Coupled Deformations of Elastic Curves and Surfaces

2000 ◽  
Author(s):  
David Steigmann
Keyword(s):  
Three Dimensional ◽  
Finite Deformations ◽  
Rubber Elasticity ◽  
Curves And Surfaces ◽  
Elastic Curves ◽  
The Subject ◽  
Coupled Response ◽  
Structural Networks

Abstract Theories of perfectly flexible elastic curves and surfaces are frequently used to describe diverse phenomena ranging from bioelasticity and fluid capillarity to rubber elasticity and the mechanics of structural networks. It is our aim here to present a treatment of the coupled response of such continua accounting for three-dimensional interactions in the presence of finite deformations and strains. A more expansive discussion of the subject of the present paper may be found in [1].

Geological Field Sketches and Illustrations

2019 ◽  
Author(s):  
Matthew J. Genge
Keyword(s):  
Cross Sections ◽  
Earth Science ◽  
Three Dimensional ◽  
Worked Examples ◽  
Scientific Publications ◽  
Thin Sections ◽  
Geological Features ◽  
Different Types ◽  
The Subject

Drawings, illustrations, and field sketches play an important role in Earth Science since they are used to record field observations, develop interpretations, and communicate results in reports and scientific publications. Drawing geology in the field furthermore facilitates observation and maximizes the value of fieldwork. Every geologist, whether a student, academic, professional, or amateur enthusiast, will benefit from the ability to draw geological features accurately. This book describes how and what to draw in geology. Essential drawing techniques, together with practical advice in creating high quality diagrams, are described the opening chapters. How to draw different types of geology, including faults, folds, metamorphic rocks, sedimentary rocks, igneous rocks, and fossils, are the subjects of separate chapters, and include descriptions of what are the important features to draw and describe. Different types of sketch, such as drawings of three-dimensional outcrops, landscapes, thin-sections, and hand-specimens of rocks, crystals, and minerals, are discussed. The methods used to create technical diagrams such as geological maps and cross-sections are also covered. Finally, modern techniques in the acquisition and recording of field data, including photogrammetry and aerial surveys, and digital methods of illustration, are the subject of the final chapter of the book. Throughout, worked examples of field sketches and illustrations are provided as well as descriptions of the common mistakes to be avoided.

Graphed equilibrium parameters of channels formed in sediment

1980 ◽  
Vol 7 (1) ◽  
pp. 93-104 ◽  
Author(s):  
A.W. Peterson ◽  
T. Blench
Keyword(s):  
Subject Matter ◽  
Three Dimensional ◽  
Numerical Data ◽  
Reference List ◽  
Laboratory Measurements ◽  
Practical Applications ◽  
Circular Pipes ◽  
The Subject ◽  
Specialized Mathematics ◽  
Major Reference

This paper, for river engineers and their environmental counterparts, presents and explains the origin and potential of four-dimensional charts that smooth most of the world's numerical data obtained from the equilibrium dimensions of sand rivers, gravel rivers, and laboratory flumes. These charts aim to provide a practical service comparable with that provided by factual plots on the comprehensive classic three-dimensional Stanton friction-factor diagram for circular pipes and clean Newtonian fluid. In the river problems, especially, the existence of different phases (whose transitions are not susceptible to formulation), the inadequacies of textbook theories even for simple phases, and the unavoidable imperfections of both field and laboratory measurements combine to prevent responsible design. The remedy is a graphing of total information backed by references from which its reliability and practicability can be assessed.The references have been chosen to contain principal information in the forms of: (i) usable photos, graphs, and tables; (ii) explanations free from specialized mathematics and speculative arguments; and (iii) papers with discussions, authors' replies, and further useful references (since a major reference list would be too long for this paper). Because condensation has had to be extreme the authors will be glad to attempt answers to discussions and questions on the subject matter, its practical applications, and its implications in teaching and research.

Mathematical aspects of molecular replacement. IV. Measure-theoretic decompositions of motion spaces

2017 ◽  
Vol 73 (5) ◽  
pp. 387-402 ◽  
Author(s):  
Gregory S. Chirikjian ◽  
Sajdeh Sajjadi ◽  
Bernard Shiffman ◽  
Steven M. Zucker
Keyword(s):  
General Theory ◽  
Rigid Body ◽  
Three Dimensional ◽  
Molecular Replacement ◽  
Translation Group ◽  
Common Occurrence ◽  
Space Group ◽  
Space Groups ◽  
Relevant Case ◽  
The Subject

