scholarly journals SOME PROPERTIES OF THE HYPERSPHERE IN N-DIMENSIONAL SPACE

2021 ◽  
pp. 153-161
Author(s):  
Sergiy Kovalov ◽  
Oleksandr Mostovenko
Keyword(s):  
Geometric Modeling ◽  
Dimensional Space ◽  
Geometric Model ◽  
Physical Nature ◽  
Arbitrary Point ◽  
Point Sources ◽  
Energy Sources ◽  
Point Energy ◽  
Energy Field ◽  
Multidimensional Geometry

The study of the properties of surfaces contributes to the expansion of their use in solving various practical problems, especially if such properties can be generalized to manifolds of n-dimensional space. The most thoroughly studied are the properties of the simplest surfaces, including the properties of a sphere. That is why the simplest surfaces are most often used in practice. Each property not covered in the existing literature expands the indicated possibilities. Therefore, the purpose of this article is to identify the properties of the hypersphere unknown from the literature. Most of the properties of a circle and a sphere have been known since ancient times [1, 4, 5]. The generalized concept of a sphere into multidimensional spaces is based on the general principles of multidimensional geometry [3]. In [4], eleven basic properties of the sphere are listed and analyzed. In works [8, 10] it is shown that a circle can be considered as an isoline, and a sphere as an isosurface when modeling energy fields. In geometric modeling of energy fields with point energy sources, an essential role is played by the distances from the points of the field to the given energy sources [6, 7]. In [9], two schemes are given for determining the parameter t, taking into account the effect of the distance from the points of the field to the point sources of energy on the potentials of the points of the field. In a particular case, if this parameter is determined according to a simplified scheme with f(l)=al2, then the formula for calculating the potential of an arbitrary point of the energy field is a mathematical model of the energy field generated by the number n of point energy sources. The geometric model of the field will be a manifold that can be foliated into a one-parameter set of isospheres [8, 10]. Abstracting from the physical nature of the field, simplifying the equation for calculating the potential of an arbitrary point of the energy field and generalizing it to n-dimensional space, we can formulate the following properties: Property 1. A hypersphere can be considered as a locus of points, the sum of the squared distances from which to n given points is a constant value. Property 2. Arbitrary coefficients ki at distances li affect the parameters of the hypersphere without changing the type of surface.

scholarly journals Geometrical Model of the Manufacturing Surface of the Equivalent Working Surface of the Fine Tooth Dolbyak

2019 ◽  
Author(s):  
С. Рязанов ◽  
S. Ryazanov ◽  
Михаил Решетников ◽  
Mihail Reshetnikov
Keyword(s):  
Computer Modeling ◽  
Geometric Modeling ◽  
Dimensional Space ◽  
Geometric Model ◽  
Three Dimensional ◽  
Geometrical Model ◽  
Analytic Description ◽  
Computer Algorithms ◽  
Gear Cutting ◽  
Working Surface

Existing mathematical models for calculating gearing are quite complex and do not always make it possible to quickly and accurately obtain the desired result. A simpler way to find a suitable gear option that satisfies the task is to use computer modeling and computer graphics methods, and in particular solid-state modeling algorithms. The use of geometric modeling techniques to simulate the process of shaping the working surface of gearing is based on the relative movement of intersecting objects in the form of a “workpiece-tool” system. This allows you to obtain the necessary geometric model that accurately reproduces the geometric configuration of the surfaces of the teeth of spatial gears, taking into account the technological features of their production on gear cutting machines. This information allows you to perform on the computer imitation control the movement of the cutting tool. Ultimately, this boils down to the problem of analytic description and computer representation of curves and surfaces in three-dimensional space. As the gear cutting tools, the most widely used are disk and worm modular mills (shaver), gear cutting heads, dolbyaki and lath tools. At the moment there are no computer algorithms for obtaining the “dolbyak” producing surfaces, which are obtained by a tool with a modified producing surface. A change in the geometric shape of the tool producing surface will lead to a change in its working surfaces, which may lead to an improvement in their contact. This article shows the application of the developed methods and algorithms of geometric and computer modeling, which are intended for shaping the working surfaces of the Dolbyak tool. Their application will speed up the process of calculating intermediate adjustments of machines used for cutting gears, bypassing complex mathematical calculations that, under conditions of aging of the gear-cutting machines, their wear and the inevitable reduction in the accuracy of their kinematic chains.

