Theoretical analyses of interaction forces acting between solid surfaces considering one-dimensional periodic material distribution based on Lennard-Jones potential

2016 ◽  
Vol 2016 (0) ◽  
pp. J1610304
Author(s):  
Toshiki OTANI ◽  
Ryoya MIYAKE ◽  
Satoru MAEGAWA ◽  
Hiroshige MATSUOKA ◽  
Shigehisa FUKUI
Keyword(s):  
Solid Surfaces ◽  
Lennard Jones Potential ◽  
Material Distribution ◽  
Interaction Forces ◽  
Jones Potential ◽  
One Dimensional ◽  
Lennard Jones ◽  
Theoretical Analyses

Theoretical Analyses of Surface Interaction Stresses Considering Two-Dimensional Periodic Material Distributions

2017 ◽  
Author(s):  
Hiroshige Matsuoka ◽  
Ryoya Miyake ◽  
Satoru Maegawa ◽  
Shigehisa Fukui
Keyword(s):  
Half Space ◽  
Shear Stresses ◽  
Material Distribution ◽  
Two Dimensional ◽  
Jones Potential ◽  
Lennard Jones ◽  
Complex Fourier Series ◽  
Spatially Periodic ◽  
Basic Characteristics ◽  
Theoretical Analyses

The interaction stresses (pressure and shear stress) for (001) surface between a half-space consisting of a uniform material and a half-space with a spatially periodic material distribution have been derived based on the Lennard-Jones potential. The periodically distributed material property function is expanded as a complex Fourier series. The interaction pressures consist of non-fluctuation terms and fluctuation terms, while the shear stresses have only fluctuation terms. The interaction stresses for a distribution of two materials were then calculated as a typical example of a periodic material distribution. The basic characteristics of the interaction stresses are clarified.

Theoretical Study of Surface Interaction Stresses Considering One-Dimensional Material Distributions in the In-Plane Direction Based on the Lennard-Jones Potential

2016 ◽  
Author(s):  
Hiroshige Matsuoka ◽  
Teppei Tanaka ◽  
Ryoya Miyake ◽  
Shigehisa Fukui
Keyword(s):  
Half Space ◽  
Material Distribution ◽  
Elementary Functions ◽  
Jones Potential ◽  
One Dimensional ◽  
Single Interface ◽  
Periodic Distribution ◽  
Lennard Jones ◽  
Plane Direction ◽  
Basic Characteristics

The interaction stresses acting between a half-space consisting of a uniform material and a half-space with a one-dimensional material distribution in the in-plane direction have been derived. Two patterns of the material distribution are considered: a periodic distribution of materials (Pattern 1) and a distribution of two materials with a single interface (Pattern 2). The interaction stresses for Pattern 1 were derived using a Fourier series, while the interaction stresses for Pattern 2 were derived as elementary functions. The basic characteristics of these interaction stresses were clarified.

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.

Sign in / Sign up

Export Citation Format

Share Document