A perturbation expression for the angular pair correlation function g (2)(r 12, ω1, ω2) is derived for systems interacting via non central potentials based on the method developed by Gubbins and Gray [1]. The method uses the ‘correct’ (in the sense of Rushbrooke [3] and Cook and Rowlinson [4]) angle-averaged potential as the reference system about which the perturbation is made. A preliminary comparison between the original Gubbins-Gray expression for g (2)(r 12, ω1, ω2) and the present expression is made for a system of two-dimensional point dipoles.

The effect of the spatial variation of the dielectric constant across the air/water and metal/water interfaces on the energy of an ion in those regions is considered. This extends the recent work of Clay, Goel and Buff in two ways. Firstly, a single dielectric profile of finite range is constructed, for which analytic calculation of image potentials is possible. These solutions have a much simpler mathematical structure than those obtained by Clay et al. Secondly, the effect of the adjacent diffuse layer on image potentials at the metal/water interface is investigated. In all cases the answers are consistent with previous multiple imaging calculations on discontinuous interfaces, without the divergences at boundaries predicted by these models.

A reformulation of the Ornstein-Zernike equation permits rapid and simple numerical calculation of the total correlation functions for single and multi-component systems of hard spheres. Such correlation functions permit the application of sophisticated statistical mechanical perturbation theories to more complicated systems than has been possible heretofore.

We have studied protein-ligand interactions by molecular dynamics simulations using software designed to exploit parallel computing architectures. The trajectories were analyzed to extract the essential motions and to estimate the individual contributions of fragments of the ligand to overall binding enthalpy. Two forms of the bound ligand are compared, one with the termini blocked by covalent derivatization, and one in the underivatized, zwitterionic form. The ends of the peptide tend to bind more loosely in the capped form. We can observe significant motions in the bound ligand and distinguish between motions of the peptide backbone and of the side chains. This could be useful in designing ligands, which fit optimally to the binding protein. We show that it is possible to determine the different contributions of each residue in a peptide to the enthalpy of binding. Proline is a major net contributor to binding enthalpy, in keeping with the known propensity for this family of proteins to bind proline-rich peptides.

RoBlock is the first phase of an internally financed project at the Institute aimed at building a system in which two industrial robots suspended from a gentry, as shown below, cooperate to perform a task specified by an external user, in this case, assembling an unstructured collection of coloured wooden blocks into a specified 3-dimensional pattern. The blocks are indentified and localised using computer vision and grasped with a suction cup mechanism.Future phases of the project will involve other processes such as grasping and lifting, as well as other types of robot such as autonomous vehicles or variable geometry trusses.Innovative features of the control software system include:The use of an advanced trajectory planning system which ensures collision avoidance based on a generalisation of the method of artificial potential fields [1],The use of a generic model-based controller which "learns" the values of parameters, including static and kinetic friction, of a detailed mechanical model of itself by comparing actual with planned movements [2],The use of fast, flexible, and robust pattern recognition and 3D-interpretation strategies,Integration of trajectory planning and control with the sensor systems in a distributed Java application running on a network of PC's attached to the individual physical components.In designing this first stage, the aim was to build in the minimum complexity necessary to make the system non-trivially autonomous and to minimize the technological risks.The aims of this project, which is planned to be operational during 2000, are as follows:To provide a platform for carrying out experimental research in multi-agent systems and autonomous manufacturing systems,To test the interdisciplinary cooperation architecture of the Maersk Institute, in which researchers in the fields of applied mathematics (modelling the physical world), software engineering (modelling the system) and sensor/actuator technology (relating the virtual and real worlds) could collaborate with systems integrators to construct intelligent, autonomous systemsTo provide a showpiece demonstrator in the entrance hall of the Institute's new building.

