Analysis of an atomistic model for anti-plane fracture

We develop a model for an anti-plane crack defect posed on a square lattice under an interatomic pair-potential with nearest-neighbour interactions. In particular, we establish existence, local uniqueness and stability of solutions for small loading parameters and further prove qualitatively sharp far-field decay estimates. The latter requires establishing decay estimates for the corresponding lattice Green’s function, which are of independent interest.

Surface Tension Evaluation of Lennard-Jones Fluid System With Untruncated Potentials

In typical atomistic simulations of simple liquids, the Lennard-Jones interatomic pair potential is truncated so that algorithms scale as Natoms rather Natoms2, which would be the case if an interaction were computed explicitly for all atom pairs. However, it is known that interfacial properties are sensitive to the cutoff radius selected. Corrections for the missing ‘tails’ of the potential can reduce the error, but cannot eliminate it because the liquid and vapor densities are also sensitive to the cutoff radius. In light of this, we have developed and implemented a NlogN particle-particle particle-mesh (P3M) algorithm to evaluate the 1/r6 dispersive forces between Lennard-Jones fluid molecules without truncation. Statistical expression for the surface tension also scale as N2 if potentials are not truncated, so we also developed a P3M formulation for computing surface tension. The techniques are demonstrated on a thin liquid film suspended in equilibrium with its own vapor. Simulations at several temperatures between the triple point and the critical point are compared with the available data. The expense of the algorithm is competitive for simple geometries and seems preferable in non-trivial geometries without the possibility of tail corrections.

THERMOMECHANICAL PROPERTIES OF CERTAIN ELEMENTAL CRYSTALS

We have investigated the temperature variation of the Einstein temperatures and elastic constants of various metallic crystals. In this respect we have employed the interatomic pair potential involving pseudopotential and an appropriate exchange and correlation function. The temperature dependence of the properties concerned is taken into account through changes in the number densities. The systematic compilation of these thermomechanical properties may prove to be useful for various metallurgical purposes.