Approach to approximating the pair distribution function of inhomogeneous hard-sphere fluids

Area of Science:

• Statistical Mechanics
• Computational Physics
• Fluid Dynamics

Background:

• The pair distribution function is crucial for understanding fluid properties.
• Previous methods for inhomogeneous hard sphere fluids were computationally intensive.
• Accurate calculation of the pair distribution function is essential for modeling complex systems.

Purpose of the Study:

• To introduce a computationally efficient approximation for the pair distribution function of inhomogeneous hard sphere fluids.
• To leverage recent advancements in averaged pair distribution functions at contact.
• To improve the speed of simulations involving hard sphere fluids.

Main Methods:

• Utilizing a recently developed averaged pair distribution function at contact.
• Implementing exclusively fixed-kernel convolutions.
• Employing fast Fourier transforms for computational acceleration.

Main Results:

• The proposed approximation accurately reproduces the averaged pair distribution function at contact for inhomogeneous densities.
• The method demonstrates favorable agreement with existing literature and Monte Carlo simulations.
• Achieved significant computational efficiency gains compared to previous approaches.

Conclusions:

• The new approximation offers a computationally efficient and accurate tool for studying inhomogeneous hard sphere fluids.
• This method can accelerate simulations in statistical mechanics and fluid dynamics.
• The approach validates the utility of averaged pair distribution functions at contact for complex fluid systems.