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We report on a set of experiments directed to a problem of microparticles interaction with a disclination in a nematic liquid crystal matrix. The idea of the study consists in the visualization of the disclination by filling it with particles efficiently scattering light. A θ-cell possessing a topological defect of undetermined twist which can capture micro-sized objects was exploited. The results obtained for samples of different shape can be used as for the understanding of the nature of self-assembling clusters, as for the practical goal of increasing the visibility of a disclination being a dynamic object sensitive to temperature and other external factors and able to move the trapped particles. [ABSTRACT FROM AUTHOR]

In solids, external stress induces the Peach-Koehler force, which drives dislocations to move. Similarly, in liquid crystals, an external angular stress creates an analogous force, which drives disclinations to move. In this work, we develop a method to calculate the relevant angular stress either analytically or numerically, and hence to determine the force on a disclination. We demonstrate this method by applying the Peach-Koehler force theory to four problems: (a) Single disclination in a liquid crystal cell between two uniform in-plane alignments perpendicular to each other. (b) Array of disclinations in a liquid crystal cell with patterned substrates. (c) Pair of disclinations in a long capillary tube with homeotropic anchoring. (d) Radial hedgehog or disclination loop inside a sphere with homeotropic anchoring, and its response to an applied magnetic field. In all of these problems, the Peach-Koehler force theory predicts the equilibrium defect structure, and the predictions are consistent with the results of minimising the total free energy. [ABSTRACT FROM AUTHOR]

In this paper, our principal objective is to investigate the impact of disclination and throat radius of a three-dimensional traversable wormhole on quantum oscillator fields. Specifically, we focus on Perry–Mann-type wormhole with disclination while also considering the influence of rainbow gravity's. We derive the radial equation of the relativistic Klein–Gordon oscillator within this wormhole background under the effects of gravity's rainbow and the analytical eigenvalue solution is obtained using the confluent Heun function. In fact, we show that the behavior of the oscillator fields is significantly influenced not only by the presence of disclination and the throat radius but also by the parameter of rainbow gravity's. We choose various such rainbow functions to present and analyze the eigenvalue solutions of the quantum oscillator fields. [ABSTRACT FROM AUTHOR]

The classical description of the elastic field of an edge dislocation is modified by the addition of a line force to the Burgers vector. Also, partitioning of displacements is imposed, consistent with the topological theory of defects at interfaces, agreeing with symmetry requirements as are inherent in nonlinear or atomistic calculations. Much of the classical theory is unchanged. However, displacement fields and image effects differ. [ABSTRACT FROM AUTHOR]

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.

Severe plastic deformation drives bulk materials far away from equilibrium and thus opens up a new opportunity to explore hitherto uncharted regions of structure-property correlations with respect to grain size, strain and defect density under extreme conditions. This allows addressing long-standing issues in materials research, such as the validity of "effective temperature" concept and provides a set-screw for exploring the possible levels of defect design and property tuning by deformation processing. As a pre-requisite, basic issues concerning the interaction of defects of different dimensionality during deformation and their interrelation with fluxes of solutes or with segregation fields, resulting in chemo-mechanical coupling effects need to be analyzed quantitatively. In the following review, we address issues related to internal interfaces in severely deformed metals and alloys by highlighting recent observations. [ABSTRACT FROM AUTHOR]

Disclinations in nematic liquid crystals are of great interest both theoretically and practically. The ability to create and reconfigure disclinations connecting predetermined points on substrates could enable novel applications such as directed self-assembly of micro/nanoparticles and molecules. In this study, we present a novel approach to design and create disclination interconnects that connect predetermined positions on substrates. We demonstrate that these interconnects can be switched between different states by re-writing photoalignment materials with linearly polarised light and can be switched between metastable states using electric fields. [ABSTRACT FROM AUTHOR]

We analyzed the kinematic (geometric) aspects of kink bands with multiple basal shear using rank-1 connection to investigate the type of disclination and annihilation of disclinations in kink microstructures. We found that wedge disclinations occur in connecting kink bands for realistic magnitude of shear that can occur, regardless of the shear direction. The normal vector of the junction plane between kink bands and Frank vector of the resulting wedge-disclination varied continuously with respect to the changes in the magnitude and direction of the basal shear. Annihilation of disclinations is possible even between the kinks which are formed by multiple basal shears. Kinematical model of the three-dimensional wavy kinks are proposed using the obtained results. [ABSTRACT FROM AUTHOR]

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.

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.

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.

