation followed by a phason wall, along which the material opens up.

A MOLECULAR DYNAMICS RUN WITH 5 180 116 000 PARTICLES

We report on the development of IMD, a scalable program for classical molecular dynamics simulations on massively parallel supercomputers. New features like online-visualization and metacomputing are described.

Simulation of shear stress in icosahedral quasicrystals

By a numerical relaxation scheme we have simulated the plastic deformation of a quasicrystal. Shear stress was applied to a quasiperiodic icosahedral atomic configuration of Lennard-Jones particles, and nucleation of dislocation dipoles was observed which move in a slip plane. We also found climb motion and dissociation of a perfect dislocation into a pair of partials. A plane of phasonic defects is left in the wake of the propagating dislocations.

MOLECULAR DYNAMICS SIMULATIONS OF A GAY-BERNE NEMATIC LIQUID CRYSTAL : ELASTIC PROPERTIES FROM DIRECT CORRELATION FUNCTIONS

We report molecular dynamics simulations of a Gay–Berne nematic liquid crystal at constant temperature and density/pressure using the generalization of an algorithm recently proposed by Toxvaerd [Phys. Rev. E 47, 343 (1993)]. On the basis of these simulations the absolute values of the Oseen–Zocher–Frank elastic constants K11, K22, and K33 as well as the surface constants K13 and K24 have been calculated ab initio within the framework of the direct correlation function approach of Lipkin et al. [J. Chem. Phys. 82, 472 (1985)]. The angular coefficients of the direct pair correlation function, which enter the final equations, have been determined from the computer simulation data for the pair correlation function of the nematic by combining the Ornstein–Zernike relation and the Wiener–Hopf factorization scheme. The unoriented nematic approximation has been assumed when constructing the reference state of Lipkin et al. By an extensive study of the model over a wide range of temperatures, densities and pressu...

Simulation of shear stress in two-dimensional decagonal quasicrystals

To analyse the plasticity of quasicrystals a numerical simulation method has been developed by which shear stress is applied to a two-dimensional atomic configuration of Lennard-Jones particles. The method is based on a microconvergence relaxation procedure. We present results of simulations on a simple binary tiling which is obtained by decoration of the Tubingen triangle tiling. Slip through dislocations is observed. In contrast with periodic crystals the motion of dislocations through a quasicrystal does not leave the configuration undisturbed but creates a wall of phasons.