The Analysis of Measurement Systems for the Construction of Geometrical Models of the Product

2016 ◽  
Vol 4 (1) ◽  
pp. 34-43 ◽  
Author(s):  
Браилов ◽  
A. Brailov
Keyword(s):  
Three Dimensional ◽  
Dimensional System ◽  
Two Dimensional ◽  
Side View ◽  
Horizontal Projection ◽  
American System ◽  
Geometrical Modeling ◽  
The Right ◽  
Frontal Projection ◽  
The Way

In the present work, on the basis of the analysis of existing systems of measurement for geometrical modeling, their components are defined. The system of measurement for geometrical modeling consists of three mutually perpendicular planes H-П1, F-П2, P-П3 and connected with them right three-dimensional system of coordinates OXYZ. The major features of such system related to ways of formation of the two-dimensional complex drawing of a geometrical image on the basis of laws of projective connections are revealed. As the first feature of systems of measurement for geometrical modeling it is possible to allocate a way of orientation (binding) of the right three-dimensional system of co-ordinates OXYZ concerning the set planes of projections H-П1, F-П2, P-П3. The second feature of systems of measurement for geometrical modeling is the way of conditional division of space on a part (semi spaces, quadrants, and octants). The third feature of systems of measurement for geometrical modeling is the way of numbering of the allocated parts of space (semi spaces, quadrants, and octants). Interrelations of elements of different systems of measurement with different projections of a geometrical image are defined. The relative location of projections of a geometrical image into the constructed two-dimensional complex drawings for various systems of measurement is determined. For the American system of measurement in the two-dimensional complex drawing of a geometrical image the horizontal projection is located above a frontal projection, and the profile projection is located to the right of a frontal projection. For the European system of measurement in the two-dimensional complex drawing of a geometrical image the horizontal projection is located below a frontal projection, and the profile projection is located to the right of a frontal projection. The logic behind a particular arrangement of views in the projective drawing of a product in the analyzed systems of measurement is explained. For the realized way of construction of the complex drawing in the American system of measurement the horizontal projection is the bottom view, and the profile projection is the left-side view. For the realized way of construction of the complex drawing in the European system of measurement the horizontal projection is the top view, and the profile projection is the left-side view.

scholarly journals Discrete-to-continuum modelling of weakly interacting incommensurate two-dimensional lattices

2018 ◽  
Vol 474 (2209) ◽  
pp. 20170612 ◽  
Author(s):  
Malena I. Español ◽  
Dmitry Golovaty ◽  
J. Patrick Wilber
Keyword(s):  
Continuum Model ◽  
Domain Walls ◽  
Three Dimensional ◽  
Variational Model ◽  
Dimensional System ◽  
Two Dimensional ◽  
Starting Point ◽  
Continuum Modelling ◽  
Three Dimensional System ◽  
The Continuum

In this paper, we derive a continuum variational model for a two-dimensional deformable lattice of atoms interacting with a two-dimensional rigid lattice. The starting point is a discrete atomistic model for the two lattices which are assumed to have slightly different lattice parameters and, possibly, a small relative rotation. This is a prototypical example of a three-dimensional system consisting of a graphene sheet suspended over a substrate. We use a discrete-to-continuum procedure to obtain the continuum model which recovers both qualitatively and quantitatively the behaviour observed in the corresponding discrete model. The continuum model predicts that the deformable lattice develops a network of domain walls characterized by large shearing, stretching and bending deformation that accommodates the misalignment and/or mismatch between the deformable and rigid lattices. Two integer-valued parameters, which can be identified with the components of a Burgers vector, describe the mismatch between the lattices and determine the geometry and the details of the deformation associated with the domain walls.

