Reconstructing three-dimensional (3D) chromosomal structures based on single-cell Hi-C data is a challenging scientific problem due to the extreme sparseness of data. In this research, we used Lennard-Jones potential reconstruct both 500 kb and high-resolution 50 A chromosome was represented by string or DNA beads put into 3D cubic lattice for simulations. 2D Gaussian function impute sparse con...

The analogue of the hydrophobic hydration is explored for Lennard-Jones solutions. The free energy of solvation and its temperature derivatives, both in the constant-pressure process and in the constant-volume process, are obtained numerically for a variety of the size and energy parameters for the solute-solvent Lennard-Jones potential. We identify in the parameter space a region in which the ...

Using extensive molecular dynamics simulations, we have investigated the extensivity of the internal energy and entropy as well as the intensivity of temperature and pressure in small thermodynamic systems. Atomic systems consisting of n3 n = 2 3 10 argon-like particles interacting through the Lennard-Jones potential energy function have been studied. It is found that in small systems, contrary...

For the Sturm-Liouville operator L =L,: .VP+ -p” +pv one seeks to reconstruct the coefficient p from knowledge of the sequence of eigen-frequencies (Aj with LJ? =Ajn for some y j # 0). An implementable scheme is: for some N determine pnr so (approximately) pN has minimum norm with eigen-frequencies { A , . . . . .IN/ as given. This is the method ot’ ’generalised interpolation‘ and is shown to g...

This work represents an extended computational study of the Fermi-Pasta-Ulam experiment for the dynamical nature of energy transfer among normal modes. A 2D lattice system with 40 particles is placed on a torus, where each particle is allowed to interact with its six nearest neighbors under the Lennard-Jones potential force law. Trajectories of the particles are analyzed through a Fourier trans...

In Chapter 5 we demonstrated that in the case of the Lennard-Jones fluid, the viscosity, pressure and energy exponents are not fixed values. They depend on state point, namely, the temperature and density. We gave the results of simulations for the exponents varying with temperature and density, and we also found that the relationship can be expressed easily by a linear function of both tempera...

We consider the low-density equation of state of a fluid along its critical isotherm. An asymptotically consistent approximant is formed having the correct leading-order scaling behavior near the vapor-liquid critical point, while retaining correct low-density behavior as expressed by the virial equation of state. The formulation is demonstrated for the Lennard-Jones fluid, and models for heliu...