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The definitions of breaks and clusters in a one-dimensional chain in equilibrium are discussed. Analytical expressions are obtained for the expected cluster length, $langle K rangle$, as a function of temperature and pressure in a one-dimensional Lennard-Jones chain. These expressions are compared with results from molecular dynamics simulations. It is found that $langle K rangle$ increases exponentially with $beta = 1/k_BT$ and with pressure, $P$ in agreement with previous results in the literature. A method is illustrated for using $langle K rangle (beta, P)$ to generate a phase diagram for the Lennard-Jones chain. Some implications for the study of heat transport in Lennard-Jones chains are discussed.
The phase diagram of the prototypical two-dimensional Lennard-Jones system, while extensively investigated, is still debated. In particular, there are controversial results in the literature as concern the existence of the hexatic phase and the melti
The homogeneous and heterogeneous nucleation of a Lennard-Jones liquid is investigated using the umbrella sampling method. The free energy cost of forming a nucleating droplet is determined as a function of the quench depth, and the saddle point natu
We numerically investigated the connection between isobaric fragility and the properties of high-order stationary points of the potential energy surface in different supercooled Lennard-Jones mixtures. The increase of effective activation energies up
Efficient implementations of the classical molecular dynamics (MD) method for Lennard-Jones particle systems are considered. Not only general algorithms but also techniques that are efficient for some specific CPU architectures are also explained. A
We present a systematic study of the thermodynamics of two and three-dimensional generalized Lennard-Jones ($LJ$) systems focusing on the relationship between the range of the potential, the system density and its dimension. We found that the existen