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 Effect of Short-range Repulsive Interactions on the Dynamics of the Methane Molecule

1993 ◽  
Vol 46 (2) ◽  
pp. 305
Author(s):  
MK Kansal ◽  
SK Trikha
Keyword(s):  
Short Range ◽  
Torsional Oscillation ◽  
Three Dimensional ◽  
Direction Cosine ◽  
Dynamical Behaviour ◽  
Methane Molecule ◽  
Repulsive Interaction ◽  
Lennard Jones ◽  
Nearest Neighbours ◽  
Before And After

Using a computer simulation technique, an attempt has been made to explain the A-type transition in the specific heat of solid methane at around 20 K in terms of the changes in the dynamical behaviour of the methane molecule under the influence of its nearest neighbours. Different exponents of the short-range repulsive interaction occurring in the expression for the potential energy have been tried in order to select the appropriate value. The well known Lennard-Jones (6-12) and (6-15) potentials are found to reveal a phase transition in a well defined region. From an analysis of the direction cosine data, the three-dimensional motion of the central methane molecule has been visualised before and after the transition. Pertaining to the Lennard-Jones potential, the period of the torsional oscillation (libration) of the methane molecule comes out to be of the order of 0�3xlO-12 s. From the computed critical rotational kinetic. energy, the transition temperature is found to be 20�2 K which agrees well with experimental observations.

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.

A new method of solving the Born-Green equation for the radial distribution function

1952 ◽  
Vol 210 (1103) ◽  
pp. 509-517 ◽  
Keyword(s):  
Distribution Function ◽  
Radial Distribution Function ◽  
Numerical Integration ◽  
Potential Function ◽  
Radial Distribution ◽  
Lennard Jones Potential ◽  
Jones Potential ◽  
Lennard Jones ◽  
Central Molecule ◽  
Close Range

A solution of the Born-Green equation for the radial distribution function may be found as a series in ascending powers of the density. This method is applied to a fluid of rigid spherical molecules, and the results are compared with those which Kirkwood, Maun & Alder obtained by means of numerical integration. For such molecules it is possible to show that the close-range structure at a distance between n and n + 1 diameters from a central molecule is of the order of the density raised to the n th power ( n integral). When the Lennard-Jones potential function is employed, the first and second approximations to the radial distribution function thus obtained are shown to be identical with those resulting from a rigorous development of this function in powers of the density.

scholarly journals The Three Phases of Solid Deuterated Methane

1994 ◽  
Vol 47 (1) ◽  
pp. 97
Author(s):  
MK Kansal ◽  
SK Trikha
Keyword(s):  
Dynamical Behaviour ◽  
Unit Cell ◽  
Nearest Neighbour ◽  
Jones Potential ◽  
Lennard Jones ◽  
Tetragonal Unit Cell ◽  
Tetrahedral Molecule ◽  
Lower Transition ◽  
Computer Simulation Technique ◽  
Three Phases

By using a computer simulation technique, the three phases of solid deuterated methane have been interpreted in terms of the changes in dynamical behaviour of the CD4 molecule located at the centre of a tetragonal unit cell having dimensions a = b = 5�872 A and c = 5�95 A. The central molecule is influenced by twelve nearest neighbour molecules situated at the mid-points of the sides of the unit cell. The rotational motion of the tetrahedral molecule is described by the appropriate algorithm equations, as well as by the well-known Lennard-Jones potential. The present calculations reveal two transition regions separating three distinct phases, which can be attributed to the two ,x-type transitions depicted by Clusius et al. (1937). Making use of the (dimensionless) average rotational kinetic energy corresponding to the lower transition region, (ERK)critical = 4�8, and the experimental libration frequency 6700 m-1 reported by Savoie and Fournier (1970), the transition temperature turns out to be 21�2 K, close to the experimentally observed value.

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).

The transition temperature in liquid helium

1957 ◽  
Vol 242 (1231) ◽  
pp. 544-557 ◽  
Keyword(s):  
Transition Temperature ◽  
Collective Excitations ◽  
Lennard Jones Potential ◽  
Jones Potential ◽  
Helium Atoms ◽  
Lennard Jones ◽  
Mass Approximation ◽  
Order Of Magnitude ◽  
The Individual ◽  
Bose Einstein

The partition function for an imperfect Bose-Einstein assembly of atoms is evaluated following Feynman’s method, as modified by Kikuchi. The ‘effective mass’ approximation is avoided, and instead a factor depending explicitly on interatomic forces is introduced. This factor is evaluated approximately for pairs of atoms interacting with a Lennard-Jones potential. The calculation involves only the properties of the individual helium atoms and disregards collective excitations. No adjustable parameters are used. A peak in the specific heat at 2-0°K is found (experimental, 2·2°K), and this transition temperature decreases with density. There is another transition at about 3·0°K which is probably a liquid-gas transition. If the interatomic forces are very weak one would only get this second transition; the λ transition does not occur at all unless the forces are of the order of magnitude of those actually found in helium.

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