The sources of internal stresses in nanowires are considered, the model of which is an infinite elastically isotropic cylinder of circular cross section. Sources of internal stresses are defects that have their own distortion (eigenstrain) and are localized either at a point, on a line, on the surface, or in a region inside the nanowire. Relations are given for the elastic fields and energies of some defects in nanowires, including rectilinear (straight) dislocations and disclinations, dislocation loops, and dilatation inclusions. The interaction between sources of internal stresses in an elastic cylinder is analyzed. The role of the found solutions to the problems of solid mechanics in the interpretation of relaxation processes in pentagonal nanowires and hybrid semiconductor nanostructures with radial and axial heterointerfaces is discussed. [ABSTRACT FROM AUTHOR]

Experimental observations reveal that disclinated non-equilibrium grain boundaries (GBs) exist extensively in polycrystalline metals; however, the interaction between these GBs and irradiation-induced point defects is rarely reported. In the present work, Molecular statics simulation was used to evaluate the capacity of disclinated non-equilibrium GBs to accommodate point defects in tungsten. Simulation results showed that disclinated non-equilibrium GBs are more efficient sinks for point defects than their equilibrium counterparts because of long-range stress field around them. Continuous segregation of point defects will change the structure of the disclinated non-equilibrium GBs and leads to the GBs tending to relax to equilibrium state. According to theoretical calculation, the disclinated non-equilibrium GBs can absorb a large number of point defects before transforming into equilibrium state; therefore, disclinated non-equilibrium GBs have very strong capacity to accommodate point defects and can be used as strong defect sinks for developing radiation resistance materials. [ABSTRACT FROM AUTHOR]

Twisting is a simple and effective method for assembling individual carbon nanotubes (CNTs) into high-strength, tough, and continuous CNT yarns. However, the unexpectedly low stretching performance of the resulting carbon nanotube bundle (CNTB) structures is a problem that must be resolved. In this study, we investigated the impact of twisting on the structure and stretching performance of CNTBs through molecular dynamics (MD) simulations while considering the presence of disclinations within the CNTB structure. We found that disclinations nucleate in twisted CNTBs, and the longer the disclination line in CNTBs, the lower the Young's modulus. The presence of disclination lines in the twisted CNTBs may be an important reason for the decrease in the tensile properties of the CNT yarns. Although the theoretical equations in textile field can be applied to describe the mechanical properties of CNT yarns, there are significant relative errors between the equations and the MD simulation results presented herein. Therefore, we revised the equations based on the simulation results to reduce the relative error for seven-layer CNTBs to less than 10 %. This paper provides new insights into the low tensile performance of CNT yarns and offers potential guidance for the production of high-performance CNT yarns through twisting. [Display omitted] • Twisting loads induces the nucleation of disclination in carbon nanotube bundles. • The more layers in the bundle, the smaller the twist angle when disclination occurs. • Disclination partially counteracts torque accumulation in carbon nanotube bundles. • Disclination manifests as curved lines in carbon nanotube bundles. • Longer disclination lines correlate with lower Young's modulus of bundles. [ABSTRACT FROM AUTHOR]

Grain boundary junction (GBJ) disclinations are ubiquitous at the nanoscale in icosahedra and decahedra. These structural motifs consist of several tetrahedra sharing a twin grain boundary. According to the coincident site lattice (CSL) theory this twin grain boundary is referred to as Σ 3 < 110 > {111} grain boundary. In the present work, GBJ disclinations involving a low energy grain boundary Σ 11 < 110 > {113} are reported. Σ 3 − Σ 3 − Σ 11 triple junction disclination is energetically preferred at the nanoscale as opposed to the ideal (without any misorientation mismatch) Σ 3 − Σ 3 − Σ 9 triple junction. Molecular dynamics simulations are employed to study the disclinations in three dynamical processes key for nanoparticle synthesis − growth, coalescence, and solidification; across three metal systems Ag, Cu, and Pt which cover a range of stacking fault energies. Results indicate that Pt has a higher preference for disclinations while they are almost non-existent in Cu and to a lesser degree in Ag. Several types of disclinations have been identified and catalogued. Gaussian images (used as a proxy for simulating scanning transmission electron microscopy high angle annular dark field images) reveal that some of the disclinations induce artifacts which makes it non-trivial to identify them even when they are present in experimental particles. A key characteristic of the GBJ disclinations is the rapid change in misorientation angle around Σ 11 grain boundary with distance away from the disclination. In this scenario, there is a need to reassess the methodology currently in use for identification of grain boundary type at the nanoscale. [Display omitted] [ABSTRACT FROM AUTHOR]

