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Mechanical fields over thin elastic surfaces can develop singularities at isolated points and curves in response to constrained deformations (e.g., crumpling and folding of paper), singular body forces and couples, distributions of isolated defects (e.g., dislocations and disclinations), and singular metric anomaly fields (e.g., growth and thermal strains). With such concerns as our motivation, we model thin elastic surfaces as von K{\'a}rm{\'a}n plates and generalize the classical von K{\'a}rm{\'a}n equations, which are restricted to smooth fields, to fields which are piecewise smooth, and can possibly concentrate at singular curves, in addition to being singular at isolated points. The inhomogeneous sources to the von K{\'a}rm{\'a}n equations, given in terms of plastic strains, defect induced incompatibility, and body forces, are likewise allowed to be singular at isolated points and curves in the domain. The generalized framework is used to discuss the singular nature of deformation and stress arising due to conical deformations, folds, and folds terminating at a singular point.

We derive two consequences of the distributional form of the stress equilibrium condition while incorporating piecewise smooth stress and body force fields with singular concentrations on an interface. First we obtain the local equilibrium conditions in the bulk and at the interface, the latter including conditions on the interfacial stress and stress dipole. Second we obtain the necessary and the sufficient conditions on the divergence-free non-smooth stress field for there to exist a stress function field such that the equilibrium is trivially satisfied. In doing so we allow the domain to be non-contractible with mutually disjoint connected boundary components. Both derivations illustrate the utility of the theory of distributions in dealing with singular stress fields.

The equations of stress equilibrium and strain compatibility/incompatibility are discussed for fields with point singularities in a planar domain. The sufficiency (or insufficiency) of the smooth maps, obtained by restricting the singular fields to the domain away from the singularities, in completely characterizing the equations of equilibrium and compatibility/incompatibility over the entire domain, is established and illustrated with examples. The uniqueness of the solution to the stress problem of incompatible linear elasticity, allowing for singular fields, is proved. The uniqueness fails when the problem is considered solely in terms of the restricted maps. As applications of our framework, a general stress solution, in response to point supported body force and defect fields, is derived and a generalized notion of the force acting on a defect is developed.

An isolated positive wedge disclination deforms an initially flat elastic sheet into a perfect cone when the sheet is of infinite extent and is elastically inextensible. The latter requires the elastic stretching strains to be vanishingly small. In this paper, rigorous analytical and numerical results are obtained for the disclination induced deformed shape and stress field of a bounded F{\"o}ppl-von K{\'a}rm{\'a}n elastic sheet with finite extensibility, while emphasising the deviations from the perfect cone solution. In particular, the Gaussian curvature field is no longer localised as a Dirac singularity at the defect location whenever elastic extensibility is allowed and is necessarily negative in large regions away from the defect. The stress field, similarly, has no Dirac singularity in the presence of elastic extensibility. However, with increasing Young's modulus of the sheet, while keeping the bending modulus and the domain size fixed, both of these fields tend to develop a Dirac singularity. Noticeably, in this limiting behaviour, inextensibility eludes the bounded elastic sheet due to persisting regions of non-trivial Gaussian curvature away from the defect. Other results in the paper include studying the effect of specific boundary conditions (free, simply supported, or partially clamped) on the Gaussian curvature field away from the defect and on the buckling transition from the flat to a conical solution.

Milling of 2D flakes is a simple method to fabricate nanomaterial of any desired shape and size. Inherently milling process can introduce the impurity or disorder which might show exotic quantum transport phenomenon when studied at the low temperature. Here we report temperature dependent weak antilocalization (WAL) effects in the sculpted nanowires of topological insulator in the presence of perpendicular magnetic field. The quadratic and linear magnetoconductivity (MC) curves at low temperature indicate the bulk contribution in the transport. A cusp feature in magnetoconductivity curves (positive magnetoresistance) at ultra low temperature and at magnetic field, less than 1T represent the WAL indicating the transport through surface states. The MC curves are discussed by using the 2D Hikami Larkin Nagaoka theory. The crossover interplay nature of positive and negative magnetoresistance observed in the MR curve at ultra low temperature. Our results indicate that transport through topological surface states (TSS) in sculpted nanowires of Bi2Te3 can be achieved at mK range and linear MR observed at 2 K could be the coexistence of electron transport through TSS and contribution from the bulk band., Comment: 8 pages 3 fig

The incompatibility of linearized piecewise smooth strain field, arising out of volumetric and surface densities of topological defects and metric anomalies, is investigated. First, general forms of compatibility equations are derived for a piecewise smooth strain field, defined over a simply connected domain, with either a perfectly bonded or an imperfectly bonded interface. Several special cases are considered and discussed in the context of existing results in the literature. Next, defects, representing dislocations and disclinations, and metric anomalies, representing extra matter, interstitials, thermal, and growth strains, etc., are introduced in a unified framework which allows for incorporation of their bulk and surface densities, as well as for surface densities of defect dipoles. Finally, strain incompatibility relations are derived both on the singular interface, and away from it, with sources in terms of defect and metric anomaly densities. With appropriate choice of constitutive equations, the incompatibility relations can be used to determine the state of internal stress within a body in response to the given prescription of defects and metric anomalies.

Myers-Briggs Type Indicator (MBTI) types depict the psychological preferences by which a person perceives the world and make decisions. There are 4 principal functions through which the people see the world: sensation, intuition, feeling, and thinking. These functions along with the Introverted\Extroverted nature of the person, there are 16 personalities types, the humans are divided into. Here an idea is presented where a user can get recommendations for books, web media content, music and movies on the basis of the users' MBTI type. Only things like books and other media content has been chosen because the preferences in such things are mostly subjective. Apart from the recommended content that is generally generated on the basis of the previous purchases, searches can be enhanced by using the MBTI. A minimalist survey was designed for collecting the data. This has a more than 100 features that show the preference of a personality type. Those include preferences in book genres, music genres, movie genres and even video games genres. After analyzing the data that is collected from the survey, some inferences were drawn from it which can be used to design a new recommendation engine for recommending the content that coincides with the personality of the user., Comment: 7 Pages, 13 Figures