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In this work, we simulate mechanical properties of pseudo-graphene crystals G5-7v1, G5-6-7v2, G4-8v1, G5-6-8v2, G5-6-8v4, G5-8v1, which include dense networks of wedge disclinations of alternate signs. The crystals were studied using the molecular dynamics method. The paper compares the values of elastic properties of graphene and pseudo-graphene obtained through AIREBO, Tersoff, and LCBOP interatomic interaction potentials. It shows that the application of these potentials in modeling pseudographene crystals is limited. The study concludes that it is necessary to update the existing potentials of interatomic interaction in allotropes of carbon or create a new one.

Focusing on the two-dimensional (2D) Su-Schrieffer-Heeger (SSH) model, we propose an additive rule between the real-space topological invariant s of disclinations (related to the Burgers vector B) and the reciprocal-space topological invariant p of bulk wave functions (the vectored Zak phase). The disclination-induced bound states in the 2D SSH model appear only if (s + p/2π) is nonzero modulo the lattice constant. These disclination-bound states are robust against perturbations respecting C4 point group symmetry and other perturbations within an amplitude determined by p. Besides the disclination-bound states, the proposed additive rule also suggests that a half-bound state extends over only half of a sample and a hybrid-bound state, which always have a nonvanishing component of s + p/2π.

The review describes general principles and characteristics of inhomogeneously polarized paraxial optical fields and, especially, the polarization singularities (PSs). Main parameters of the optical vector waves are discussed, with the emphasis on the physical relevance and topological distinctiveness of the PSs. Special features of the stochastic vector fields are considered in the context of the PSs’ genericity and structural stability. A detailed attention is paid to interrelations between the PSs and the phase singularities of scalar fields formed by the orthogonal polarization projections of the total field, and their derivatives (complex Stokes fields, phase-difference fields, etc.). On this base, the practical approaches are discussed for the experimental PS identification and characterization. A particular examination of the internal energy flows associated with the PSs, and accompanying distributions of the optical momentum and angular momentum, reveals meaningful dynamical features of PSs and supplies additional physically transparent and informative means for their studies and characterization.

This article is the third in our series dedicated to the analysis of cardiac myoarchitecture as a nematic chiral liquid crystal (NCLC). Previously, we introduced the concept of topological defects (disclinations) and focused on their visual identification inside the compact myocardium. Herein, we investigate these using a mathematical and automated algorithm for the reproducible identification of a larger panel of topological defects throughout the myocardium of 13 perinatal and 11 early infant hearts. This algorithm identified an average of 29 ± 11 topological defects per slice with a 2D topological charge of m = +1/2 and an average of 27 ± 10 topological defects per slice with a 2D topological charge of m = −1/2. The excess of defects per slice with a 2D topological charge of m = +1/2 was statistically significant (p < 0.001). There was no significant difference in the distribution of defects with a 2D topological charge of m = +1/2 and m = −1/2 between perinatal and early infant hearts. These defects were mostly arranged in pairs, as expected in nematics, and located inside the trabecular myocardium. When isolated, defects with a 2D topological charge of m = +1/2 were located near the luminal extremity of the trabeculae and those with a 2D topological charge of m = −1/2 were located at the anterior and posterior part of the interventricular septum. These findings constitute an advance in the characterization of the deep cardiac myoarchitecture for application in developmental and pathological studies.

This is our second article devoted to the cardiac myoarchitecture considered as a nematic chiral liquid crystal (NCLC). While the first article focused on the myoarchitecture of the left ventricle (LV), this new article extends to the whole ventricular mass and introduces the concept of disclinations and topological singularities, which characterize the differences and relationships between the left and right ventricles (RV). At the level of the ventricular apices, we constantly observed a vortex shape at the LV apex, corresponding, in the terminology of liquid crystals, to a “+1 disclination”; we never observed this at the RV apex. At the level of the interventricular septum (IVS), we identified “−1/2 disclinations” at the anterior and posterior parts. During the perinatal period, there was a significant difference in their distribution, with more “−1/2 disclinations” in the posterior part of the IVS. After birth, concomitant to major physiological changes, the number of “−1/2 disclinations” significantly decreased, both in the anterior and posterior parts of the IVS. Finally, the description of the disclinations must be considered in any attempt to segment the whole ventricular mass, in biomechanical studies, and, more generally, for the characterization of myocardial remodeling.

A bidimensional (2D) thermotropic liquid crystal (LC) is investigated with Molecular Dynamics (MD) simulations. The Gay-Berne mesogen with parameterization GB(3, 5, 2, 1) is used to model a calamitic system. Spatial orientation of the LC samples is probed with the nematic order parameter: a sharp isotropic-smectic (I-Sm) transition is observed at lower pressures. At higher pressures, the I-Sm transition involves an intermediate nematic phase. Topology of the orthobaric phase diagram for the 2D case differs from the 3D case in two important respects: 1) the nematic region appears at lower temperatures and slightly lower densities, and 2) the critical point occurs at lower temperature and slightly higher density. The 2D calamitic model is used to probe the structural behavior of LC samples under strong confinement when either planar or homeotropic anchoring prevails. Samples subjected to circular, square, and triangular boundaries are gradually cooled to study how orientational order emerges. Depending on anchoring mode and confining geometry, characteristic topological defects emerge. Textures in these systems are similar to those observed in experiments and simulations of lyotropic LCs.

