| Summary: | <p>We use the Potential Distribution Theorem to evaluate distribution functions from equilibrium configurations using test-particle insertion. We use this methodology to determine the contact value of the pair distribution function in hard-disk systems: in contrast with the conventional distance-histogram method, the insertion measurement is exact and does not require an approximate extrapolation. The resulting equations of state in both simulations and a hard-disk colloidal model system agree well with the predictions of Scaled Particle Theory. We also provide the first experimental measurement of the cavity distribution function y<sup>(2)</sup>(r) inside the hard core.</p>
<p>We next develop a model-free technique for measuring the pair potential u<sup>(2)</sup>(r) in pairwise-additive fluids, by matching the insertion and distance-histogram measurements of g<sup>(2)</sup>(r) using an iterative predictor-corrector scheme. We test the method extensively in simulation, before applying it successfully in a fluid of superparamagnetic colloidal particles, obtaining the anticipated form of u<sup>(2)</sup>(r) and the correct dependence on the applied magnetic field. We then extend the scheme to measure the full set of pair potentials in multicomponent fluids, demonstrating its efficacy in a three-component simulation.</p>
<p>We show that a given n-body distribution function g<sup>(n)</sup> (n>2) can be measured using n different insertion routes, which correspond to simultaneous insertion of between 1 and n test particles. We use these methods to measure g<sup>(3)</sup> in simulation: while the noise depends strongly on the number of simultaneous insertions, the resolution is superior to that of the distance-histogram method. Finally, we consider systems with three-body interactions. We show that matching g<sup>(2)</sup>(r) alone gives an effective pair potential which is unable to reproduce g<sup>(3)</sup> in pairwise-additive simulations. We therefore extend the predictor-corrector scheme to measure the three-body interaction u<sup>(3)</sup> by matching g<sup>(3)</sup>, and test it in simulation. The scheme broadly recovers the correct u<sup>(3)</sup>, but requires further development to reduce the noise.</p>
|
|---|