Separation of the 3D stress state of a loaded plate into two-dimensional tasks: bending and symmetric compression of the plate

2021 ◽  
Vol 103 (3) ◽  
pp. 53-62
Author(s):  
Victor Revenko ◽  
Andrian Revenko
Keyword(s):  
Boundary Conditions ◽  
Harmonic Functions ◽  
Three Dimensional ◽  
Partial Solution ◽  
Theory Of Elasticity ◽  
Two Dimensional ◽  
Normal Stresses ◽  
Equilibrium Equations ◽  
Dimensional Boundary ◽  
The Right

The three-dimensional stress-strain state of an isotropic plate loaded on all its surfaces is considered in the article. The initial problem is divided into two ones: symmetrical bending of the plate and a symmetrical compression of the plate, by specified loads. It is shown that the plane problem of the theory of elasticity is a special case of the second task. To solve the second task, the symmetry of normal stresses is used. Boundary conditions on plane surfaces are satisfied and harmonic conditions are obtained for some functions. Expressions of effort were found after integrating three-dimensional stresses that satisfy three equilibrium equations. For a thin plate, a closed system of equations was obtained to determine the harmonic functions. Displacements and stresses in the plate were expressed in two two-dimensional harmonic functions and a partial solution of the Laplace equation with the right-hand side, which is determined by the end loads. Three-dimensional boundary conditions were reduced to two-dimensional ones. The formula was found for experimental determination of the sum of normal stresses via the displacements of the surface of the plate.

scholarly journals Making Anaglyphs in Photoshop

2005 ◽  
Vol 13 (3) ◽  
pp. 36-39 ◽  
Author(s):  
Jerry Sedgewick
Keyword(s):  
Imaging System ◽  
Three Dimensional ◽  
Ct Scans ◽  
Two Dimensional ◽  
The Right ◽  
Two Dimensional Images

In order to achieve a three dimensional appearance to a pair of two dimensional images, two off-axis images can be produced and colorized. These can be overlayed slightly apart and then viewed through glasses with two differently colored sides, one color for the left eye and another for the right eye in combinations containing red, green or blue colors. These off-axis and colorized images are referred to as anaglyphs.Off-axis images can be achieved through the use of a tilting stage on a microscope, by physically changing the position of a camera in relation to a still object, or through changing the axis of an optical stack of sections, such as what is created by confocal/CT scans. Some images lend themselves more to a 3D look both by virtue of inherent three dimensionality limited by the resolution of the imaging system.

scholarly journals Stability and Bifurcation Analysis for a Predator-Prey Model with Discrete and Distributed Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Ruiqing Shi ◽  
Junmei Qi ◽  
Sanyi Tang
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Three Dimensional ◽  
Distributed Delay ◽  
Dimensional System ◽  
Two Dimensional ◽  
Normal Form Theory ◽  
Predator Prey Model ◽  
Prey Model ◽  
Form Theory

We propose a two-dimensional predatory-prey model with discrete and distributed delay. By the use of a new variable, the original two-dimensional system transforms into an equivalent three-dimensional system. Firstly, we study the existence and local stability of equilibria of the new system. And, by choosing the time delayτas a bifurcation parameter, we show that Hopf bifurcation can occur as the time delayτpasses through some critical values. Secondly, by the use of normal form theory and central manifold argument, we establish the direction and stability of Hopf bifurcation. At last, an example with numerical simulations is provided to verify the theoretical results. In addition, some simple discussion is also presented.

scholarly journals The interaction of atoms and molecules with solid surfaces XII—Critical phenomena in a two-dimensional gas

1937 ◽  
Vol 163 (912) ◽  
pp. 132-138 ◽  
Keyword(s):  
Critical Temperature ◽  
Equation Of State ◽  
Critical Phenomena ◽  
Three Dimensional ◽  
Inert Gases ◽  
Two Dimensional ◽  
Lennard Jones ◽  
Low Concentrations ◽  
High Concentrations ◽  
The Right