scholarly journals The Concept of Multiple Impacts of Renewable Energy Sources: A Critical Review

Energies ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 3183
Author(s):  
Michaela Makešová ◽  
Michaela Valentová
Keyword(s):  
Renewable Energy ◽  
Energy Policy ◽  
Renewable Energy Sources ◽  
Energy Sources ◽  
The European Union ◽  
Multiple Impacts ◽  
Energy Field ◽  
Full Picture ◽  
The Difference ◽  
Social Environmental

Reaching climate neutrality by 2050 is one of the main long-term objectives of the European Union climate and energy policy, and renewable energy sources (RES) are integral parts of this transition. RES development results in many effects, direct and indirect, linked to each other, societal, local and individual, i.e., “multiple impacts of RES” (MI RES). These effects need to be carefully assessed and evaluated to obtain the full picture of energy field transformation and its context, and enable further development of RES. Nevertheless, the MI RES concept is often presented misleadingly and its scope varies throughout the literature. This paper provides a literature overview of the methodologies of this concept and presents a new concept of MI RES, respecting the difference between effects resulting from the implementation of RES and ultimate multiple impacts. We have summarized the effects into four groups: economic, social, environmental, and technical, which all lead to group of ultimate multiple impacts. Finally, we provide the complex overview of all MI RES and present the framework, which is used to analyze the multiple impacts and effects of RES and to show how the RES development leads and contributes to these impacts and effects. The concept is recommended to be considered in designing a robust energy policy by decision-makers.

scholarly journals The Method of High Accuracy Calculation of Robot Trajectory for the Complex Curves

2020 ◽  
Vol 28 (4) ◽  
pp. 247-252
Author(s):  
Alexander Lozhkin ◽  
Pavol Bozek ◽  
Konstantin Maiorov
Keyword(s):  
Calculation Method ◽  
Geometric Modeling ◽  
Classical Method ◽  
Geometric Model ◽  
New Method ◽  
Approximation Methods ◽  
Linear Transformations ◽  
Design Quality ◽  
Complex Curves ◽  
Internal Properties

AbstractThe geometric model accuracy is crucial for product design. More complex surfaces are represented by the approximation methods. On the contrary, the approximation methods reduce the design quality. A new alternative calculation method is proposed. The new method can calculate both conical sections and more complex curves. The researcher is able to get an analytical solution and not a sequence of points with the destruction of the object semantics. The new method is based on permutation and other symmetries and should have an origin in the internal properties of the space. The classical method consists of finding transformation parameters for symmetrical conic profiles, however a new procedure for parameters of linear transformations determination was acquired by another method. The main steps of the new method are theoretically presented in the paper. Since a double result is obtained in most stages, the new calculation method is easy to verify. Geometric modeling in the AutoCAD environment is shown briefly. The new calculation method can be used for most complex curves and linear transformations. Theoretical and practical researches are required additionally.

scholarly journals VISUAL GEOMETRIC POWER FIELD MODEL WITH TWO POINT ENERGY SOURCES

2019 ◽  
Vol 16 ◽  
pp. 140-146
Author(s):  
S. Kovalov ◽  
◽  
O. Mostovenko ◽  
Keyword(s):  
Field Model ◽  
Energy Sources ◽  
Point Energy

scholarly journals MODELING ARCHITECTURAL FORM SURFACE DEPENDENT SECTIONS

2021 ◽  
pp. 53-58
Author(s):  
A. A. Chekalin ◽  
M. K. Reshetnikov ◽  
V. V. Shpilev ◽  
S. V. Borodulina ◽  
S. A. Ryazanov
Keyword(s):  
Geometric Modeling ◽  
Geometric Model ◽  
Residential Building ◽  
Cubic Splines ◽  
Piecewise Smooth ◽  
Additional Parameter ◽  
Mathematical Apparatus ◽  
Surface Design ◽  
Fourth Degree ◽  
Architectural Form

