scholarly journals APPLICATION OF THE LENNARD-JONES POTENTIAL IN MODELLING ROBOT MOTION

2019 ◽  
Vol 9 (4) ◽  
pp. 14-17
Author(s):  
Piotr Wójcicki ◽  
Tomasz Zientarski
Keyword(s):  
Interaction Strength ◽  
Robot Motion ◽  
Lennard Jones Potential ◽  
Ordered Group ◽  
Jones Potential ◽  
Lennard Jones ◽  
Optimal Value ◽  
Potential Impact ◽  
Moving Groups ◽  
Dynamics Simulations

The article proposes a method of controlling the movement of a group of robots with a model used to describe the interatomic interactions. Molecular dynamics simulations were carried out in a system consisting of a moving groups of robots and fixed obstacles. Both the obstacles and the group of robots consisted of uniform spherical objects. Interactions between the objects are described using the Lennard-Jones potential. During the simulation, an ordered group of robots was released at a constant initial velocity towards the obstacles. The objects’ mutual behaviour was modelled only by changing the value of the interaction strength of the potential. The computer simulations showed that it is possible to find the optimal value of the potential impact parameters that enable the implementation of the assumed robotic behaviour scenarios. Three possible variants of behaviour were obtained: stopping, dispersing and avoiding an obstacle by a group of robots.

MASS DISTRIBUTION OF A TWO-DIMENSIONAL FRAGMENTATION PROCESS

2005 ◽  
Vol 16 (02) ◽  
pp. 253-258 ◽  
Author(s):  
L. E. ARARIPE ◽  
A. DIEHL ◽  
J. S. ANDRADE ◽  
R. N. COSTA FILHO
Keyword(s):  
Mass Distribution ◽  
Radial Component ◽  
Fragmentation Process ◽  
Lennard Jones Potential ◽  
Two Dimensional ◽  
Jones Potential ◽  
Lennard Jones ◽  
Mass Size ◽  
Dynamics Simulations ◽  
Number Of Particles

We perform extensive molecular dynamics simulations to study the mass size distribution of a two-dimensional fragmentation process. Our model consists of a large number of particles interacting through the Lennard–Jones potential. The fragmentation is induced by suddenly imposing a radial component on the particles' velocities, in order to mimic an explosion phenomenon. We then investigate the effect of the input energy on the resulting mass distribution of fragments.

scholarly journals Data driven inference for the repulsive exponent of the Lennard-Jones potential in molecular dynamics simulations

2017 ◽  
Vol 7 (1) ◽  
Author(s):  
Lina Kulakova ◽  
Georgios Arampatzis ◽  
Panagiotis Angelikopoulos ◽  
Panagiotis Hadjidoukas ◽  
Costas Papadimitriou ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Molecular Dynamics Simulations ◽  
Data Driven ◽  
Lennard Jones Potential ◽  
Jones Potential ◽  
Lennard Jones ◽  
Dynamics Simulations

scholarly journals Modeling Interactions between Graphene and Heterogeneous Molecules

Computation ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 107
Author(s):  
Kyle Stevens ◽  
Thien Tran-Duc ◽  
Ngamta Thamwattana ◽  
James M. Hill
Keyword(s):  
Molecular Dynamics ◽  
Molecular Dynamics Simulations ◽  
Continuous Model ◽  
Atomic Density ◽  
Lennard Jones Potential ◽  
Jones Potential ◽  
New Model ◽  
Lennard Jones ◽  
Continuous Surface ◽  
Dynamics Simulations

The Lennard–Jones potential and a continuum approach can be used to successfully model interactions between various regular shaped molecules and nanostructures. For single atomic species molecules, the interaction can be approximated by assuming a uniform distribution of atoms over surfaces or volumes, which gives rise to a constant atomic density either over or throughout the molecule. However, for heterogeneous molecules, which comprise more than one type of atoms, the situation is more complicated. Thus far, two extended modeling approaches have been considered for heterogeneous molecules, namely a multi-surface semi-continuous model and a fully continuous model with average smearing of atomic contribution. In this paper, we propose yet another modeling approach using a single continuous surface, but replacing the atomic density and attractive and repulsive constants in the Lennard–Jones potential with functions, which depend on the heterogeneity across the molecules, and the new model is applied to study the adsorption of coronene onto a graphene sheet. Comparison of results is made between the new model and two other existing approaches as well as molecular dynamics simulations performed using the LAMMPS molecular dynamics simulator. We find that the new approach is superior to the other continuum models and provides excellent agreement with molecular dynamics simulations.

scholarly journals Effect of Impurities on a Two-Dimensional Dodecagonal Quasicrystal

2021 ◽  
Author(s):  
Masahiro Fuwa ◽  
Masahide Sato
Keyword(s):  
Interaction Potential ◽  
Rotational Symmetry ◽  
Lennard Jones Potential ◽  
Two Dimensional ◽  
Jones Potential ◽  
Lennard Jones ◽  
Impurity Density ◽  
Effect Of Impurities ◽  
Potential Matrix ◽  
Dynamics Simulations

Abstract Langevin dynamics simulations are performed to examine how impurities affect two-dimensional dodecagonal quasicrystals. We assumed that the interaction potential between two particles is the Lennard-Jones-Gauss potential if at least one of these particles is a matrix particle and that the interaction potential between two impurities is the Lennard-Jones potential. Matrix particles and impurities impinge with constant rates on the substrate created by a part of a dodecagonal quasicrystal consisting of square and triangular tiles. The dependences of the twelve-fold rotational order and the number of shield-like tiles on the impurity density are examined after sufficient solid layers are grown. While the change in the twelve-fold rotational symmetry is small, the number of shield-like tiles in the solid increases greatly with increasing impurity density.

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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