An affine generalized optimal scheme with improved free-surface expression using adaptive strategy for frequency-domain elastic wave equation

Effective frequency-domain numerical schemes were central for forward modeling and inversion of the elastic wave equation. The rotated optimal nine-point scheme was a highly used finite-difference numerical scheme. This scheme made a weighted average of the derivative terms of the elastic wave equations in the original and the rotated coordinate systems. In comparison with the classical nine-point scheme, it could simulate S-waves better and had higher accuracy at nearly the same computational cost. Nevertheless, this scheme limited the rotation angle to 45°; thus, the grid sampling intervals in the x- and z-directions needed to be equal. Otherwise, the grid points would not lie on the axes, which dramatically complicates the scheme. Affine coordinate systems did not constrain axes to be perpendicular to each other, providing enhanced flexibility. Based on the affine coordinate transformations, we developed a new affine generalized optimal nine-point scheme. At the free surface, we applied the improved free-surface expression with an adaptive parameter-modified strategy. The new optimal scheme had no restriction that the rotation angle must be 45°. Dispersion analysis found that our scheme could effectively reduce the required number of grid points per shear wavelength for equal and unequal sampling intervals compared to the classical nine-point scheme. Moreover, this reduction improved with the increase of Poisson’s ratio. Three numerical examples demonstrated that our scheme could provide more accurate results than the classical nine-point scheme in terms of the internal and the free-surface grid points.

Neuromaps: structural and functional interpretation of brain maps

Imaging technologies are increasingly used to generate high-resolution reference maps of brain structure and function. Modern scientific discovery relies on making comparisons between new maps (e.g. task activations, group structural differences) and these reference maps. Although recent data sharing initiatives have increased the accessibility of such brain maps, data are often shared in disparate coordinate systems (or ``spaces''), precluding systematic and accurate comparisons among them. Here we introduce the neuromaps toolbox, an open-access software package for accessing, transforming, and analyzing structural and functional brain annotations. We implement two registration frameworks to generate high-quality transformations between four standard coordinate systems commonly used in neuroimaging research. The initial release of the toolbox features >40 curated reference maps and biological ontologies of the human brain, including maps of gene expression, neurotransmitter receptors, metabolism, neurophysiological oscillations, developmental and evolutionary expansion, functional hierarchy, individual functional variability, and cognitive specialization. Robust quantitative assessment of map-to-map similarity is enabled via a suite of spatial autocorrelation-preserving null models. By combining open-access data with transparent functionality for standardizing and comparing brain maps, the neuromaps software package provides a systematic workflow for comprehensive structural and functional annotation enrichment analysis of the human brain.

GIS, Positioning, and Imagery Tools

The catastrophic eruption in the world scenario of the breaking pandemic forced the application of all existent scientific knowledge, but also triggered the development of new technical tools and procedures. This chapter is focused on setting forth the practical technological efforts based on the spatial georeferencing by coordinate systems and on the treatment of satellite images as means for tracking the positive cases, for recognizing the spatial infection´s behavior, and for identifying the real physical changes in the spatial landscape. The cases set forth here pertain to three techniques, namely the development of visual dashboards, the tracking resources developed, and the deployment of imagery captured by satellite perception.

The generalized stokes integral theorem for a covariant pseudotensor field

Ориентируемые континуумы играют важную роль в микрополярной теории упругости, все реализации которой возможны только в рамках псевдотензорного формализма и представления об ориентируемом многообразии. Особенно это касается теории микрополярных гемитропных упругих сред. В настоящей работе рассматриваются различные формулировки интегральной теоремы Стокса для асимметричного ковариантного пседотензорного поля, заданного веса. Тем самым достигается распространение известной интегральной формулы Стокса на случай псевдотензоров. Последнее обстоятельство позволяет использовать, указанное обобщение для микрополярных континуумов. Исследование существенно опирается на класс специальных координатных систем. Oriented continua play an important role in the micropolar theory of elasticity, all realizations of which are possible only within the framework of the pseudotensor formalism and the orientable manifold concept. This especially concerns the theory of micropolar hemitropic elastic media. In this paper, we consider various formulations of the Stokes integral theorem for an asymmetric covariant pseudotensor field of a given weight. This extends the well-known Stokes integral formula to the case of pseudotensors. The latter circumstance makes it possible to use the manifistated generalization for micropolar continua. The study relies heavily on the class of special coordinate systems.