[Display omitted] • A geometric model for bent kinks is developed based on Inamura's kink model. • Gibbs free energies of systems containing different bent kinks are investigated. • Bending morphology is related to the relaxation of the elastic energy of disclinations. • Theoretical geometry of a smoothly bent kink is confirmed by experiments. In this study, we have developed a geometric model for bent kinks by introducing sequences of ortho-connected kink bands into ridge-kinks to provide insights into the possible reasons why kinks are bent and the resulting geometry when they are bent. We first formulated the Frank angles and coordinates of the disclinations formed in the bent kinks, which enable our discussion on the influence of the introduction of ortho-kinks on the Gibbs energy by utilizing Romanov's disclination model. It turns out that the introduction of ortho-kinks can relax the elastic strain energy and thus reduce the Gibbs energy of the system under compression states with lower external stresses. On the other hand, the introduction of ortho-kinks increases the Gibbs energy at higher compression stresses, implying sharp ridge-kinks are preferred under such conditions. This trend resembles the experimental observations reported by previous studies that the shapes of newly formed kinks tend to transition from pre-kinks with bent shapes to ridge-kinks with sharp shapes as the compression test progresses. The smoothly bent kink with smoothly distributed misorientation, formed by increasing the number of introduced ortho-kinks, can further reduce the Gibbs energy at lower applied stresses. Subsequently, based on the Rank-1 condition for the connection of kink bands, we further analyzed the geometry of such smoothly bent kinks and derived the analytical equations for the constraints on the orientation distribution. Finally, we conducted EBSD measurements on bent kinks observed in directionally solidified (DS) LPSO-Mg alloys and confirmed that the derived equations for the orientation distribution are in good agreement with the experimental results. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the effects of the topology of a disclination on quantum revivals when a quantum particle is subject to an infinite cylindrical well and a logarithmic potential. By using the WKB (Wentzel, Kramers and Brillouin) approximation, we obtain the eigenvalues of energy and show that the influence of the topology of the disclination on them gives rise to an Aharonov–Bohm-type effect. Further, we discuss how the topology of a disclination influences the classical periods and the revival times. [ABSTRACT FROM AUTHOR]

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.

The standard model is applied for partial disclination pairs in hard materials. These defects comprise two partial disclinations and an intervening fault that can be a twin boundary, grain boundary or interphase boundary. In three dimensions there are six types. Two of them can be considered Somigliana disclinations. The standard model includes geometrically nonlinear embedded coordinates. It entails partitioning of displacements that result in configurations and strain fields not considered classically for partial disclinations. These concepts are applied to boundary junctions, disconnections, and multiple twins. Recovered stress-free structures are considered. [ABSTRACT FROM AUTHOR]

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.

We use the Chern–Simons action for a 𝕊 𝕆 (3) -connection for the description of point disclinations in the geometric theory of defects. The most general spherically symmetric 𝕊 𝕆 (3) -connection with zero curvature is found. The corresponding orthogonal spherically symmetric 𝕊 𝕆 (3) matrix and n -field are computed. Two examples of point disclinations are described. [ABSTRACT FROM AUTHOR]

We analyze the interaction of the induced electric dipole moment of a neutral particle with an electric field in elastic medium with a charged disclination from a semiclassical point of view. We show that the interaction of the induced electric dipole moment of a neutral particle with an electric field can yield an attractive inverse-square potential, where it is influenced by the topology of the disclination. Then, by using the Wentzel, Kramers and Brillouin approximation based on the Langer transformation, we show that the centrifugal term of the radial equation must be modified due to the influence of the topology of the disclination. Besides, we obtain the bound states solutions to the Schrödinger equation. [ABSTRACT FROM AUTHOR]

The 't Hooft–Polyakov monopole solution in Yang–Mills theory is given new physical interpretation in the geometric theory of defects. It describes solids with continuous distribution of dislocations and disclinations. The corresponding densities of Burgers and Frank vectors are computed. It means that the 't Hooft–Polyakov monopole can be seen, probably, in solids. [ABSTRACT FROM AUTHOR]

We demonstrate that a first order isotropic-to-nematic phase transition in liquid crystals can be succesfully modeled within the generalized Landau-de Gennes theory by selecting an appropriate combination of elastic constants. The numerical simulations of the model established in this paper qualitatively reproduce the experimentally observed configurations that include interfaces and topological defects in the nematic phase. [ABSTRACT FROM AUTHOR]

