The mechanical properties of perfect crystals II. The stability and mode of fracture of highly stressed ideal crystals

1972 ◽  
Vol 330 (1582) ◽  
pp. 309-317 ◽  
Keyword(s):  
Sodium Chloride ◽  
Strain Curve ◽  
Lennard Jones Potential ◽  
Stability Criteria ◽  
Stress Strain Curve ◽  
Jones Potential ◽  
Lennard Jones ◽  
The Stability ◽  
Highly Strained ◽  
The Ideal

The Born stability criteria are applied to variously elastically deformed perfect crystals of argon, represented by a Lennard-Jones potential, and sodium chloride, represented by a Born-Mayer potential. It is shown that when highly strained in tension argon and sodium chloride crystals become unstable before the maximum in the ideal stress-strain curve is reached. The consequent reductions in our previous estimates of the ideal tensile strength (part I) are small (< 10 %) except for unconstrained tension of argon (20 %).

Planar Defects on (112) in BCC Crystals

2007 ◽  
Vol 567-568 ◽  
pp. 69-72 ◽  
Author(s):  
Andriy Ostapovets ◽  
Václav Paidar
Keyword(s):  
Crystal Lattice ◽  
Crystal Structures ◽  
Stacking Faults ◽  
Lattice Stability ◽  
Lennard Jones Potential ◽  
Many Body ◽  
Planar Defects ◽  
Jones Potential ◽  
Lennard Jones ◽  
The Stability

The parameters of exponential many-body Finnis-Sinclair potentials corresponding to qualitatively different crystal lattice stability were selected and their behaviour was studied. Furthermore, a model with pairwise Lennard-Jones potential was also considered. The attention was paid to the stability of different crystal structures and the properties of simple interfaces such as stacking faults and twin boundaries were investigated.

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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