Using a generalized molecular dynamics force model for random microstructure generation of different aspect-ratios and orientation for use in the optical design of an LED edge-lit backlight

We propose a method for the pattern generation on the base of a light guide for application in an edge-lit backlight. This method uses the molecular dynamics method of a generalized force model as a generation scheme to produce a microstructure with a pattern combining a variable aspect ratio and a variable microstructure orientation. This generation scheme can accommodate the needs of the subsequent optical design phase, and allows for easier optical optimization to reach the equal luminance condition. The scheme is incorporated into several new schemes to meet these needs, the most important of which is the cell division technique, which allows the adjustment of the microstructure density in each sub-domain, or cell. In addition, the boundary treatments allow the precise control of the microstructure density in each cell and the ability to smooth the microstructure distribution across the cell boundary. Finally, we present an example of a backlight with one light emitting diode showing the integration of the generation scheme and the optical design phase in order to assess the validation of the proposed scheme.     

Noise-driven numerical irreversibility in molecular dynamics technique

It is widely believed that, in molecular dynamics (MD) simulations, round-off errors can cause numerical irreversibility since, in the standard MD, floating-point real number arithmetic is employed and round-off errors cannot be avoided. To investigate the characteristic of this numerical irreversibility, the ‘bit-reversible algorithm’, which is completely time-reversible and is free from any round-off error, is made use of as a test bed. Through this study, it is clearly demonstrated that, other than the extent of the stability of the system, the appearance of irreversibility is related to the ‘quantity’ of the controlled noise. By means of the bit-reversible simulation added to the controlled noise of an appropriate ‘quantity’, the characteristic of the numerical irreversibility in the standard MD is revealed.     

An efficient parallel implementation of the smooth particle mesh Ewald method for molecular dynamics simulations

This paper focuses on the implementation and the performance analysis of a smooth particle mesh Ewald method on several parallel computers. We present the details of the algorithms and our implementation that are used to optimize parallel efficiency on such parallel computers.     

Scalable and portable visualization of large atomistic datasets

A scalable and portable code named Atomsviewer has been developed to interactively visualize a large atomistic dataset consisting of up to a billion atoms. The code uses a hierarchical view frustum-culling algorithm based on the octree data structure to efficiently remove atoms outside of the user's field-of-view. Probabilistic and depth-based occlusion-culling algorithms then select atoms, which have a high probability of being visible. Finally a multiresolution algorithm is used to render the selected subset of visible atoms at varying levels of detail. Atomsviewer is written in C++ and OpenGL, and it has been tested on a number of architectures including Windows, Macintosh, and SGI. Atomsviewer has been used to visualize tens of millions of atoms on a standard desktop computer and, in its parallel version, up to a billion atoms.

Program summary

Title of program: AtomsviewerCatalogue identifier: ADUMProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUMProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandComputer for which the program is designed and others on which it has been tested: 2.4 GHz Pentium 4/Xeon processor, professional graphics card; Apple G4 (867 MHz)/G5, professional graphics cardOperating systems under which the program has been tested: Windows 2000/XP, Mac OS 10.2/10.3, SGI IRIX 6.5Programming languages used: C++, C and OpenGLMemory required to execute with typical data: 1 gigabyte of RAMHigh speed storage required: 60 gigabytesNo. of lines in the distributed program including test data, etc.: 550 241No. of bytes in the distributed program including test data, etc.: 6 258 245Number of bits in a word: ArbitraryNumber of processors used: 1Has the code been vectorized or parallelized: NoDistribution format: tar gzip fileNature of physical problem: Scientific visualization of atomic systemsMethod of solution: Rendering of atoms using computer graphic techniques, culling algorithms for data minimization, and levels-of-detail for minimal renderingRestrictions on the complexity of the problem: NoneTypical running time: The program is interactive in its executionUnusual features of the program: NoneReferences: The conceptual foundation and subsequent implementation of the algorithms are found in [A. Sharma, A. Nakano, R.K. Kalia, P. Vashishta, S. Kodiyalam, P. Miller, W. Zhao, X.L. Liu, T.J. Campbell, A. Haas, Presence—Teleoperators and Virtual Environments 12 (1) (2003)].     