In a paper recently published by Professor Lennard-Jones and the author (Lennard-Jones and Devonshire 1937) the equation of state of a gas at high concentrations has been calculated in terms of the interatomic fields. The equation found had the right kind of properties and, in particular, using the interatomic fields previously determined from the observed equation of state at low concentrations (Lennard-Jones 1931), the critical temperature was given correctly to within a few degrees for the inert gases. In this paper we shall apply the same method to determine the equation of state of a two-dimensional gas. Although such a gas cannot strictly be obtained in practice, an inert gas adsorbed on a surface (or in fact any gas held by van der Waals’ forces only) would probably behave very much like one, the fluctuations of the potential field over the surface not being of much importance. In confirmation of this it may be noted that the specific heat of argon adsorbed on charcoal was found by Simon (Simon 1935) to be equal to that of a perfect two-dimensional gas down to 60° K. A gas adsorbed on a liquid would be an even better representation of a two-dimensional one. Some measurements on the adsorption of krypton and xenon on liquid mercury have been made by Cassel and Neugebauer (Cassel and Neugebauer 1936), and they found no trace of any critical phenomena though they worked at temperatures considerably below the critical temperature of xenon. Our results are in agreement with this, for they show that the critical temperature of a two-dimensional gas should be about half that of the corresponding three-dimensional one.

Action potential morphology heterogeneity in the atrium and its effect on atrial reentry: a two-dimensional and quasi-three-dimensional study

2006 ◽  
Vol 364 (1843) ◽  
pp. 1349-1366 ◽  
Author(s):  
Samuel R Kuo ◽  
Natalia A Trayanova
Keyword(s):  
Action Potential ◽  
Action Potentials ◽  
Three Dimensional ◽  
Spiral Wave ◽  
Spiral Waves ◽  
Two Dimensional ◽  
Crista Terminalis ◽  
Wave Dynamics ◽  
Continuous Surface ◽  
The Right

Atrial fibrillation (AF) is believed to be perpetuated by recirculating spiral waves. Atrial structures are often characterized with action potentials of varying morphologies; however, the role of the structure-dependent atrial electrophysiological heterogeneity in spiral wave behaviour is not well understood. The purpose of this study is to determine the effect of action potential morphology heterogeneity associated with the major atrial structures in spiral wave maintenance. The present study also focuses on how this effect is further modulated by the presence of the inherent periodicity in atrial structure. The goals of the study are achieved through the simulation of electrical behaviour in a two-dimensional atrial tissue model that incorporates the representation of action potentials in various structurally distinct regions in the right atrium. Periodic boundary conditions are then imposed to form a cylinder (quasi three-dimensional), thus allowing exploration of the additional effect of structure periodicity on spiral wave behaviour. Transmembrane potential maps and phase singularity traces are analysed to determine effects on spiral wave behaviour. Results demonstrate that the prolonged refractoriness of the crista terminalis (CT) affects the pattern of spiral wave reentry, while the variation in action potential morphology of the other structures does not. The CT anchors the spiral waves, preventing them from drifting away. Spiral wave dynamics is altered when the ends of the sheet are spliced together to form a cylinder. The main effect of the continuous surface is the generation of secondary spiral waves which influences the primary rotors. The interaction of the primary and secondary spiral waves decreased as cylinder diameter increased.

Wayfaring Images

2018 ◽  
Author(s):  
Nathalie Collé-Bak
Keyword(s):  
Three Dimensional ◽  
Photographic Film ◽  
Two Dimensional ◽  
Book Market ◽  
Pilgrim's Progress ◽  
Cultural Boundaries ◽  
Three Dimensional Images ◽  
The Way

The Pilgrim’s Progress (1678; 1684) has been illustrated in many different forms and media, from its early days on the book market up until today. For over the last three centuries, John Bunyan’s allegory has inspired illustrators in numerous and varied ways, the images born of the text having materialized on book pages as well as on individual sheets, but also on canvas, photographic film, glass panes, and walls. Two-dimensional creations have also led the way to three-dimensional images, exhibited or performed in a variety of places and for a whole range of publics. This chapter contends that these sundry ‘illustrations’, by professional as well as amateur artists, have secured the diffusion and the popularity of the text through its temporal and geographical journeys, and across cultural boundaries.

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