Atom-Based Geometrical Fingerprinting of Conformal Two-Dimensional Materials

The shape of two-dimensional materials plays a significant role on their chemical and physical properties. Two-dimensional materials are basic meshes that are formed by mesh points (vertices) given by atomic positions, and connecting lines (edges) between points given by chemical bonds. Therefore the study of local shape and geometry of two-dimensional materials is a fundamental prerequisite to investigate physical and chemical properties. Hereby the use of discrete geometry to discuss the shape of two-dimensional materials is initiated. The local geometry of a surface embodied in 3D space is determined using four invariant numbers from the metric and curvature tensors which indicates how much the surface is stretched and curved under a deformation as compared to a reference pre-deformed conformation. Many different disciplines advance theories on conformal two-dimensional materials by relying on continuum mechanics and fitting continuum surfaces to the shape of conformal two-dimensional materials. However two-dimensional materials are inherently discrete. The continuum models are only applicable when the size of two-dimensional materials is significantly large and the deformation is less than a few percent. In this research, the knowledge of discrete differential geometry was used to tell the local shape of conformal two-dimensional materials. Three kind of two-dimensional materials are discussed: 1) one atom thickness structures such as graphene and hexagonal boron nitride; 2) high and low buckled 2D meshes like stanene, leadene, aluminum phosphate; and, 3) multi layer 2D materials such as Bi2Se3 and WSe2. The lattice structures of these materials were created by designing a mechanical model - the mechanical model was devised in the form of a Gaussian bump and density-functional theory was used to inform the local height; and, the local geometries are also discussed

Multi-field approach in mechanics of structural solids

We overview the basic concepts, models, and methods related to the multi-field continuum theory of solids with complex structures. The multi-field theory is formulated for structural solids by introducing a macrocell consisting of several primitive cells and, accordingly, by increasing the number of vector fields describing the response of the body to external factors. Using this approach, we obtain several continuum models and explore their essential properties by comparison with the original structural models. Static and dynamical problems as well as the stability problems for structural solids are considered. We demonstrate that the multi-field approach gives a way to obtain families of models that generalize classical ones and are valid not only for long-, but also for short-wavelength deformations of the structural solid. Some examples of application of the multi-field theory and directions for its further development are also discussed.Comment: 25 pages, 18 figure

Analytical method for parameterizing the random profile components of nanosurfaces imaged by atomic force microscopy

The functional properties of many technological surfaces in biotechnology, electronics, and mechanical engineering depend to a large degree on the individual features of their nanoscale surface texture, which in turn are a function of the surface manufacturing process. Among these features, the surface irregularities and self-similarity structures at different spatial scales, especially in the range of 1 to 100 nm, are of high importance because they greatly affect the surface interaction forces acting at a nanoscale distance. An analytical method for parameterizing the surface irregularities and their correlations in nanosurfaces imaged by atomic force microscopy (AFM) is proposed. In this method, flicker noise spectroscopy - a statistical physics approach - is used to develop six nanometrological parameters characterizing the high-frequency contributions of jump- and spike-like irregularities into the surface texture. These contributions reflect the stochastic processes of anomalous diffusion and inertial effects, respectively, in the process of surface manufacturing. The AFM images of the texture of corrosion-resistant magnetite coatings formed on low-carbon steel in hot nitrate solutions with coating growth promoters at different temperatures are analyzed. It is shown that the parameters characterizing surface spikiness are able to quantify the effect of process temperature on the corrosion resistance of the coatings. It is suggested that these parameters can be used for predicting and characterizing the corrosion-resistant properties of magnetite coatings.Comment: 7 pages, 3 figures, 2 tables; to be published in Analys

Fuzzy simulation of forest road surface parameters

The problem of construction of forest roads with the use of local low-strength substandard materials and industrial waste is considered. To solve the problem, the primary task is to develop a method for estimating the parameters of road surfaces taking into account the conditions of uncertainties in the data. This technique allows us to reasonably clarify some of the regulatory parameters and improve the technology of construction of forest roads, which was the goal of the work. To formalize the task, experimental studies were performed and on the basis of these results, the statement of the task of fuzzy derivation of the function for estimating the bearing capacity of the coating was performed. The synthesis of the output function is performed by means of Matlab. © 2019 IOP Publishing Ltd. All rights reserved

Computation of protein geometry and its applications: Packing and function prediction

This chapter discusses geometric models of biomolecules and geometric constructs, including the union of ball model, the weigthed Voronoi diagram, the weighted Delaunay triangulation, and the alpha shapes. These geometric constructs enable fast and analytical computaton of shapes of biomoleculres (including features such as voids and pockets) and metric properties (such as area and volume). The algorithms of Delaunay triangulation, computation of voids and pockets, as well volume/area computation are also described. In addition, applications in packing analysis of protein structures and protein function prediction are also discussed.Comment: 32 pages, 9 figure