On the statements of boundary conditions in models of the woven materials production

В статье обсуждаются проблемы постановка краевых задач при моделировании процессов аддитивного производства 3D материала, при учете наличия в нем дополнительных выделенных направлений (выкладки волокон в тканых материалах, арматуры в бетонных конструкциях, биоволокон в мышечной ткани и т.д.). Выводится общая форма тензорного соотношения на поверхности наращивания, при учете дополнительного выделенного направления. Определяется необходимая система независимых аргументов определяющей тензорной функции на поверхности наращивания в рассматриваемом случае. Определяется полный набор совместных рациональных инвариантов тензора напряжений и характерных директоров. Дается инвариантно-полная формулировка определяющих соотношений на поверхности наращивания. Предложены постановки краевых задач, моделирующих процессы синтеза тканых 3D материалов. Полученные дифференциальные ограничения конкретизируются для ортогональных систем координат, учитывающих геометрию процесса наращивания. The article discusses the problem of boundary value problems in models of the additive production processes of a 3D material, taking into account the presence of additional selected directions in it (laying out fibers in woven materials, reinforcement in concrete structures, biofibers in muscle tissue, etc.). The general form of the tensor relation on the growing surface is shown, taking into account the additional selected direction. The necessary system of independent arguments of the constitutive tensor function on the growing surface in the considered case is determined. A complete set of joint rational invariants of the stress tensor and characteristic directors is determined. An invariant-complete formulation of the constitutive relations on the growing surface is given. The formulation of boundary value problems that simulate the processes of synthesis of woven 3D materials are proposed. The resulting differential constraints are specified for orthogonal coordinate systems taking account of the geometry of the growing process.

INFLUENCE OF OBJECT TECHNOLOGICAL PHANTOM’S TRANSFORMATIONS OF THE PRODUCTION’S QUALITY

The article states that the relevance of modeling processes, followed by analysis of the features of the transformation of the technological phantom of the real object, in particular precision instrumentation products, which affects the accuracy of shaping the formation of this object in automated production. The main purpose of this study was to substantiate analytical models of transformations of the technological phantom of the object, taking into account the type of coordinate systems, which can be observed transformation of some coordinates into others. These features of the transformations significantly affect the accuracy of the formation of this object. The main analytical models that determine the features of the formation of the technological phantom and the need to combine the technological phantom with the mass of the object, which provides opportunities to take into account the problems of manufacturing surface elements, determine the features of shaping the accuracy of reproduction of objects From the analytical models obtained in our work, we have the opportunity to say that for any object the technological phantom has a geometric construction, and the shape of this construction is the main factor influencing the accuracy of object formation. The research substantiates the analytical model of transformations of the technological phantom of the object, which determines the dependence of the geometric characteristics of the formation of the precision object, which is made using certain additive or destructive (with decreasing mass of the real object) technological processes. In further research, the model of shaping technological objects in space requires modeling of the peculiarities of mass representation in view of the energy connections of the technological phantom of the object in a certain volume, which has the task of determining and improving manufacturing accuracy.

Geodetic foundations of cartography in Europe in 19th century

Geodetic surveying comprises the determination of locations on and the dimensions of the earth’s surface at a various scales. In the 19th century, its technologies are those of direct measurement of the earth’s surface combined with astronomical observations. Its social context encompasses all those individuals and institutions involved in the creation, preservation, use, and arrangement of knowledge of the earth. In the introductory part of the paper the author mentions several important events in the history of the 19th century geodesy. Geodetic work on determining the size of the Earth by measuring the lengths of the meridian arcs continues in this century. An international surveying organization was established and the international meter convention adopted. Basing on a detailed research of geodetic surveying in Central, Eastern and Southeastern Europe in the 19th century, a part of these surveys is presented that relates to Switzerland, Austro-Hungarian Monarchy, Austria, Hungary, Slovenia and Croatia. Common to all these geodetic surveys is that they were necessary for the development of cartography and were carried out by military institutions. The developed geodetic networks are characterized by the use of different ellipsoids, different prime meridians, different coordinate systems and their origin. In the area under consideration in the 19th century, there were five different ellipsoids in use suggested by Bessel, Bonenberger, Schmidt, Valbeck and Zach. Prime meridians were