In this article, we present a new LINear Constraint Solver (LINCS) for molecular simulations with bond constraints. The algorithm is inherently stable, as the constraints themselves are reset instead of derivatives of the constraints, thereby eliminating drift. Although the derivation of the algorithm is presented in terms of matrices, no matrix matrix multiplications are needed and only the nonzero matrix elements have to be stored, making the method useful for very large molecules. At the same accuracy, the LINCS algorithm is three to four times faster than the SHAKE algorithm. Parallelization of the algorithm is straightforward. (C) 1997 John Wiley & Sons, Inc.

LINCS : A linear constraint solver for molecular simulations

By removing the fastest degrees of freedom, constraints allow for an increase of the time step in molecular simulations. In the last decade parallel simulations have become commonplace. However, up till now efficient parallel constraint algorithms have not been used with domain decomposition. In this paper the parallel linear constraint solver (P-LINCS) is presented, which allows the constraining of all bonds in macromolecules. Additionally the energy conservation properties of (P-)LINCS are assessed in view of improvements in the accuracy of uncoupled angle constraints and integration in single precision.

P-LINCS: A Parallel Linear Constraint Solver for Molecular Simulation

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Metal–Organic Frameworks and Self-Assembled Supramolecular Coordination Complexes: Comparing and Contrasting the Design, Synthesis, and Functionality of Metal–Organic Materials

Over the 100 years since its discovery, liquid crystals have been the intriguing subject for both academia and industries. The textbook of de Gennes The Physics of Liquid Crystals published in 1974 is still the bible for many LC researchers, but new subjects unmentioned in the book have also risen for these years. This chapter describes the story of the recent developments and the future perspectives in physics of liquid crystals, especially focusing on the contributions by Japanese research groups for the last decade.

Physics of Liquid Crystals

The variability of El Nino/Southern Oscillation (ENSO) during the Holocene epoch, in particular on millennial timescales, is poorly understood. Palaeoclimate studies have documented ENSO variability for selected intervals in the Holocene, but most records are either too short or insufficiently resolved to investigate variability on millennial scales1,2,3. Here we present a record of sedimentation in Laguna Pallcacocha, southern Ecuador, which is strongly influenced by ENSO variability, and covers the past 12,000 years continuously. We find that changes on a timescale of 2–8 years, which we attribute to warm ENSO events, become more frequent over the Holocene until about 1,200 years ago, and then decline towards the present. Periods of relatively high and low ENSO activity, alternating at a timescale of about 2,000 years, are superimposed on this long-term trend. We attribute the long-term trend to orbitally induced changes in insolation, and suggest internal ENSO dynamics as a possible cause of the millennial variability. However, the millennial oscillation will need to be confirmed in other ENSO proxy records.

Variability of El Niño/Southern Oscillation activity at millennial timescales during the Holocene epoch

It has long been appreciated that liquid-crystal (LC) devices in which the LC molecules adopt multiple stable orientations could drastically reduce the power consumption required for high-information-content displays. But for the commonly used nematic LCs, which are intrinsically uniaxial in symmetry, no industrially feasible multi-stable LC device has been realized1,2,3,4,5,6,7. Recently we demonstrated how bistability can be robustly engineered into a nematic LC device, by patterning a substrate with an orientational chequerboard pattern that enforces orthogonal LC alignment in neighbouring square domains8,9. As a result of the four-fold symmetry of the pattern, the two diagonal axes of the chequerboard become equally stable macroscopic orientations. Here we extend this symmetry approach to obtain a tristable surface-aligned nematic LC. A microscopic pattern exhibiting six-fold symmetry is inscribed on a polyimide surface using the stylus of an atomic force microscope. The hexagonal symmetry of the microscopic orientational domains in turn gives rise to three stable macroscopic LC orientations, which are mutually switchable by an in-plane electric field. The resulting switching mode is surface driven, and hence should be compatible with demanding flexible display applications.

Tristable nematic liquid-crystal device using micropatterned surface alignment

Effects of Substituted Alkyl Chain Length on Solution-Processable Layered Organic Semiconductor Crystals

We demonstrate a robust in-plane bistability of liquid-crystal surface alignment based on tailored submicrometer-sized surface domains imposing a frustrated alignment. By a nanorubbing technique utilizing the atomic force microscope, we prepared an orientational checkerboard pattern on polyimide layer, consisting of square unit domains on which the alignment is locally constrained to be planar yet orthogonal between the neighboring domains. Due to the four-fold rotational symmetry of the pattern, the two diagonal axes of the square domain become equally stable directions for the macroscopic liquid crystal alignment. The alignment could be switched between these two states by an in-plane electric field above a certain threshold, determined by the local azimuthal anchoring.

Surface alignment bistability of nematic liquid crystals by orientationally frustrated surface patterns

We numerically investigate the interaction between two spherical particles in a nematic liquid crystal mediated by elastic distortions in the orientational order. We pay attention to the cases where two particles with equal radii R0 impose rigid normal anchoring on their surfaces and carry a pointlike topological defect referred to as a hyperbolic hedgehog. To describe the geometry of our system, we use bispherical coordinates, which prove useful in the implementation of boundary conditions at the particle surfaces and at infinity. We adopt the Landau-de Gennes continuum theory in terms of a second-rank tensor order parameter Q(ij) for the description of the orientational order of a nematic liquid crystal. We also utilize an adaptive mesh refinement scheme that has proven to be an efficient way of dealing with topological defects whose core size is much smaller than the particle size. When the two "dipoles," composed of a particle and a hyperbolic hedgehog, are in parallel directions, the two-particle interaction potential is attractive for large interparticle distances D and proportional to D-3 as expected from the form of the dipole-dipole interaction, until the well-defined potential minimum at D approximately 2.46 R0 is reached. For the antiparallel configuration with no hedgehogs between the two particles, the interaction potential is repulsive and behaves as D-2 for D less than or approximately equal 10R0, which is stronger than the dipole-dipole repulsion (approximately D-3 ) expected theoretically as an asymptotic behavior for large D.

Makoto Yoneya

Papers

Physics of Liquid Crystals

Tristable nematic liquid-crystal device using micropatterned surface alignment

Effects of Substituted Alkyl Chain Length on Solution-Processable Layered Organic Semiconductor Crystals

Surface alignment bistability of nematic liquid crystals by orientationally frustrated surface patterns

Interaction between two spherical particles in a nematic liquid crystal.