scholarly journals Binary scattering model for Lennard-Jones potential: Transport coefficients and collision integrals for non-equilibrium gas flow simulations

2012 ◽  
Vol 24 (2) ◽  
pp. 027101 ◽  
Author(s):  
Ayyaswamy Venkattraman ◽  
Alina A. Alexeenko
Keyword(s):  
Gas Flow ◽  
Transport Coefficients ◽  
Lennard Jones Potential ◽  
Collision Integrals ◽  
Jones Potential ◽  
Scattering Model ◽  
Flow Simulations ◽  
Lennard Jones ◽  
Non Equilibrium

scholarly journals High-Temperature Collision Integrals for m-6-8 and Hulburt–Hirschfelder Potentials

2022 ◽  
Vol 43 (3) ◽  
Author(s):  
Marcin Buchowiecki
Keyword(s):  
High Temperature ◽  
Electronic State ◽  
Ground Electronic State ◽  
Quality Data ◽  
Lennard Jones Potential ◽  
High Quality ◽  
Collision Integrals ◽  
High Quality Data ◽  
Jones Potential ◽  
Lennard Jones

AbstractThis study is aimed to determine collision integrals for atoms interacting according to the m-6-8 and Hulburt–Hirschfelder potentials and analyze the differences between potentials. The precision of four significant digits was reached at all tested temperatures, and for high-temperature applications, six digits were calculated. The proposed method was tested on the Lennard-Jones potential and found to excellently agree with the recent high-quality data. In addition, the Hulburt–Hirschfelder potential was used for determining the collision integrals of the interaction of nitrogen atoms in the ground electronic state and compared with other known values. The calculations were performed using Mathematica computation system which can deal with singularities (so-called orbiting).

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.

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