A different type of defect, the coherency disclination, is added to disclination types. Disconnections that include disclination content are considered. A criterion is suggested to distinguish disconnections with dislocation content from those with disclination content. Electron microscopy reveals unit disconnections in a low albite grain boundary, defects important in grain boundary sliding. Disconnections of varying step heights are displayed and shown to define both deformed and recovered structures. [ABSTRACT FROM AUTHOR]

Abstract—Molecular dynamics is used to study the fracture of pseudo-graphenes, namely, allotropic forms of carbon that are modifications of graphene with a high density of periodically distributed disclinations with zero total charge. Disclinations in pseudo-graphenes are associated with improper carbon rings, that is, rings having 4, 5, 7, or 8 members, in contrast to the proper 6-member carbon rings constituting the ideal crystal lattice of graphene. Pseudo-graphenes, which have a significant excess of energy relative to graphene, show a significant (up to 50%) decrease in the critical tensile stress compared to defect-free graphene. [ABSTRACT FROM AUTHOR]

We investigate geometry and mechanics of the buckled orthotropic von Kármán elastic plate, with free boundary condition, in the presence of an isolated positive, or negative, disclination. The buckled shape of an isotropic elastic plate is cone-like for a positive disclination and saddle-like for a negative disclination. In either case, with increasing orthotropy, the shape of the buckled plate becomes more tent-like. The Gaussian curvature accordingly spreads along the ridge of the tent. The stress fields too remain focused in the neighbourhood of the defect point and the ridge, indicating that most of the stretching energy is accommodated in these singular regions. • Geometry and mechanics of a disclination in an orthotropic elastic plate are investigated. • A strongly orthotropic elastic sheet buckles into a tent-like shape in the presence of a disclination. • Novel insights into the micromechanics of thin elastic sheets with topological defects. [ABSTRACT FROM AUTHOR]

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.

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.

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.

Polymer-stabilised blue phase (PSBP) could be employed in novel fast response optical and photonic devices. It is inferred that inside PSBPs, the polymers are selectively aggregated by location in −1/2 disclinations, which are defects coexisting with the blue phase as a periodic lattice, thereby extending the temperature range of the blue phase. The polymer aggregate structure in PSBPs strongly affects their physical properties. In this study, we employed a non-destructive synchrotron ultra-small-angle X-ray diffraction analysis to investigate the effect of polymerisation rates on the polymer aggregate structure in PSBPs prepared with monomers of different polymerisation rates and examined the structure formation process of the polymer during polymerisation. When methacrylate monomers, which exhibit a relatively low polymerisation rate, were used to form polymers in PSBP, the resulting polymer was more selectively aggregated at disclinations in the PSBP. Furthermore, the electro-optical effect in the PSBP was successfully improved by reducing the polymer concentration in the PSBPs prepared with the optimised monomer combinations.

We consider an elastic medium with a disclination and investigate the topological effects on the interaction of a spinless electron with radial electric fields through the WKB (Wentzel, Kramers, Brillouin) approximation. We show how the centrifugal term of the radial equation must be modified due to the influence of the topological defect in order that the WKB approximation can be valid. Then, we search for bound states solutions from the interaction of a spinless electron with the electric field produced by this linear distribution of electric charges. In addition, we search for bound states solutions from the interaction of a spinless electron with radial electric field produced by uniform electric charge distribution inside a long non-conductor cylinder. [ABSTRACT FROM AUTHOR]

We present singularity-free solution for cracks within polar media in which material points possess both position and orientation. The plane strain problem is addressed in this study for which the generalized continua including micropolar, nonlocal micropolar, and gradient micropolar elasticity theories are employed. For the first time, the variationally consistent boundary conditions are derived for gradient micropolar elasticity. Moreover, having reviewed the solution to line defects including glide edge dislocation and wedge disclination from the literature, the fields of a climb edge dislocation within micropolar, nonlocal micropolar and gradient micropolar elasticity are derived. This completes the collection of line defects needed for an inplane strain analysis. Afterward, as the main contribution, using both types of line defects (i.e., dislocation being displacement discontinuity and disclination being rotational discontinuity), the well-established dislocation-based fracture mechanics is systematically generalized to the dislocation- and disclination-based fracture mechanics of polar media for which we have three translations together with three rotations as degrees of freedom. Due to the application of the line defects, incompatible elasticity is employed throughout the paper. Cracks under three possible loadings including stress and couple stress components are analyzed, and the corresponding line defect densities and stress and couple stress fields are reported. The singular fields are obtained once using the micropolar elasticity, while nonlocal micropolar, and gradient micropolar elasticity theories give rise to singularity-free fracture mechanics. [ABSTRACT FROM AUTHOR]

