scholarly journals Convergence of Coupling-Parameter Expansion-Based Solutions to Ornstein–Zernike Equation in Liquid State Theory

2021 ◽  
Vol 6 (3) ◽  
pp. 29
Author(s):  
S. V. G. Menon
Keyword(s):  
Vapor Phase ◽  
Liquid State ◽  
Coupling Parameter ◽  
State Theory ◽  
Lennard Jones Potential ◽  
Simulation Data ◽  
Jones Potential ◽  
Parameter Expansion ◽  
Lennard Jones ◽  
Liquid State Theory

The objective of this paper is to investigate the convergence of coupling-parameter expansion-based solutions to the Ornstein–Zernike equation in liquid state theory. The analytically solved Baxter’s adhesive hard sphere model is analyzed first by using coupling-parameter expansion. It was found that the expansion provides accurate approximations to solutions—including the liquid-vapor phase diagram—in most parts of the phase plane. However, it fails to converge in the region where the model has only complex solutions. Similar analysis and results are obtained using analytical solutions within the mean spherical approximation for the hardcore Yukawa potential. However, numerical results indicate that the expansion converges in all regions in this model. Next, the convergence of the expansion is analyzed for the Lennard-Jones potential by using an accurate density-dependent bridge function in the closure relation. Numerical results are presented which show convergence of correlation functions, compressibility versus density profiles, etc., in the single as well as two-phase regions. Computed liquid-vapor phase diagrams, using two independent schemes employing the converged profiles, compare excellently with simulation data. The results obtained for the generalized Lennard-Jones potential, with varying repulsive exponent, also compare well with the simulation data. Solution-spaces and the bifurcation of the solutions of the Ornstein–Zernike equation that are relevant to coupling-parameter expansion are also briefly discussed. All of these results taken together establish the coupling-parameter expansion as a practical tool for studying single component fluid phases modeled via general pair-potentials.

scholarly journals Convergence of coupling-parameter expansion-based solutions to Ornstein-Zernike equation in liquid state theory

2021 ◽  
Author(s):  
S. V. G. MENON
Keyword(s):  
Vapor Phase ◽  
Liquid State ◽  
Coupling Parameter ◽  
State Theory ◽  
Spherical Approximation ◽  
Hard Sphere Model ◽  
Simulation Data ◽  
Parameter Expansion ◽  
Liquid State Theory ◽  
Liquid Vapor

The objective of this paper is to investigate the convergence of coupling-parameter expansion-based solutions to Ornstein-Zernike equation in liquid state theory. The analytically solved Baxter's adhesive hard sphere model is analyzed first using coupling-parameter expansion. It is found that the expansion provides accurate approximations to solutions - including the liquid-vapor phase diagram - in most parts of the phase plane. However, it fails to converge in the region where the model has only complex solutions. Similar analysis and results are, then, obtained using analytical solutions within the mean spherical approximation for the hard-core Yukawa potential. Next, convergence of the expansion is analyzed for the Lennard-Jonnes potential using an accurate density-dependent bridge function in the closure relation. Numerical results are presented which show convergence of correlation functions, compressibility versus density profiles, etc., in the single as well as two phase regions. Computed liquid-vapor phase diagrams, using two independent schemes employing the converged profiles, compare excellently with simulation data. Results obtained for the generalized Lennard-Jonnes potential, with varying repulsive exponent, also compare well with simulation data. All these results together establish the coupling-parameter expansion as a practical tool for studying single component fluid phases modeled via general pair-potentials.

scholarly journals Inferring Single-Cell 3D Chromosomal Structures Based on the Lennard-Jones Potential

2021 ◽  
Vol 22 (11) ◽  
pp. 5914
Author(s):  
Mengsheng Zha ◽  
Nan Wang ◽  
Chaoyang Zhang ◽  
Zheng Wang
Keyword(s):  
Single Cell ◽  
Loss Function ◽  
Gaussian Function ◽  
Three Dimensional ◽  
Lennard Jones Potential ◽  
Jones Potential ◽  
Cubic Lattice ◽  
Lennard Jones ◽  
3D Fish ◽  
Well Depth

Reconstructing three-dimensional (3D) chromosomal structures based on single-cell Hi-C data is a challenging scientific problem due to the extreme sparseness of the single-cell Hi-C data. In this research, we used the Lennard-Jones potential to reconstruct both 500 kb and high-resolution 50 kb chromosomal structures based on single-cell Hi-C data. A chromosome was represented by a string of 500 kb or 50 kb DNA beads and put into a 3D cubic lattice for simulations. A 2D Gaussian function was used to impute the sparse single-cell Hi-C contact matrices. We designed a novel loss function based on the Lennard-Jones potential, in which the ε value, i.e., the well depth, was used to indicate how stable the binding of every pair of beads is. For the bead pairs that have single-cell Hi-C contacts and their neighboring bead pairs, the loss function assigns them stronger binding stability. The Metropolis–Hastings algorithm was used to try different locations for the DNA beads, and simulated annealing was used to optimize the loss function. We proved the correctness and validness of the reconstructed 3D structures by evaluating the models according to multiple criteria and comparing the models with 3D-FISH data.

Liquid‐state theory of the density dependent conformation of nonpolar linear polymers

1994 ◽  
Vol 100 (9) ◽  
pp. 6857-6872 ◽  
Author(s):  
Christopher J. Grayce ◽  
Arun Yethiraj ◽  
Kenneth S. Schweizer
Keyword(s):  
Liquid State ◽  
State Theory ◽  
Linear Polymers ◽  
Density Dependent ◽  
Liquid State Theory
Sign in / Sign up

Export Citation Format

Share Document