Local Self-Consistent Ornstein−Zernike Integral Equation Theory and Application to a Generalized Lennard-Jones Potential

2010 ◽  
Vol 114 (35) ◽  
pp. 11525-11534 ◽  
Author(s):  
Shiqi Zhou
Keyword(s):  
Integral Equation ◽  
Integral Equation Theory ◽  
Lennard Jones Potential ◽  
Jones Potential ◽  
Lennard Jones ◽  
Self Consistent

scholarly journals Wave propagation and Landau-type damping in liquids

Open Physics ◽  
2012 ◽  
Vol 10 (3) ◽  
Author(s):  
Vincenzo Molinari ◽  
Domiziano Mostacci
Keyword(s):  
Wave Propagation ◽  
Dispersion Relation ◽  
Intermolecular Forces ◽  
Landau Damping ◽  
Lennard Jones Potential ◽  
Jones Potential ◽  
Lennard Jones ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field

AbstractIntermolecular forces are modeled by means of a modified Lennard-Jones potential, introducing a distance of minimum approach, and the effect of intermolecular interactions is accounted for with a self consistent field of the Vlasov type. A Vlasov equation is then written and used to investigate the propagation of perturbations in a liquid. A dispersion relation is obtained and an effect of damping, analogous to what is known in plasmas as “Landau damping”, is found to take place.

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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