In molecular-replacement (MR) searches, spaces of motions are explored for determining the appropriate placement of rigid-body models of macromolecules in crystallographic asymmetric units. The properties of the space of non-redundant motions in an MR search, called a `motion space', are the subject of this series of papers. This paper, the fourth in the series, builds on the others by showing that when the space group of a macromolecular crystal can be decomposed into a product of two space subgroups that share only the lattice translation group, the decomposition of the group provides different decompositions of the corresponding motion spaces. Then an MR search can be implemented by trading off between regions of the translation and rotation subspaces. The results of this paper constrain the allowable shapes and sizes of these subspaces. Special choices result when the space group is decomposed into a product of a normal Bieberbach subgroup and a symmorphic subgroup (which is a common occurrence in the space groups encountered in protein crystallography). Examples of Sohncke space groups are used to illustrate the general theory in the three-dimensional case (which is the relevant case for MR), but the general theory in this paper applies to any dimension.

Influence of Ball and Background Patterns on Perception of Visual Direction of a Moving Object

1979 ◽  
Vol 49 (2) ◽  
pp. 343-346 ◽  
Author(s):  
Marcella V. Ridenour
Keyword(s):  
Analysis Of Variance ◽  
Moving Objects ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Moving Object ◽  
Visual Direction ◽  
Visual Patterns ◽  
Prediction Time ◽  
The Subject ◽  
Three Dimensional Space

30 boys and 30 girls, 6 yr. old, participated in a study assessing the influence of the visual patterns of moving objects and their respective backgrounds on the prediction of objects' directionality. An apparatus was designed to permit modified spherical objects with interchangeable covers and backgrounds to move in three-dimensional space in three directions at selected speeds. The subject's task was to predict one of three possible directions of an object: the object either moved toward the subject's midline or toward a point 18 in. to the left or right of the midline. The movements of all objects started at the same place which was 19.5 ft. in front of the subject. Prediction time was recorded on 15 trials. Analysis of variance indicated that visual patterns of the moving object did not influence the prediction of the object's directionality. Visual patterns of the background behind the moving object did not influence the prediction of the object's directionality except during the conditions of a light nonpatterned moving object. It was concluded that visual patterns of the background and that of the moving object have a very limited influence on the prediction of direction.

scholarly journals IMAGES OF MENTAL VISUALIZATION IN BIOETHICS

2021 ◽  
pp. 140-152
Author(s):  
Вячеслав Иванович Моисеев
Keyword(s):  
Local Community ◽  
Three Dimensional ◽  
Unit Vector ◽  
Vector Model ◽  
Vector Representation ◽  
Three Dimensional Objects ◽  
The Status ◽  
The Subject ◽  
Vector Sum ◽  
Sum Vector

