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Manuscript Title: Vectorized program of order N for molecular dynamics simulation of condensed matter. II. MDSLAB1: slab, short-range interactions.
Authors: Z.A. Rycerz, P.W.M. Jacobs
Program title: MDSLAB1
Catalogue identifier: ABTQ_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 62(1991)145
Programming language: Fortran.
Computer: ETA 10-P* 108.
Operating system: VSOS 2.1.6.
Word size: 64
Peripherals: disc.
Keywords: Solid state physics, Other, Condensed matter simulation, Vector processing.
Classification: 7.7.

Nature of problem:
Study of the thermodynamic, structural and dynamic properties of liquids or solids.

Solution method:
A system of N mutually interacting particles is simulated. The classical equations of motion are solved at successive time steps, at each of which the force acting upon each particle, due to its interaction with the other particles contained in the sphere of cut-off radius Rc, is calculated. Periodic Boundary Conditions (PBC) are applied to the system in order to make it pseudo-infinite. When the system reaches thermal equilibrium, thermodynamic measurements are made by averaging over time. The basic quantities which are (or, optionally, can be) calculated directly in the program are: average temperature, potential energy, kinetic energy, total energy, virial, internal pressure, radial distribution function, mean square displacement, diffusion coefficient and 4th moment of dynamic structure factor. Data such as coordinates, velocities and forces at successive time steps are saved for further analysis.

In the present program the simulation is restricted to monoatomic systems in which the particles interact by simple, central short-range forces. Because the cpu time depends linearly on the number of particles, there are no special restrictions on the size of the simulated system. Depending on available computer memory and computer speed, N may change from about 10**2 to 10**5 (10**6) particles. The program does not involve any instructions outside of standard Fortran 77 and does not use any specific routines (e.g. special calls on the ETA 10 that directly generate machine language instructions), so it can be easily applied on any vector computer. High speed storage required The core memory requirement depends on the number of particle in the system N and on the value of cut-off radius Rc and it can be expressed as: 23*N + 2*NNNmax*N + 60000 [words], where NNNmax is the maximum number of nearest neighbours (NN) which appear in the neigbours list. For example for liquid lead, the NNNmax is equal to 27 and 43, for Rc = 6.4 and 8.0 Angstrom, respectively.

Running time:
The speed (or cpu time) which seems to be most useful from the viewpoint of comparsion with another MD algorithms of order N, is that one which gives the number of calculated interactions per cpu sec (int/sec), since this speed is practically constant and does not depend on the kind of simulated substance, the size of the system (N), the value of Rc or the value of NTUPDA parameter which specifies how often the nearest neighbour list is updated. This speed for the SLAB1 program is around 1.5*10**6 [int/sec] on the ETA 10-P (or 0.68 musec/int), which means that for liquid lead with Rc = 6.4 Angstrom, where the average number of NN is around 30, it attains the speed 1500000/30 = 50000 particles per cpu sec ([p/sec]). The over-all program speed in this case is ca.35000 [p/sec] and thus, the cpu time for runs of 1000 time steps with N = 1000 and 54000 are equal roughly to 0.5 min and 30 min, respectively (for Rc = 6.4 Angstrom).