Enhanced sampling in simulations of dense systems

In the simulations of a variety of systems we encounter the problem of large relaxation times due to the dense packing of the systems constituents. We propose an algorithm to overcome this slowing down by temporarily allowing the constituents of a 3d systems to escape into a 4th space coordinate. The idea will be exemplified for the problem of a homopolymer collapse.     

BRANECODE: A program for simulations of braneworld dynamics

We describe an algorithm and a C++ implementation that we have written and made available for calculating the fully nonlinear evolution of 5D braneworld models with scalar fields. Bulk fields allow for the stabilization of the extra dimension. However, they complicate the dynamics of the system, so that analytic calculations (performed within an effective 4D theory) are usually only reliable for static bulk configurations or when the evolution of the extra dimension is negligible. In the general case, the nonlinear 5D dynamics can be studied numerically, and the algorithm and code we describe are the first ones of that type designed for this task. The program and its full documentation are available on the Web at http://www.cita.utoronto.ca/~jmartin/BRANECODE/.¹ In this paper we provide a brief overview of what the program does and how to use it.

Program summary

Title of program: BRANECODECatalogue identifier: ADVXProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVXProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions: noneOperating systems under which the program has been tested: LinuxProgramming language used: C++Memory required to execute with typical data: less than 1 MBHas the code been vectorized?: noPeripherals used: noneNo. of lines in distributed program, including test data, etc.: 8277No. of bytes in distributed program, including test data, etc.: 74 939CPC Program Library subprograms used: noneNature of physical problem: Dynamics of two co-dimension one branes in a five-dimensional spacetime with a bulk scalar field and arbitrary potentials. The dynamics is governed by the five dimensional Einstein equations of gravity and the junction conditions at the position of the branes.Method of solution: Leapfrog algorithm to solve system of (1+1)-dimensional partial differential equations; Initial and boundary value problem.Restrictions on the complexity of the problem: Assumption of homogeneity along three spatial dimensions parallel to the branes.Typical running time: Depending on the grid size and length of the time evolution: from ∼1 s to ∼1 h or longer.Unusual features of the program:none     

Towards an atomistic understanding of solid friction by computer simulations

Friction between two solid bodies in sliding motion takes place on a large spectrum of length and time scales: From the nanometer/second scale in an atomic force microscope up to the extremely macroscopic scales of tectonic motion. Despite our familiarity with friction, fundamental questions about its atomistic origins remain unanswered. Phenomenological laws that describe the friction in many systems were published more than 300 years ago by Amontons: The frictional force is proportional to the applied load and independent of the apparent area of contact. The atomistic origins of this simple law is still controversial. Many explanations, which seemed to be well-established until recently, have been called into question by new experimental results. Computer simulations have also revealed flaws in previous theoretical approaches and led to new insights into the atomistic processes responsible for friction. In this paper, selected computer simulation studies of friction will be discussed. Special attention will be given to how it is possible to gain insight into tribological processes that take place on macroscopic time scales with the help of atomistic computer simulations which are typically constrained to the nanometer and nanosecond regime.     

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.     

Three-dimensional spectral element simulations of variable density and viscosity, miscible displacements in a capillary tube

A high-accuracy numerical approach is introduced for three-dimensional, time-dependent simulations of variable density and viscosity, miscible flows in a circular tube. Towards this end, the conservation equations are treated in cylindrical coordinates. The spatial discretization is based on a mixed spectral element/Fourier spectral scheme, with careful treatment of the singularity at the axis. For the temporal discretization, an efficient semi-implicit method is applied to the variable viscosity momentum equation. This approach results in a constant coefficient Helmholtz equation, which is solved by a fast diagonalization method. Numerical validation data are presented, and simulations are conducted for the three-dimensionally evolving instability resulting from an unstable density stratification in a vertical tube. Some preliminary comparisons with corresponding experiments are undertaken.     

One-Dimensional Turbulence: A new approach to high-fidelity subgrid closure of turbulent flow simulations

Consideration of the requirements for robust, high-fidelity subgrid closure of large-eddy simulations of multiphysics turbulent flows indicates the need for a spatially and temporally resolved representation of fine-scale physical and chemical processes that are coupled to fluid motion. One-Dimensional Turbulence (ODT), a potentially cost-effective approach for this purpose, captures these couplings by means of a stochastic simulation implemented on a one-dimensional domain. A subgrid implementation of ODT is formulated and its potential advantages and limitations are assessed.     

Global optimization and finite temperature simulations of atomic clusters: Use of XenArm clusters as test systems

The large potential energy barriers separating local minima on the potential energy surface of cluster systems pose serious problems for optimization and simulation methods. This article discusses algorithms for dealing with these problems. Lennard-Jones clusters are used to illustrate the important issues. In addition, the complexities in going from one-component to binary Lennard-Jones clusters are explored.     

Recent advances in 2+1-dimensional simulations of the pattern-forming Kuramoto–Sivashinsky equation

We present an overview of recent advances in numerical simulations of the 2+1-dimensional Kuramoto–Sivashinsky equation, describing the flame-front deformation in a combustion experiment. Algorithmic development includes a second-order unconditionally A-stable Crank–Nicolson scheme, using distributed approximating functionals (DAFs) for well-tempered, highly accurate, representation of the physical quantity and its derivatives. The simulator reproduces a multitude of patterns observed in experiments-in-the-wild, including rotating 2-cell, 3-cell, hopping 3-cell, stationary 2, 3, 4, 5-cell, stationary 5/1, 6/1, 7/1, 8/2 two-ring patterns, etc. The numerical observation of hopping flame patterns – characterized by non-uniform rotations of a ring of cells, in which individual cells make abrupt changes in their angular positions while they rotate around the ring – is the first outside of physical experiments. We show modal decomposition analysis of the simulated patterns, via the singular value decomposition (SVD), which exposes the spatio-temporal behavior in which the overall temporal dynamics is similar to that of equivalent experimental states. Symmetry-based arguments are used to derive normal form equations for the temporal behavior, and a bifurcation analysis of the associated normal form equations quantifies the complexity of hopping patterns. Conditions for their existence and their stability are also derived from the bifurcation analysis. Further, we study the effects of thermal noise in a stochastic formulation of the Kuramoto–Sivashinsky equation. Numerical integration reveals that the presence of noise increases the propensity of dynamic cellular states, which seems to explain the generic behavior of related laboratory experiments. Most importantly, we also report on observations of certain dynamic states, homoclinic intermittent states, previously only observed in physical experiments.     

Real-time approximation of molecular interaction interfaces based on hierarchical space decomposition

The interaction interface between two molecules can be represented as a bisector surface equidistant from the two sets of spheres of varying radii representing atoms. We recursively divide a box containing both sphere-sets into uniform pairs of sub-boxes. The distance from each new box to each sphere-set is conservatively approximated by an interval, and the number of sphere-box computations is greatly reduced by pre-partitioning each sphere-set using a kd-tree. The subdivision terminates at a specified resolution, creating a box partition (BP) tree. A piecewise linear approximation of the bisector surface is then obtained by traversing the leaves of the BP tree and connecting points equidistant from the sphere-sets. In 124 experiments with up to 16,728 spheres, a bisector surface with a resolution of 1/2⁴ of the original bounding box was obtained in 28.8 ms on average.