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The radial distribution function is an important measure because several key thermodynamic properties, such as potential energy and pressure can be calculated from it. For a 3-D system where particles interact via pairwise potentials, the potential energy of the system can be calculated as follows: [ 6 ]
One common correlation function is the radial distribution function which is seen often in statistical mechanics and fluid mechanics. The correlation function can be calculated in exactly solvable models (one-dimensional Bose gas, spin chains, Hubbard model) by means of Quantum inverse scattering method and Bethe ansatz .
In statistical mechanics the hypernetted-chain equation is a closure relation to solve the Ornstein–Zernike equation which relates the direct correlation function to the total correlation function.
Radial functions are contrasted with spherical functions, and any descent function (e.g., continuous and rapidly decreasing) on Euclidean space can be decomposed into a series consisting of radial and spherical parts: the solid spherical harmonic expansion. A function is radial if and only if it is invariant under all rotations leaving the ...
Approximate solutions for the pair distribution function in the extensional and compressional sectors of shear flow and hence the angular-averaged radial distribution function can be obtained, as shown in Ref., [6] which are in good parameter-free agreement with numerical data up to packing fractions .
The Statistics Online Computational Resource (SOCR) [1] is an online multi-institutional research and education organization. SOCR designs, validates and broadly shares a suite of online tools for statistical computing, and interactive materials for hands-on learning and teaching concepts in data science, statistical analysis and probability theory.
The potential of mean force () is usually applied in the Boltzmann inversion method as a first guess for the effective pair interaction potential that ought to reproduce the correct radial distribution function in a mesoscopic simulation. [5]
In statistical mechanics the Ornstein–Zernike (OZ) equation is an integral equation introduced [1] by Leonard Ornstein and Frits Zernike that relates different correlation functions with each other.