Dynamical Recovery of Complex Networks under a Localised Attack

In real systems, some damaged nodes can spontaneously become active again when recovered from themselves or their active neighbours. However, the spontaneous dynamical recovery of complex networks that suffer a local failure has not yet been taken into consideration. To model this recovery process, we develop a framework to study the resilience behaviours of the network under a localised attack (LA). Since the nodes’ state within the network affects the subsequent dynamic evolution, we study the dynamic behaviours of local failure propagation and node recoveries based on this memory characteristic. It can be found that the fraction of active nodes switches back and forth between high network activity and low network activity, which leads to the spontaneous emergence of phase-flipping phenomena. These behaviours can be found in a random regular network, Erdős-Rényi network and Scale-free network, which shows that these three types of networks have the same or different resilience behaviours under an LA and random attack. These results will be helpful for studying the spontaneous recovery real systems under an LA. Our work provides insight into understanding the recovery process and a protection strategy of various complex systems from the perspective of damaged memory.

HPT-Deformation of Copper and Nickel Single Crystals

Copper and nickel single crystals of high purity with a crystallographic orientation, (001) and (111) respectively, were deformed by applying high pressure torsion (HPT) at room temperature. Special interest was devoted to the structural evolution of the material, which was characterized by electron backscatter diffraction (EBSD) and X-ray texture analysis as well. In addition back scatter electron investigations were applied to characterize shape and size of the new formed structure. Furthermore the study is focused on the micro structural and micro textural evolution that lead to the increase of missorientation angle with increasing plastic deformation. We observed an increasing fragmentation of the structure with increasing plastic equivalent strain up to a level where the grain size is saturated. The saturation could be traced back to dynamical recovery and recrystallisation during the deformation process that is depending on the purity of the material.

A Statistical Mechanics Theory of Grain Deformation and Its Prediction of Dynamical Recovery and Recrystallization

A novel statistical mechanics approach to quantify the effects of hot rolling and deformation on the formation of dislocations in a single grain scenario is presented. The dislocations are dealt as equilibrium defects in the crystal structure, which is assumed to be deformed via the formation of dislocations or single atom displacements at the grain boundary, which involve breaking their bonds and are thus termed “bond breaking atoms”. The deformation process is applied to steels of a variety of grain size and dislocations densities. The model has the capacity to describe the grain energy increase as a function of crystallography, grain sizes, temperature and degree of deformation, providing thus an aid in predicting the conditions for dynamic recovery and recrystallization.