Evaluation of impact characteristics of carbon nanomaterials is very important and helpful for their application in nanoelectromechanical systems (NEMS). Furthermore, disclination lattice defects can generate out-of-plane deformation to control the mechanical behavior of carbon nanomaterials. In this study, we design novel stable wavy graphene sheets (GSs) using a technique based on origami and kirigami to control the exchange of carbon atoms and generate appropriate disclinations. The impact characteristics of these GSs are evaluated using molecular dynamics (MD) simulation, and the accuracy of the simulation results is verified via a theoretical analysis based on continuum mechanics. In the impact tests, the C60 fullerene is employed as an impactor, and the effects of the different shapes of wavy GSs with different disclinations, different impact sites on the curved surface, and different impact velocities are examined to investigate the impact characteristics of the wavy GSs. We find that the newly designed wavy GSs increasingly resist the kinetic energy (KE) of the impactor as the disclination density is increased, and the estimated KE propagation patterns are significantly different from those of the ideal GS. Based on their enhanced performance in the impact tests, the wavy GSs possess excellent impact behavior, which should facilitate their potential application as high-impact-resistant components in advanced NEMS.

The atomic structure of medium-range order in metallic glasses is investigated by using molecular dynamics (MD) simulations. Glass formation processes were simulated by rapid cooling from liquid phases of a model binary alloy system of different-sized elements. Two types of short-range order of atomic clusters with the five-fold symmetry are found in glassy phases: icosahedral clusters (I-clusters) formed around the smaller-sized atoms and Frank–Kasper clusters (i.e., Z14, Z15, and Z16 clusters (Z-clusters)) formed around the bigger-sized atoms. Both types of clusters (I-and Z-clusters) are observed even in liquid phases and the population of them goes up as the temperature goes down. A considerable atomic size difference between alloying elements would enhance the formation of both the I- and Z-clusters. In glassy phases, the I- and Z-clusters are mutually connected to form a complicated network, and the network structure becomes denser as the structural relaxation goes on. In the network, the medium-range order is mainly constructed by the volume sharing type connection between I- and Z-clusters. Following Nelson’s disclination theory, the network structure can be understood as a random network of Z-clusters, which is complimentarily surrounded by another type of network formed by I-clusters.

A controversy concerning the description of $ \{ \bar 1012\} $ $ \langle 10\bar 11\rangle $ twinning, whether it is shear-shuffle or pure glide-shuffle or pure shuffle, has developed. There is disagreement about the interpretation of transmission electron microscopic observations, atomistic simulations and theories for twin growth. In this article, we highlight the atomic-level, characteristic, equilibrium and non-equilibrium boundaries and corresponding boundary defects associated with the three-dimensional ‘normal’, ‘forward’ and ‘lateral’ propagation of $ \{ \bar 1012\} $ growth/annealing and deformation twins. Although deformation twin boundaries (TBs) after recovery exhibit some similarity to growth/annealing TBs because of the plastic accommodation of stress fields, there are important distinctions among them. These distinctions distinguish among the mechanisms of twin growth and resolve the controversy. In addition, a new type of disconnection, a glide disclination, is described for twinning. Synchroshear, seldom considered, is shown to be a likely mechanism for $ \{ \bar 1012\} $ twinning.

Recently the ’t Hooft–Polyakov monopole solutions in Yang–Mills theory were given new physical interpretation in the geometric theory of defects describing the continuous distribution of dislocations and disclinations in elastic media. It means that the ’t Hooft–Polyakov monopole can be seen, probably, in solids. To this end we need to compute the corresponding spin distribution on lattice sites of crystals. The paper describes one of the possible spin distributions. The Bogomol’nyi–Prasad–Sommerfield solution is considered as an example.

We review the mechanical theory of dislocation and disclination density fields and its application to grain boundary modeling. The theory accounts for the incompatibility of the elastic strain and curvature tensors due to the presence of dislocations and disclinations. The free energy density is assumed to be quadratic in elastic strain and curvature and has nonlocal character. The balance of loads in the body is described by higher-order equations using the work-conjugates of the strain and curvature tensors, i.e., the stress and couple-stress tensors. Conservation statements for the translational and rotational discontinuities provide a dynamic framework for dislocation and disclination motion in terms of transport relationships. Plasticity of the body is therefore viewed as being mediated by both dislocation and disclination motion. The driving forces for these motions are identified from the mechanical dissipation, which provides guidelines for the admissible constitutive relations. On this basis, the theory is expressed as a set of partial differential equations where the unknowns are the material displacement and the dislocation and disclination density fields. The theory is applied in cases where rotational defects matter in the structure and deformation of the body, such as grain boundaries in polycrystals and grain boundary-mediated plasticity. Characteristic examples are provided for the grain boundary structure in terms of periodic arrays of disclination dipoles and for grain boundary migration under applied shear.

We examined the stress concentration that would occur at grain boundary triple lines during deformation in two copper tricrystals with [011] tilt boundaries; one was a symmetrical tricrystal with respect to the loading axis and the other was an anti-symmetrical one. In principle, the finite element method can provide solutions with prescribed amount of precision for the anisotropic elasticity problem. It was shown that a close approximation was possible by means of a disclination model in elastically homogeneous material. This disclination model was numerically solved with the finite element method proposed in a previous paper (Hosoya, Kato, Sasaki, Trans. JSME, Vol.80, No.819 (2014 ). It was concluded that the disclination model is appropriate for estimating the stress concentration at the grain boundary triple lines in deformed polycrystals.

Numerical analysis of the elastic stress field around a wedge-type disclination is first presented. Disclinations are lattice defects accompanied by multi-valued displacement field. The discontinuity in displacement is dealt with finite element method in two different ways; one is to build up finite element model with rotational discontinuity in its original shape, and the other is to give the initial strain capable of expressing the displacement field. Good agreement with the analytical solution in elasticity was obtained in both of the two methods. It is suggested that the initial strain method may be more appropriate when solving complex structures numerically because it does not need starting with cut-and-joint procedure to create a disclination.