How would you integrate the equations of motion in dissipative particle dynamics simulations?

In this work we assess the quality and performance of several novel dissipative particle dynamics integration schemes that have not previously been tested independently. Based on a thorough comparison we identify the respective methods of Lowe and Shardlow as particularly promising candidates for future studies of large-scale properties of soft matter systems.     

TiReX: Replica-exchange molecular dynamics using Tinker

We present a driver program for performing replica-exchange molecular dynamics simulations with the Tinker package. Parallelization is based on the Message Passing Interface, with every replica assigned to a separate process. The algorithm is not communication intensive, which makes the program suitable for running even on loosely coupled cluster systems. Particular attention is paid to the practical aspects of analyzing the program output.

Program summary

Program title: TiReXCatalogue identifier: AEEK_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEK_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 43 385No. of bytes in distributed program, including test data, etc.: 502 262Distribution format: tar.gzProgramming language: Fortran 90/95Computer: Most UNIX machinesOperating system: LinuxHas the code been vectorized or parallelized?: parallelized with MPIClassification: 16.13External routines: TINKER version 4.2 or 5.0, built as a libraryNature of problem: Replica-exchange molecular dynamics.Solution method: Each replica is assigned to a separate process; temperatures are swapped between replicas at regular time intervals.Running time: The sample run may take up to a few minutes.     

Oedometric test, Bauer's law and the micro-macro connection for a dry sand

What is the relationship between the macroscopic parameters of the constitutive equation for a granular soil and the microscopic forces between grains? In order to investigate this connection, we have simulated by molecular dynamics the oedometric compression of a granular soil (a dry and bad-graded sand) and computed the hypoplastic parameters hs (the granular skeleton hardness) and η (the exponent in the compression law) by following the same procedure than in experiments, that is by fitting the Bauer's law e/e₀=exp(−n(3p/hs)), where p is the pressure and e₀ and e are the initial and present void ratios. The micro-mechanical simulation includes elastic and dissipative normal forces plus slip, rolling and static friction between grains. By this way we have explored how the macroscopic parameters change by modifying the grains stiffness, V; the dissipation coefficient, γn; the static friction coefficient, μs; and the dynamic friction coefficient, μk. Cumulating all simulations, we obtained an unexpected result: the two macroscopic parameters seems to be related by a power law, hs=0.068(4)η9.88(3). Moreover, the experimental result for a Guamo sand with the same granulometry fits perfectly into this power law. Is this relation real? What is the final ground of the Bauer's Law? We conclude by exploring some hypothesis.     

Cell neighbor list method for planar elongational flow: rheology of a diatomic fluid

We present simple changes to the cell method for neighbor list construction that enable it to be used in molecular dynamics studies of systems subject to a planar elongational flow field. The modifications for planar elongational flow are similar to those required for planar shear flow and should be easy to incorporate into any cell neighbor list method that is used in simulations of homogeneous shear. The execution time of the code at equilibrium is shown to be proportional to the number of particles N. The introduction of the modifications allowing shear, and more importantly, elongational flow are shown to affect the performance of the code in both CPU time and memory usage. The modifications to enable the simulation of planar elongational flow using the cell method of neighbor list construction will not introduce any higher order dependency if applied to code that is N-dependent in planar shear flow. We use this code to study large systems of diatomic molecules at low strain-rates, and find that the linear regime in planar elongational flow can be determined by the ratio of the two planar elongational viscosity functions. The properties investigated in planar shear flow, such as angular velocity and alignment angle, were inconsistent with the shear viscosity results in their evaluation of where the linear regime ends. The high precision of the results allowed us to accurately determine the coefficients in the retarded-motion expansion.     