For the design of surfaces in architecture, as a rule, universal techniques developed for other technical industries are used. First of all, these are general kinematic surfaces and interpolation cubic splines for modeling complex piecewise smooth surfaces. The authors propose to use the fourth degree inerodifferential spline developed by them for problems of geometric modeling of architectural forms. For calculations and constructions on a computer, the proposed spline is not much more complicated than traditional cubic splines, since it has one additional parameter - a coefficient. However, this allows you to locally control the shape of a curve or surface during design, that is, to change the shape in individual areas without affecting other areas. The article proposes a method for constructing a geometric model of the kinematic surface of dependent sections with a fourth degree parabola as a generator. When using cubic splines as a guide, the surface is a 3 × 4 non-uniform (heterogeneous) spline. The article shows that the surface on the basis of the proposed mathematical apparatus can be composite piecewise-smooth. A particular case of surface design is considered on the example of creating a model of the surface of the facade of a residential building according to the existing concept. The algorithm can be easily programmed and added as a tool to existing CAD systems.

BIOMECHANICAL MODEL PREDICTING VALUES OF MUSCLE FORCES IN THE SHOULDER GIRDLE DURING ARM ELEVATION

2010 ◽  
Vol 10 (04) ◽  
pp. 643-666 ◽  
Author(s):  
ERIC BERTHONNAUD ◽  
MELISSA MORROW ◽  
GUILLAUME HERZBERG ◽  
KAI-NAN AN ◽  
JOANNES DIMNET
Keyword(s):  
Geometric Modeling ◽  
Geometric Model ◽  
Contractile Element ◽  
Muscle Forces ◽  
Active Muscle ◽  
Cross Sectional ◽  
Shoulder Complex ◽  
Arm Elevation

A three-dimensional (3D) geometric model for predicting muscle forces in the shoulder complex is proposed. The model was applied throughout the range of arm elevation in the scapular plan. In vitro testing has been performed on 13 cadaveric shoulders. The objectives were to determine homogeneous values of physiological parameters of shoulder muscles and to locate sites of muscular attachment to any bone of the shoulder complex. Muscular fiber lengths, lengths of contractile element (CE), and muscle volumes were measured, corresponding physiological cross-sectional area (PCSA) were calculated, and force/length muscle relations were found. An in vivo biplanar radiography was performed on five volunteers. The photogrammetric reconstruction of bone axes and landmarks were coupled with a geometric modeling of bones and muscle sites of attachment. Muscular paths were drawn and changes in lengths during movement have been estimated. Directions of muscle forces are the same as that of muscular path at the point of attachment to bone. Magnitudes of muscular forces were found from muscle lengths coupled with force/length relations. Passive forces were directly determined contrary to active muscle forces. A resulting active muscle force is calculated from balancing weight and passive forces at each articular center. Active muscle forces were calculated by distributing the resulting force among active muscles based on the muscular PCSA values.

scholarly journals Geometric modeling of surfaces dependent cross sections in the tasks of spinning and laying

2019 ◽  
Vol 110 ◽  
pp. 01057
Author(s):  
Yuri Deniskin ◽  
Pavel Miroshnichenko ◽  
Andrew Smolyaninov
Keyword(s):  
Composite Materials ◽  
Cross Sections ◽  
Geometric Modeling ◽  
Geometric Model ◽  
Solid Modeling ◽  
Uniform Method ◽  
Calculation Methods ◽  
Related Process

The article is devoted to the development of a geometric model of surfaces of dependent sections to solve the problems of winding by continuous fibers in the direction of the force and its related process of automated winding of composite materials. A uniform method for specifying the surfaces of dependent sections with a curvilinear generator and a method for solid modeling of the shell obtained by winding or calculation methods are described.