This article is meant as a contribution to the debate about the meaning and the prediction of emergent behaviour. By means of a number of examples, we show that reactive multi-agent systems have much in common with the statistical mechanical systems studied by physicists.The PHAMUS (PHysics-based Approaches to MUltiple computing Systems) model of an agent is an entity which possesses a number of internal states about which it can communicate with other agents. PHAMUS agents pass through a sequence of time frames, at each one being able to update their internal states as a result of interaction with other agents or with the external environment.By showing that societies of such agents are generalizations of statistical mechanical systems, we demonstrate the extreme difficulty of being able to reason about and to prove the collective behaviour of multi-agent systems from the only knowledge of the agents and their interactions. Simulation must be the main tool for assessing whether a particular agent design will lead to a multi-agent system capable of solving a particular application efficiently.This rather negative result is balanced by our promotion in this paper of a revisited methodology far studying reactive multi-agent systems that is close to the one used by physicists in statistical mechanics. Lu particular, and given our previous experience, this analogy suggests to us that the problem of simulating the behaviour of large collections of agents can be efficiently executed on multi-processor computing systems.

The constrained Lagrangian and constrained Hamiltonian equations of motion for a general non-relativistic classical mechanical system subject to rheonomous holonomic constraints are derived in an easy and straightforward manner.The numerical integration of the constrained equations of motion are discussed. It is shown how constraint errors introduced by the numerical integration can be avoided by introducing simple constraint correction schemes.As an example, the developed constrained methods are applied to the periodically driven inverted n-linked pendulum. It is demonstrated how the constrained methods leads to very efficient numerical algorithms. In the case of the n-linked pendulum, the computational complexity using the constrained methods is O(n) compared to O(n(3)) using the conventional unconstrained approach.

This paper reports the first phase of a project whose aim is the automatic generation of tool center trajectories for robots engaged in spray painting of arbitrary surfaces. The first phase consists of proposing a mathematical model for the paint flux field within the spray cone. We have called this quantity the paint flux field partly to emphasize that it is a vector field and partly to distinguish it from a paint flux distribution function, which describes the angular variation of the flux field within the spray cone. It is shown that this flux field can be derived from experimental measurements performed by robots, of coverage profiles of paint strips on flat plates by solving a singular integral equation. This flux field is derived both for published experimental data as well as two sets of data from experiments performed by the authors. The correctness of the model is demonstrated by using the underlying distribution function to predict coverage profiles for other experiments in which the spray gun is no longer vertical to the plane surface.

Consider molecular dynamics simulations of systems containing large molecules such as proteins, where all fast bond vibrations are frozen. An important part of the computational overhead then comes from solving a large set of linear equations for determining the bonded forces (constraint forces). The corresponding matrix is symmetric, positive definite and has a very sparse nature. in this article we compare efficient implementations of the Conjugate Gradient method and an improved version of Cholesky Factorization for solving such types of linear equations. Based on both theoretical predictions and practical simulation tests on three different proteins, we show that the improved Cholesky method is a factor 15 faster than the Conjugate Gradient method.

We present an efficient approach to reactive robot motion planning and collision avoidance. Unlike the traditional methods, there is no centralized control; instead the links and the joints of the robot are autonomous agents. This is a completely new approach. A set of dynamic equations of motion for an arbitrary robot is derived Artificial forces are introduced to express and combine multiple, possibly conflicting objectives, such as avoiding obstacles while approaching a goal. The joint agents impose forces of constraint between the link agents, and these forces establish a flow of information among the agents. The emergent behavior of the multiagent system gives an impression of surprisingly intelligent overall control. The developed method is used in actual industrial applications to control welding robot installations for ship building with up to II degrees of freedom (DOF). Experimental results from the simulation of a 25-DOF snakelike robot operating in a complex three-dimensional structure are given. It is demonstrated that the time complexity is O(n(3)) for branched n-DOF robots, while for serial robots such as standard manipulators and the snake, it is O(n).

The Greengard-Rokhlin algorithm is a new and interesting method for computing long-range interactions in particle systems. Although the method already has been implemented and claimed to be superior to traditional and other methods, no reliable estimates of the size of the error of the method have been given. We illustrate what the error actually is for the two-dimensional case, and derive an estimate for it. The estimate has a simple analytic form which will allow its use in tuning the algorithm for best efficiency.