• Effect of nanoscale amorphization on dislocation emission from a blunt crack is studied. • Nanoscale amorphization occurs through splitting transformation of GB disclinations. • The criterion for the first dislocation emission form the elliptical blunt crack is derived. • Nanoscale amorphization can either enhance or weaken the critical applied SIFs. • There is a critical crack-junction distance making the dislocation emission most difficult. A theoretical model is established to describe the effect of nanoscale amorphization on the lattice dislocation emission from an elliptical blunt crack tip in deformed nanocrystalline and ultrafine-grained materials. Within the description, the nanoscale amorphization occurs through the splitting transformation of grain boundary disclinations which are produced by grain boundary sliding. The criterion for the first dislocation emission form the elliptical blunt crack is derived. The influence of the nanoscale amorphization and the features of the elliptical blunt crack on the critical stress intensity factors for the dislocation emission are discussed in detail. The obtained results show that the nanoscale amorphization can either enhance or weaken the critical applied SIFs for dislocation emission, depending on the emission angle, the radius of curvature of the elliptical blunt crack and the distance between the nanoscale amorphization and the crack tip. There is a critical crack-junction distance making the dislocation emission most difficult and at this critical crack-junction distance, the stress-release effect of the nanoscale amorphization is strongest. [ABSTRACT FROM AUTHOR]

The kinematical relationships among the geometric quantities that characterise kink bands, ridge kinks, and ortho kinks and the existence of disclinations in connecting kink bands were revealed based on the rank-1 connection, which is a condition of the continuity of deformation. Owing to the simple geometry of the kinks, the kink plane and the crystallographic rotation of the kink band were obtained in analytic forms as functions of the magnitude of the shears inside kinks. The geometry of the kink band predicted by the rank-1 connection agreed well with literature experimental data. Ridge kinks and ortho kinks were treated as the rank-1 connection of two kink bands. Positive and negative partial wedge disclinations were inevitably formed in any kink band connections when the junction plane of the kink bands did not reach the surface of the body. The Frank vector of the disclinations was also obtained as a function of the shear magnitudes in the kink bands. There exist compatible kink microstructures in which the disclinations are cancelled. Modes of complete relaxation and annihilation of disclinations by combinations of kinks or slip deformations were revealed. The nature of the kink microstructure and kink strengthening was discussed based on the formation and annihilation of disclinations. Image 1 [ABSTRACT FROM AUTHOR]

In this paper, linear and nonlinear optical properties of a GaAs quantum dot (QD) confined by a parabolic plus inverse square (PIS) potential with a disclination are theoretically studied under the influence of a magnetic field and the Aharonov-Bohm (AB) flux field. To achieve this, the Schrödinger equation for this system is derived, and its solutions of the wave function and the energy levels are obtained using the confluent hypergeometric equation. The effect of the disclination defect on the optical absorption coefficients (OACs) and refractive index changes (RICs) of the PIS quantum dot is examined in detail. The results obtained indicate that the peak positions and amplitudes of the OACs and RICs are significantly affected by changes in the magnitude of the disclination parameter. Furthermore, the effect of the disclination on the peak positions of the OACs and the RICs can be eliminated by adjusting the magnetic field strength. • We study the optical properties of a GaAs quantum dot with a disclination in the presence of external fields. • A disclination which is a topological defect has a great influence on the optical properties of the system. • The observed shift in the peak positions of the optical coefficients due to disclination can be controlled by the application of an external field. [ABSTRACT FROM AUTHOR]

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.

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., Competing Interests: The authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

We consider graphene disclination networks (DNs) — periodic distributions of disclination defects. Disclinations manifest themselves as 4-, 5-, 7- or 8-member carbon rings in otherwise 6-member ring ideal 2D graphene crystal lattice. Limiting cases of graphene-like 2D carbon lattices without 6-member motives, i.e., pseudographenes, are also studied. The geometry and energy of disclinated 2D carbon configurations are analyzed with the help of molecular dynamics (MD) simulation technique. A comparison of the obtained MD results with analytical calculations within the framework of the theory of defects of elastic continuum is presented. [ABSTRACT FROM AUTHOR]