ON A CLASS OF EDGE-TRANSITIVE DISTANCE-REGULAR ANTIPODAL COVERS OF COMPLETE GRAPHS

The paper is devoted to the problem of classification of edge-transitive distance-regular antipodal covers of complete graphs. This extends the classification of those covers that are arc-transitive, which has been settled except for some tricky cases that remain to be considered, including the case of covers satisfying condition \(c_2=1\) (which means that every two vertices at distance 2 have exactly one common neighbour).Here it is shown that an edge-transitive distance-regular antipodal cover of a complete graph with \(c_2=1\) is either the second neighbourhood of a vertex in a Moore graph of valency 3 or 7, or a Mathon graph, or a half-transitive graph whose automorphism group induces an affine \(2\)-homogeneous group on the set of its fibres. Moreover, distance-regular antipodal covers of complete graphs with \(c_2=1\) that admit an automorphism group acting \(2\)-homogeneously on the set of fibres (which turns out to be an approximation of the property of edge-transitivity of such cover), are described. A well-known correspondence between distance-regular antipodal covers of complete graphs with \(c_2=1\) and geodetic graphs of diameter two that can be viewed as underlying graphs of certain Moore geometries, allows us to effectively restrict admissible automorphism groups of covers under consideration by combining Kantor's classification of involutory automorphisms of these geometries together with the classification of finite 2-homogeneous permutation groups.

Molecular Dynamics Simulation of Aluminium Thin Film Surface Activated Bonding

This study used molecular dynamics simulations with an embedded-atom method (EAM) potential to investigate the effect of surface roughness on the surface activated bonding (SAB) of aluminium thin films. The simulations started with the bonding process and followed by the tensile test for estimating bonding strength. By averaging the atomic stresses over the entire system, the stress-time curves for the bonded films under a tensile condition were predicted. Moreover, the evolution of the crystal structure in the local atomic order was examined by the common neighbour analysis. The simulated results show that the decrease in the surface roughness of thin film improves the bonding strength. The observed recrystallization processes inside the bonded thin films also reveal that the plastic deformation of the aluminium surface due to atomic attracting force compensates surface roughness.

Influences of Strain Rate on Copper Nanowire in Tension

This study uses molecular dynamics simulations with an embedded-atom method (EAM) potential to investigate the effects of strain rate on a copper wire in tension at the nanoscale. By averaging the atomic stresses over the entire system, the stress-strain curves for the nanowire were predicted. The results show that an elastic region clearly exists in the early deformation of the copper nanowire and the elastic modulus is about two times of the value measured at the macroscale. The yield stress of the nanowire increases with the strain rate. Moreover, the evolution of the crystal structure was investigated in terms of the radial distribution function and the local atomic order was also examined by the common neighbour analysis. The dislocations and recrystallization processes inside the nanowire have been observed. The simulated results reveal the process of the fracture of copper nanowire in tension.

Structural and Mechanical Properties of Nanophase Ni: A Molecular-Dynamics Study of the Influence of Grain-Boundary Structure on Elastic and Plastic Behavior

ABSTRACTMolecular dynamics computer simulations of high load plastic deformation at temperatures up to 500K of Ni nanophase samples with mean grain size of 5 nm are reported. Two types of samples are considered: a polycrystal nucleated from different seeds, each having random location and random orientation, representing a sample with mainly high angle grain boundaries, and polycrystals with seeds located at the same places as before, but with a limited missorientation representing samples with mainly low angle grain boundaries. The structure of the grain boundaries is studied by means of pair distribution functions, coordination number, atom energetics, and common neighbour analysis. Plastic behaviour is interpreted in terms of grain-boundary viscosity, controlled by a self diffusion mechanism at the disordered interface activated by thermal energy and stress.

There are 2ℵα Friendship Graphs of Cardinal ℵα

A friendship graph is a graph in which every two distinct vertices have exactly one common neighbour. Finite friendship graphs were characterized by Erdös, Rényi, and Sós [1] as those for which the vertices can be enumerated as u, υ1,…υk, w1,…wk in such a way that the only edges are uυiuwi and υiwi (i = 1,…,k). Thus finite friendship graphs are rather rare. In contrast, we shall show that there are as many nonisomorphic friendship graphs of given infinite cardinal as there are nonisomorphic graphs of that cardinal altogether. In fact, we do a little more.