В статье даётся краткий очерк антиномической природы биоэтического дискурса и возможностей его геометрической визуализации. Рассматриваются два варианта визуализации. Первый связан с представлением той или иной ситуации как системы полярностей, которая в свою очередь моделируется в рамках векторной модели. В простейшем случае тезис и антитезис рассматриваются как два перпендикулярных вектора, а синтез – как их векторная сумма. В этом случае можно ввести и более количественную оценку «меры многомерности» полярной системы – как величины проекции её векторного представления на суммарный вектор. С использованием этих конструкций разбирается один пример из биоэтики, связанный со столкновением принципов милосердия и правдивости (проблема «лжи во спасение»). Деяние (действие или бездействие) интерпретируется как своеобразный оператор на событиях, который переводит одни события в другие. Предполагается, что субъект в своих деяниях рассматривает различные возможности и выбирает те из них, которые максимизируют ту или иную ценностную меру субъекта, в данном случае – меру векторной проекции полярного вектора ситуации на суммарный вектор – вектор синтеза базисных полярностей. Второй вариант визуализации связан с понятием антиномий в биоэтике – таких противоречий, которые не являются формально-логическими ошибками. В отличие от последних, в антиномиях как тезис, так и антитезис имеют свой момент оправдания в рамках тех или иных условий. Используется также понятие «антинома» – логического субъекта антиномии, который предицируется тезисом и антитезисом антиномии. Редукции антиномии соответствуют двум крайним аспектам антинома, которые называются его «редуктами» – по аналогии с редукцией волновой функции в квантовой механике. Приводятся различные примеры антиномов: биоэты, глоболоки, холомеры. В биоэтах один редукт выражает в большей мере биологические (биоредукт), второй – этические (эторедукт) определения антинома. В глоболоках выделяются глобальный (глоборедукт) и локальный (локоредукт) виды редуктов: первый выражает более глобальные (универсальные) этические определения, второй – более локальные, связанные с ценностями и нормами того или иного сообщества. Наконец, холомеры – вид антиномов, где антиномически соединяются определения целого (холоредукт) и части (мероредукт). Даётся их интерпретация как многомерных ментальных объектов в некотором обобщённом пространстве, так что крайние их аспекты (редукции антиномии) можно представить как проекции более многомерного состояния. В заключении делается предположение о связи биоэтических проблем с идеей ментальной многомерности, что составляет основу возможной визуализации как интерпретации ментальной многомерности на векторном её представлении. The article provides a brief outline of the antinomic nature of bioethical discourse and the possibilities of its geometric visualization. Two visualization options are considered. The first is associated with the representation of a particular situation as a system of polarities, which in turn is modeled in the framework of a vector model. In the simplest case, the thesis and the antithesis are considered as two orthogonal vectors P1 and P2, and the synthesis is considered as their vector sum S = P1+P2. In this case, we can also introduce a more quantitative estimate of the “measure of multidimensionality” M(P) of the polar system – as the magnitude of the projection of its vector representation P on the sum vector S, i.e. M(P) = (P,es), where es = S/|S| is the unit vector of the vector S, and (P,es) is the scalar product of the vectors P and es. Using these constructs, the author analyzes one example from bioethics related to the clash of the principles of mercy and truthfulness (the problem of “lying for salvation”). An act (action or omission) is interpreted as a kind of an operator on events that transforms some events into others. It is assumed that the subject considers various possibilities in their actions and chooses those that maximize a particular value measure of the subject, in our case, the measure M(P) of the vector projection of the polar vector P of the situation on the sum vector S – the vector of synthesis of basic polarities. The second version of visualization is related to the concept of antinomies – such contradictions that are not formal logical errors – in bioethics. In contrast to errors, in antinomies, both the thesis and the antithesis have their moment of justification within the framework of certain conditions. The concept “antinome” is also used; it is the logical subject of antinomy, which is predicated by the thesis and the antithesis of antinomy. Antinomy reductions correspond to two extreme aspects of the antinome, which are called its “reducts” – by analogy with the reduction of the wave function in quantum mechanics. Various examples of antinomes are given: bioets, globolocs, and holomers. In bioets, one reduct expresses the biological (bioreduct) definition of the antinome, another the ethical (ethoreduct) one. In globolocs, global (globoreduct) and local (locoreduct) types of reducts are distinguished: the former expresses more global (universal) ethical definitions, the latter more local ones, related to the values and norms of a particular local community. Finally, holomers are a kind of antinomes in which the definitions of the whole (holoreduct) and the part (meroreduct) are antinomically connected. They are interpreted as multidimensional mental objects in some generalized space, so that their extreme aspects (antinomy reductions) can be represented as generalized projections of a more multidimensional state within certain constricted conditions (reduction intervals). In this case, it is possible to geometrically visualize such states as, for example, three-dimensional objects in space, through which antinomes can be modeled, and their reducts as two-dimensional projections of a three-dimensional body on certain projection planes (intervals of reducts). In this case, one of the central tasks of bioethics is to determine the boundaries of the demarcation of some intervals from others. For example, in solving the problem of abortion and the status of the human embryo, such a demarcation is expressed in the search for a time point that would separate the phase of a more biological definition (bioreduct) of the embryo from its more ethical state (ethoreduct). In conclusion, the author suggests that bioethical problems are connected with the idea of mental multidimensionality, which forms the basis of a possible visualization as an interpretation of mental multidimensionality in its vector representation.

scholarly journals Fashion Window: A Conceptual Analysis Of Department Store Holiday Windows

2021 ◽  
Author(s):  
McKenzie Bohn
Keyword(s):  
Research Design ◽  
Conceptual Analysis ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Gestalt Theory ◽  
Fashion Industry ◽  
Art Object ◽  
The Subject ◽  
Window Displays ◽  
Three Dimensional Space

Window displays in the fashion industry are unique sites of meaning that combine advertising and artwork in a three-dimensional space. The current body of research surrounding window displays approaches the subject from a marketer’s position and attempts to evaluate performance. This project shifts the focus to the artistic qualities of window displays as they are used by fashion retailers. The primary theoretical lens is gestalt theory, which has applications in both psychology and design. The specific windows examined are the Christmas windows at retailer Saks Fifth Avenue Toronto in December of 2018. An autoethnographic research design is employed, resulting in an exploratory empirical analysis that serves as an entry into an under-represented area of study: the fashion window as an art object. The key findings of the project are the application of gestalt theory to the design of the windows and the researcher’s observations to suggest an explanation of the public’s response to the displays.