A semi-implicit Hall-MHD solver using whistler wave preconditioning

The dispersive character of the Hall-MHD solutions, in particular the whistler waves, is a strong restriction to numerical treatments of this system. Numerical stability demands a time step dependence of the form Δt∝²(Δx) for explicit calculations. A new semi-implicit scheme for integrating the induction equation is proposed and applied to a reconnection problem. It is based on a fix point iteration with a physically motivated preconditioning. Due to its convergence properties, short wavelengths converge faster than long ones, thus it can be used as a smoother in a nonlinear multigrid method.     

A hybrid multi-loop genetic-algorithm/simplex/spatial-grid method for locating the optimum orientation of an adsorbed protein on a solid surface

Atomistic simulation of protein adsorption on a solid surface in aqueous environment is computationally demanding, therefore the determination of preferred protein orientations on the solid surface usually serves as an initial step in simulation studies. We have developed a hybrid multi-loop genetic-algorithm/simplex/spatial-grid method to search for low adsorption-energy orientations of a protein molecule on a solid surface. In this method, the surface and the protein molecule are treated as rigid bodies, whereas the bulk fluid is represented by spatial grids. For each grid point, an effective interaction region in the surface is defined by a cutoff distance, and the possible interaction energy between an atom at the grid point and the surface is calculated and recorded in a database. In searching for the optimum position and orientation, the protein molecule is translated and rotated as a rigid body with the configuration obtained from a previous Molecular Dynamic simulation. The orientation-dependent protein-surface interaction energy is obtained using the generated database of grid energies. The hybrid search procedure consists of two interlinked loops. In the first loop A, a genetic algorithm (GA) is applied to identify promising regions for the global energy minimum and a local optimizer with the derivative-free Nelder-Mead simplex method is used to search for the lowest-energy orientation within the identified regions. In the second loop B, a new population for GA is generated and competitive solution from loop A is improved. Switching between the two loops is adaptively controlled by the use of similarity analysis. We test the method for lysozyme adsorption on a hydrophobic hydrogen-terminated silicon (110) surface in implicit water (i.e., a continuum distance-dependent dielectric constant). The results show that the hybrid search method has faster convergence and better solution accuracy compared with the conventional genetic algorithm.     

Calculation of massless Feynman integrals using harmonic sums

A method for the evaluation of the ε-expansion of multi-loop massless Feynman integrals is introduced. This method is based on the Gegenbauer polynomial technique and the expansion of the Gamma function in terms of harmonic sums. Algorithms for the evaluation of nested and harmonic sums are used to reduce the expressions to get analytical or numerical results for the expansion coefficients. Methods to increase the precision of numerical results are discussed.     

Piezoelectric coefficients by molecular dynamics simulations in the constant stress ensemble: A case study of quartz

Piezoelectric (strain) coefficients dij of quartz are calculated in terms of molecular dynamics as a function of pressure and temperature. We review the necessary formulas for the computation of electromechanical materials coefficients obtained at constant stress and temperature, and discuss how to overcome complications of the definition of polarization variations due to fluctuating box geometries. A method is employed suppressing significantly stochastic fluctuations of the estimators for piezoelectric coefficients. A recently suggested force field for the simulation of SiO₂ reproduces available experimental data quite accurately. Predictions are made for the pressure dependence of dij of quartz.     

