Three-Dimensional Generalized Graph Matrix, Harary Descriptors, and a Generalized Interatomic Lennard-Jones Potential

2004 ◽  
Vol 108 (25) ◽  
pp. 5468-5473 ◽  
Author(s):  
Ernesto Estrada
Keyword(s):  
Three Dimensional ◽  
Lennard Jones Potential ◽  
Jones Potential ◽  
Lennard Jones

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.

scholarly journals Molecular Dynamics of the Phase Transition in Solid Deuterated Methane

1993 ◽  
Vol 46 (4) ◽  
pp. 523 ◽  
Author(s):  
MK Kansal ◽  
SK Trikha
Keyword(s):  
Transition Temperature ◽  
Three Dimensional ◽  
Direction Cosine ◽  
Dynamical Behaviour ◽  
Methane Molecule ◽  
Lennard Jones Potential ◽  
Jones Potential ◽  
Lennard Jones ◽  
Central Molecule ◽  
Tetrahedral Molecule

The rotational dynamics of a single deuterated methane molecule in the presence of its twelve nearest neighbours has been studied by using a computer simulation technique. The three-dimensional motion of the tetrahedral molecule is described by the appropriate algorithm equations, as well as by the well known Lennard-Jones potential. The importance of the inverse-twelfth-power repulsive potential for the dynamics of the deuterated methane molecule is also highlighted. The second-nearest neighbour interactions contribute only 7% to the potential energy of the whole system and this hardly affects the dynamics of the central molecule. A detailed analysis of the direction cosine data reveals a change in the dynamical behaviour of the molecule around the transition temperature, which could be attributed to the singularity observed in the specific heat data. Corresponding to the Lennard-Jones potential, the period of oscillation of the central molecule comes out to be 0�38xlO-12 s. Making use of the (dimensionless) average rotational kinetic energy at the transition, (ERK)critical = 6�3, and the period, the transition temperature is found to be 27�7 K, which is in quite good agreement with one of the ..\-type transition temperatures reported by Clusius et al.

scholarly journals Rotational Motion of the NH+4 Ion in Ammonium Chloride

1984 ◽  
Vol 37 (2) ◽  
pp. 197
Author(s):  
Sadhana Pandey ◽  
SK Trikha
Keyword(s):  
Computer Simulation ◽  
Rotational Motion ◽  
Three Dimensional ◽  
Rotational Dynamics ◽  
Ammonium Ion ◽  
Lennard Jones Potential ◽  
Jones Potential ◽  
Lennard Jones ◽  
Nearest Neighbours ◽  
Computer Simulation Technique

The rotational motion of the ammonium ion in NH4CI at low temperature under the influence of its nearest neighbours has been studied using a computer simulation technique. The Lennard Jones potential is used as the representative interaction between NHt and CI-. Three values of the time increment At occurring in the algorithm equation are taken to illustrate the three-dimensional effect on the rotational dynamics of the NH: ion. In each case we notice a well defined transition gap around = 1�25 separating phases II and III which are known from the literature. The libration frequency of the ammonium ion is found to be 1"0; 170 em-1, corresponding to the transition temperature of 242 K, which is in agreement with the Raman spectra study by Couzi et af. (1973).

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