scholarly journals Celestial Spheres

2018 ◽  
Vol 2 (2) ◽  
pp. 168-186
Author(s):  
Austin M. Freeman
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Good Evidence ◽  
Medieval Period ◽  
The Bible ◽  
Higher Dimensional ◽  
Spatial Dimensions ◽  
Modern Physics ◽  
The Subject ◽  
Three Dimensional Space

Angels probably have bodies. There is no good evidence (biblical, philosophical, or historical) to argue against their bodiliness; there is an abundance of evidence (biblical, philosophical, historical) that makes the case for angelic bodies. After surveying biblical texts alleged to demonstrate angelic incorporeality, the discussion moves to examine patristic, medieval, and some modern figures on the subject. In short, before the High Medieval period belief in angelic bodies was the norm, and afterwards it is the exception. A brief foray into modern physics and higher spatial dimensions (termed “hyperspace”), coupled with an analogical use of Edwin Abbott’s Flatland, serves to explain the way in which appealing to higher-dimensional angelic bodies matches the record of angelic activity in the Bible remarkably well. This position also cuts through a historical equivocation on the question of angelic embodiment. Angels do have bodies, but they are bodies very unlike our own. They do not have bodies in any three-dimensional space we can observe, but are nevertheless embodied beings.

The Evaluation of Moments of Regions With Piecewise-Linearly Approximated Boundaries via Line Integration

1989 ◽  
Author(s):  
J. Angeles ◽  
M. J. Al-Daccak
Keyword(s):  
Euclidean Space ◽  
Three Dimensional ◽  
Inertia Tensor ◽  
Divergence Theorem ◽  
Dimensional Euclidean Space ◽  
Repeated Application ◽  
The Subject ◽  
First Moment

Abstract The subject of this paper is the computation of the first three moments of bounded regions imbedded in the three-dimensional Euclidean space. The method adopted here is based upon a repeated application of Gauss’s Divergence Theorem to reduce the computation of the said moments — volume, vector first moment and inertia tensor — to line integration. Explicit, readily implementable formulae are developed to evaluate the said moments for arbitrary solids, given their piecewise-linearly approximated boundary. An example is included that illustrates the applicability of the formulae.

GIS three-dimensional Modelling with geo-informatics techniques

2017 ◽  
Author(s):  
Katarzyna Bobkowska ◽  
Jakub Szulwic ◽  
Paweł Tysiac ◽  
Patryk Ziółkowski
Keyword(s):  
Data Model ◽  
Point Cloud ◽  
Satellite Images ◽  
Three Dimensional ◽  
Great Promise ◽  
Gis Model ◽  
High Resolution Satellite Images ◽  
Potential Applications ◽  
The Subject ◽  
Three Dimensional Models

The integration issue of virtual models and geo-referenced database have a very broad spectrum of potential applications. Before the integration issue was on the cusp, it was quite problematic to combine three-dimensional models with the geo-referenced database. An integrated database contains a variety of data including such as object orientated data model and raster data. Within this paper, authors present an integration process aiming to make real virtual GIS database which includes the creation of structures, such as bridges, buildings, roads and terrain formations. To create a three-dimensional GIS model high-resolution satellite images/point cloud has been used. For 3D modelling and reconstruction purposes, The Blender program has been used since the software provides with quick workflow and userfriendly interface. As a result of this study authors concede that integrated techniques for three-dimensional GIS databases allow conducting easy as well as sophisticated operation in an efficient and non-time consuming way. The subject holds great promise for a future, current challenges focusing on new approaches for conjectures of spatial objects that will be used to boost the capabilities for automatic visualization.

3D-Printed Conductive Filaments Based on Carbon Nanostructures Embedded in a Polymer Matrix

2021 ◽  
pp. 1725-1742
Author(s):  
Diogo José Horst ◽  
Pedro Paulo Andrade Junior
Keyword(s):  
Polymer Matrix ◽  
Carbon Nanostructures ◽  
Three Dimensional ◽  
Full Potential ◽  
Electrically Conductive ◽  
Three Dimensional Printing ◽  
Current State ◽  
3D Printed ◽  
The Subject ◽  
Dimensional Printing

Conductive and magnetic filaments are revolutionizing three-dimensional printing (3DP) to a new level. This review study presents the current state of the art on the subject, summarizing recent high impact studies about main advances regarding the application of 3DP filaments based on carbon nanostructures such as graphene, carbon fibers, nanotubes, and conductive carbon black embedded in a polymer matrix, by reviewing its main characteristics and showing the main producers and also the products available on the market. The availability of inexpensive, reliable, and electrically conductive material will be indispensable for the fabrication of circuits and sensors before the full potential of 3DP for customized products incorporating electrical elements can be fully explored.

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