LETTER: Quantum Singularity of Quasiregular Spacetimes

Some of the mildest singularities in classical general relativity are shown to be singular quantum mechanically as well. A class of the mild, topological singularities known as quasiregular singularities remains singular when probed by quantum wave packets. These static spacetimes possessing dislocations and disclinations are quantum-mechanically singular since the spatial portion of the wave operator is not essentially self-adjoint and thus the evolution of a test quantum wave packet is not uniquely determined by the initial wave function.     

Structural Characteristics and Properties of a New Graphitic‐Based Material

The hydrogenation of commercial graphite using lithium/ammonia as the reducing agent and tert‐butyl alcohol as a proton source was investigated. Characterization of the products after successive reductions of the same material by high‐resolution transmission electron microscopy revealed a new material that was replete with edge and circular dislocations. Analysis by solid‐state ¹³C NMR spectroscopy indicates that after three reductions, the remaining aromatic rings appear to be interior benzene rings. NMR spectroscopy also offers strong evidence for the presence of small amounts of tert‐butyl alcohol and ethanol (workup solvent) that could not be removed in vacuo from the samples. These compounds could be observed to move freely between the layers of the hydrographene.     

A simple model for diffusion-induced dislocations during the lithiation of crystalline materials

Assuming that the lithiation reaction occurs randomly in individual small particles in the vicinity of the reaction front, a simple model of diffusion-induced dislocations was developed. The diffusion-induced dislocations are controlled by the misfit strain created by the diffusion of solute atoms or the phase transformation in the vicinity of the reaction front. The dislocation density is proportional to the total surface area of the “lithiated particle” and inversely proportional to the particle volume. The diffusion-induced dislocations relieve the diffusion-induced stresses.     

Theoretical study of the generation of screw dislocations for Rayleigh and Lamb waves in isotropic solids

Phase singularities are generic structures which occur in all wave fields, and they are characterised by an inability to assign a value to the phase. Screw dislocations are a particular kind of phase singularity where the phase possesses a helical structure, with the singularity at the centre of the helix. In this paper we show that it is possible to generate screw dislocations on the surface of elastic isotropic solids by means of the interference of three Rayleigh waves or three Lamb waves. The dispersive character of Lamb waves leads to more complicated behaviour, which may in turn result in greater potential for applications.     

On collinear microcrack–inclusion arrays interaction and related problems

Investigated is a crack problem for an array of collinear microcracks in composite matrix. Inclusions are situated in between the neighbouring microcracks tips and exhibit different elastic properties than matrix. The problem is solved using the technique of distributed dislocations. A developed approximate fundamental solution for a single dislocation lying in a general point between inclusions is employed in the distribution of continuously distributed dislocation to cracks modelling. Stress intensity factor is calculated for various cracks/inclusions geometries and elastic moduli mismatches. Stability and/or instability of the straight microcrack paths is investigated for slowly growing microcracks with inclusions located in between the neighbouring microcracks tips. Applications to periodic microcrack tunnelling and microcracks weakening ahead of the main crack are discussed.     

Dislocation Patterns and Work-Hardening in Crystalline Plasticity

We propose a continuum model for the evolution of the total dislocation densities in fcc crystals, in the framework of rate-independent plasticity. The basic physical features which are taken into account are: (i) the role of dislocations in hardening; (ii) the relations between the slip velocity and dislocation mobility; (iii) the energetics of self and mutual interactions between dislocations; (iv) nonlocal effects in the interaction between dislocations. A set of reaction–diffusion equations is obtained, with mobilities depending on the slip velocities, which is able to describe the formation of dislocation walls and cells. To this effect, the results of numerical simulations in two special cases are presented. Mathematics Subject Classifications (2000) 74C15, 74C20.     

Modelling of the internal stress in dislocation cell structures

The nonuniform distribution of dislocations in metals gives rise to material anisotropy and internal stresses that determine the mechanical response. This paper proposes a micromechanical model of a dislocation cell structure that accounts for the material inhomogeneity and incorporates the internal stresses in a physically-based manner. A composite model is employed to describe the material with its dislocation cell structure. The internal stress is obtained as a natural result of plastic deformation incompatibility and incorporated in the composite model. Applications of this model enable the prediction of the mechanical behavior of metals under various nonuniform deformations. The implementation of the model is relatively straightforward, allowing easy use in macroscopic engineering computations.     

How to identify dislocations in molecular dynamics simulations?

Dislocations are of great importance in revealing the underlying mechanisms of deformed solid crystals.With the development of computational facilities and technologies,the observations of dislocations at atomic level through numerical simulations are permitted.Molecular dynamics(MD)simulation suggests itself as a powerful tool for understanding and visualizing the creation of dislocations as well as the evolution of crystal defects.However,the numerical results from the large-scale MD simulations are not very illuminating by themselves and there exist various techniques for analyzing dislocations and the deformed crystal structures.Thus,it is a big challenge for the beginners in this community to choose a proper method to start their investigations.In this review,we summarized and discussed up to twelve existing structure characterization methods in MD simulations of deformed crystal solids.A comprehensive comparison was made between the advantages and disadvantages of these typical techniques.We also examined some of the recent advances in the dynamics of dislocations related to the hydraulic fracturing.It was found that the dislocation emission has a significant effect on the propagation and bifurcation of the crack tip in the hydraulic fracturing.     

Calculation of the Field of Internal Stresses for a Plane-Strained State of an Elastic Body with Dislocations

Results of numerical calculations of internal stresses in a material for the case of a plane strain are presented. The dependence of the stress distribution on the spatial structure of dislocations is demonstrated.