The most efficient and proper standard method for simulating charged or dipolar systems is the Ewald method, which asymptotically scales as N-3/2 where N is the number of charges. However, recently the ''fast multipole method'' (FMM) which scales linearly with N has been developed. The break-even of the two methods (that is, the value of N below which Ewald is faster and above which FMM is faster) is very sensitive to the way the methods are optimized and implemented and to the required simulation accuracy.In this paper we use theoretical estimates and simulation results for the accuracies to carefully compare the two methods with respect to speed. We have developed and implemented highly efficient algorithms for both methods for a serial computer (a SPARCstation ELC) as well as a parallel computer (a T800 transputer based MEIKO computer). Breakevens in the range between N = 10000 and N = 30000 were found for reasonable values of the average accuracies found in our simulations. Furthermore, we illustrate how huge but rare single charge pair errors in the FMM inflate the error for some of the charges.

The fast multipole method (FMM) has become an important alternative to traditional methods such as the Ewald method for computing the long-range interactions necessary to simulate charged or dipolar systems. In this paper, we present an improvement of this method, which we shall call the very fast multipole method (VFMM). The VFMM is shown to be a factor of about 1.2 faster than the FMM for two-dimensional systems and a factor about 2–3 times faster for three-dimensional systems without losing any accuracy for the worst case error.

Monte Carlo simulations were performed on lattice gas systems with Coulombic interactions. Emphasis was placed on two lattice gases. The first consists of both mobile anions and cations while the second is composed of mobile anions and a random distribution of fixed cations. Comparisons are made to a strictly repulsive lattice gas. The addition of attractive forces is shown to significantly retard particle motion relative to the repulsive system. In the mobile-anion, mobile-cation system, at temperatures high enough to suppress ion clustering, the effect of backward correlations on the particle diffusivity is found to be similar to that for the strictly repulsive system. In the mobile-anion, fixed-cation system, however, backward correlations are much stronger due to the presence of immobile Coulomb traps. Both systems deviate from Nernst–Einstein behavior. The mobile-anion, mobile-cation system exhibits diminished conductivity (Haven ratio ≳1) due to the migration of neutral ion pairs, whereas the mobile-anion, fixed-cation system exhibits slightly enhanced conductivity (Haven ratio <1) due to the mutual repulsions between mobile charge carriers. The results of these simulations are discussed in terms of multiple timescale behavior, specifically including Funke’s jump relaxation model, and observations on relaxation times are reported.

Closed formulae for both real and reciprocal space parts of cutoff errors in the Ewald summation method in cubic periodic boundary conditions are derived. Such estimates are useful in tuning parameters in molecular simulations. Errors in both the electrostatic energy and forces are considered. The estimates apply to a disordered configuration of point charges and, with some limitations, also to point-charge molecular models. The accuracy of our estimates is tested and confirmed using simulated configurations of two systems (molten salt and diethylether) under a variety of conditions.

The implementation of a molecular dynamics simulation on a 10 transputer system is reported. The implementation exploits fully the geometric parallelism of the problem. A simple model of the computing and communications overheads leads to predictions of the optimal scaling of the problem size with the number of processors. The implementation exploits fully the domain decomposition paradigm in which load balancing is guaranteed by the compressibility theorem of statistical mechanics

We present the results of molecular dynamics simulations of the Stockmayer system in an external electric field. The dielectric properties of the system were investigated. We find that non-linear effects become important at smaller fields than previously thought. This may lead to estimates of the dielectric constant which are too low. We have also computed the dielectric function with applied field techniques and find this technique not more efficient than the usual fluctuation method.

We extend earlier work on implementing boxing algorithms for simulating very large systems of particles on massively parallel S.I.M.D. arrays to more modest ones. We report details and preliminary results obtained using an OCCAM 2 program running on a linear array of transputers.