CASIMIR FORCE BETWEEN A GRAVITATIONAL FIELD AND A FINITE OBJECT

2002 ◽  
Vol 11 (10) ◽  
pp. 1567-1572 ◽  
Author(s):  
FABRIZIO PINTO
Keyword(s):  
Gravitational Field ◽  
Casimir Force ◽  
Casimir Effect ◽  
Finite Size ◽  
Zero Point ◽  
Point Energy ◽  
Energy Field ◽  
Static Gravitational Field ◽  
Vacuum Gap ◽  
Infinite Media

In the typical Casimir effect, the boundaries of two semi-infinite media exert a force upon one another across a vacuum gap separating them. In this paper, I argue that a static gravitational field can be regarded as a "soft" boundary which interacts with a test object of finite size through the electromagnetic zero-point-energy field. Therefore, a pressure exists upon a single slab placed in a gravitational field and surrounded by a vacuum. Interestingly, this extremely small Casimir pressure of the gravitational field may cause relative displacements in ground-based sensing microstructures larger than those from astrophysical gravitational waves in macroscopic antennas.

Design Manifolds Capture the Intrinsic Complexity and Dimension of Design Spaces

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
Wei Chen ◽  
Mark Fuge ◽  
Jonah Chazan
Keyword(s):  
Geometric Modeling ◽  
Design Space ◽  
Dimensional Space ◽  
Consumer Preference ◽  
Shape Reconstruction ◽  
Pairwise Distance ◽  
Design Parameters ◽  
Improve Design ◽  
Intrinsic Complexity ◽  
Semantic Attributes

This paper shows how to measure the intrinsic complexity and dimensionality of a design space. It assumes that high-dimensional design parameters actually lie in a much lower-dimensional space that represents semantic attributes—a design manifold. Past work has shown how to embed designs using techniques like autoencoders; in contrast, the method proposed in this paper first captures the inherent properties of a design space and then chooses appropriate embeddings based on the captured properties. We demonstrate this with both synthetic shapes of controllable complexity (using a generalization of the ellipse called the superformula) and real-world designs (glassware and airfoils). We evaluate multiple embeddings by measuring shape reconstruction error, pairwise distance preservation, and captured semantic attributes. By generating fundamental knowledge about the inherent complexity of a design space and how designs differ from one another, our approach allows us to improve design optimization, consumer preference learning, geometric modeling, and other design applications that rely on navigating complex design spaces. Ultimately, this deepens our understanding of design complexity in general.

DESIGN OF A NOVEL STENTED VALVE AND 3D MODELING OF ITS IMPLANTATION IN THE AORTA

2010 ◽  
Vol 22 (02) ◽  
pp. 157-161 ◽  
Author(s):  
Gideon Praveen Kumar ◽  
Lazar Mathew
Keyword(s):  
Aortic Valve ◽  
Left Ventricle ◽  
3D Modeling ◽  
Geometric Modeling ◽  
Geometric Model ◽  
Bioprosthetic Heart Valve ◽  
3D Cad ◽  
Percutaneous Aortic Valve Replacement ◽  
Improved Design ◽  
Valve Model

Objective: To design a novel percutaneous stented valve and model its implantation in the aorta.Background: The dimensions of stented aortic valve components govern its ability to prevent backflow of blood into the left ventricle. Whilst the theoretical parameters for the best stent performance have already been established, an effective valve model and its suitability along with the stent are lacking.Methods: This article discusses the design of a stented valve suitable for percutaneous aortic valve replacement. Steps involved in 3D CAD-based geometric modeling of the stented aortic valve and its implantation in the aorta are presented. Conceptual designing of individual components was used to build the total geometric model.Results: A novel geometric model of percutaneous stented aortic valve was generated. The improved design enhances its performance during and after implantation.Conclusion: The blunt hooks in the stent model prevent its migration in either direction by getting embedded in the aortic endothelium. This novel stent aortic valve may be of great interest to designers of future bioprosthetic heart valve models, as well as to surgeons involved in minimally invasive valve surgeries.

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