A cell multipole based domain decomposition algorithm for molecular dynamics simulation of systems of arbitrary shape

A domain decomposition algorithm for molecular dynamics simulation of atomic and molecular systems with arbitrary shape and non-periodic boundary conditions is described. The molecular dynamics program uses cell multipole method for efficient calculation of long range electrostatic interactions and a multiple time step method to facilitate bigger time steps. The system is enclosed in a cube and the cube is divided into a hierarchy of cells. The deepest level cells are assigned to processors such that each processor has contiguous cells and static load balancing is achieved by redistributing the cells so that each processor has approximately same number of atoms. The resulting domains have irregular shape and may have more than 26 neighbors. Atoms constituting bond angles and torsion angles may straddle more than two processors. An efficient strategy is devised for initial assignment and subsequent reassignment of such multiple-atom potentials to processors. At each step, computation is overlapped with communication greatly reducing the effect of communication overhead on parallel performance. The algorithm is tested on a spherical cluster of water molecules, a hexasaccharide and an enzyme both solvated by a spherical cluster of water molecules. In each case a spherical boundary containing oxygen atoms with only repulsive interactions is used to prevent evaporation of water molecules. The algorithm shows excellent parallel efficiency even for small number of cells/atoms per processor.     

On the density correlation of the spontaneous fluctuation in a real-coded lattice gas

We investigate the spontaneous fluctuation in a real-coded lattice gas (RLG) model by studying the density correlation function. In particular, the dynamic structure factor obtained from RLG is in agreement with the Rayleigh-Brillouin spectrum, a spectrum which can also be measured from a real fluid at the continuum limit. We also work out the analytic form of the static structure factor for the RLG model, which is supported by the numerical results.     

?-SHAKE: An extension to SHAKE for the explicit treatment of angular constraints

This paper presents ?-SHAKE, an extension to SHAKE, an algorithm for the resolution of holonomic constraints in molecular dynamics simulations, which allows for the explicit treatment of angular constraints. We show that this treatment is more efficient than the use of fictitious bonds, significantly reducing the overlap between the individual constraints and thus accelerating convergence. The new algorithm is compared with SHAKE, M-SHAKE, the matrix-based approach described by Ciccotti and Ryckaert and P-SHAKE for rigid water and octane.     

JChainsAnalyser: an ImageJ-based stand-alone application for the study of magneto-rheological fluids

JChainsAnalyser is a Java-based program for the analysis of two-dimensional images of magneto-rheological fluids (MRF) at low concentration of particles obtained using the video-microscopy technique. MRF are colloidal dispersions of micron-sized polarizable particles in a carrier fluid with medium to low viscosity. When a magnetic field is applied to the suspension, the particles aggregate forming chains or clusters. Aggregation dynamics [P. Domínguez-García, S. Melle, J.M. Pastor, M.A. Rubio, Phys. Rev. E 76 (2007) 051403] and morphology of the aggregates [P. Domínguez-García, S. Melle, M.A. Rubio, J. Colloid Interface Sci. 333 (2009) 221-229] have been studied capturing images of the fluid and analyzing them by using this software. The program allows to analyze automatically the MRF images by means of an adequate combination of different imaging methods, while magnitudes and statistics are calculated and saved in data files. It is possible to run the program on a desktop computer, using the GUI (graphical user interface), or in a cluster of processors or remote computer by means of command-line instructions.

Program summary

Program title: JChainsAnalyserCatalogue identifier: AEDT_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDT_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 79 071No. of bytes in distributed program, including test data, etc.: 4 367 909Distribution format: tar.gzProgramming language: Java 2Computer: Any computer with Java Runtime Environment (JRE) installedOperating system: Any OS with Java Runtime Environment (JRE) installedRAM: Typically, 3.3 MBClassification: 23External routines: ImageJ, ij-imageIO, jdom, L2FProdNature of problem: The video-microscopy technique usually produces quite a big quantity of images to analyze. Although ImageJ gives the required filters and methods for image analysis, it fails when a large number of images is used. Moreover, an adequate combination of filters is needed for the segmentation and binarization of this kind of images.Solution method: JChainsAnalyser filters and analyses any quantity of MRF images automatically, so the application can be run on a desktop computer or using a cluster of processors. It can be run in a desktop computer using the GUI (graphical user interface) or by a command-line interface. JChainsAnalyser uses XML files to define input/output data and Java to ensure portability between operating systems. It also utilizes an image algorithm based on the application of different and adaptative ImageJ's filters.Running time: The test run provided takes only a few seconds.     

An efficient swap algorithm for the lattice Boltzmann method

During the last decade, the lattice-Boltzmann method (LBM) as a valuable tool in computational fluid dynamics has been increasingly acknowledged. The widespread application of LBM is partly due to the simplicity of its coding. The most well-known algorithms for the implementation of the standard lattice-Boltzmann equation (LBE) are the two-lattice and two-step algorithms. However, implementations of the two-lattice or the two-step algorithm suffer from high memory consumption or poor computational performance, respectively. Ultimately, the computing resources available decide which of the two disadvantages is more critical. Here we introduce a new algorithm, called the swap algorithm, for the implementation of LBE. Simulation results demonstrate that implementations based on the swap algorithm can achieve high computational performance and have very low memory consumption. Furthermore, we show how the performance of its implementations can be further improved by code optimization.     

Departure from elasticity in granular layers: Investigation of a crossover overload force

Aiming at characterizing the departure from elasticity in granular materials, we study, by means of numerical molecular dynamics simulations, the stress response of a layer submitted to increasing overload forces. Comparing normalized stress profiles to a reference small overload case, ∼0.1〈m〉g, we compute root mean square (RMS) differences, averaged over several independent realizations, as a function of the overload force. The results indicate two different regimes for these RMS data: an elastic plateau at small overload values and an increase of the RMS at large forces. This increase is due to small (and frequent) as well as large (and rare) rearranging events. We show that one can extract from both of these contributions a crossover value for the overload force, which separates the two regimes.     

Implementation of Green's function molecular dynamics: An extension to LAMMPS

The Green's function molecular dynamics method, which enables one to study the elastic response of a three-dimensional solid to an external stress field by taking into consideration only the surface atoms, was implemented as an extension to an open source classical molecular dynamics simulation code LAMMPS. This was done in the style of fixes. The first fix, FixGFC, measures the elastic stiffness coefficients for a (small) solid block of a given material by making use of the fluctuation-dissipation theorem. With the help of the second fix, FixGFMD, the coefficients obtained from FixGFC can then be used to compute the elastic forces for a (large) block of the same material. Both fixes are designed to be run in parallel and to exploit the functions provided by LAMMPS.

Program summary

Program title: FixGFC/FixGFMDCatalogue identifier: AECW_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECW_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: yesNo. of lines in distributed program, including test data, etc.: 33 469No. of bytes in distributed program, including test data, etc.: 1 383 631Distribution format: tar.gzProgramming language: C++Computer: AllOperating system: LinuxHas the code been vectorized or parallelized?: Parallelized via MPIRAM: Depends on the problemClassification: 7.7External routines: MPI, FFTW 2.1.5 (http://www.fftw.org/), LAMMPS version May 21, 2008 (http://lammps.sandia.gov/)Nature of problem: Using molecular dynamics to study elastically deforming solids imposes very high computational costs because portions of the solid far away from the interface or contact points need to be included in the simulation to reproduce the effects of long-range elastic deformations. Green's function molecular dynamics (GFMD) incorporates the full elastic response of semi-infinite solids so that only surface atoms have to be considered in molecular dynamics simulations, thus reducing the problem from three dimensions to two dimensions without compromising the physical essence of the problem.Solution method: See “Nature of problem”.Restrictions: The mean equilibrium positions of the GFMD surface atoms must be in a plane and be periodic in the plane, so that the Born-von Karman boundary condition can be used. In addition, only deformation within the harmonic regime is expected in the surface layer during Green's function molecular dynamics.Running time: FixGFC varies from minutes to days, depending on the system size, the numbers of processors used, and the complexity of the force field. FixGFMD varies from seconds to days depending on the system size and numbers of processors used.References: [1] C. Campañá, M.H. Müser, Phys. Rev. B 74 (2006) 075420.