scholarly journals Detection of Symmetry and Repetition in One and Two Objects

2009 ◽  
Vol 56 (1) ◽  
pp. 5-17 ◽  
Author(s):  
Arno Koning ◽  
Johan Wagemans
Keyword(s):  
Three Dimensional ◽  
Intrinsic Property ◽  
Spatial Relations ◽  
Two Dimensional ◽  
Single Object ◽  
Ground Segmentation ◽  
Matching Strategy ◽  
The One

Symmetry is usually easier to detect within a single object than in two objects (one-object advantage), while the reverse is true for repetition (two-objects advantage). This interaction between regularity and number of objects could reflect an intrinsic property of encoding spatial relations within and across objects or it could reflect a matching strategy. To test this, regularities between two contours (belonging to a single object or two objects) had to be detected in two experiments. Projected three-dimensional (3-D) objects rotated in depth were used to disambiguate figure-ground segmentation and to make matching based on simple translations of the two-dimensional (2-D) contours unlikely. Experiment 1 showed the expected interaction between regularity and number of objects. Experiment 2 used two-objects displays only and prevented a matching strategy by also switching the positions of the two objects. Nevertheless, symmetry was never detected more easily than repetition in these two-objects displays. We conclude that structural coding, not matching strategies, underlies the one-object advantage for symmetry and the two-objects advantage for repetition.

Preliminary Ship Design Using One and Two-Dimensional Models

1999 ◽  
Vol 36 (02) ◽  
pp. 102-112
Author(s):  
Michael D. A. Mackney ◽  
Carl T. F. Ross
Keyword(s):  
Finite Element ◽  
Dimensional Analysis ◽  
Three Dimensional ◽  
Two Dimensional ◽  
One Dimensional ◽  
Dimensional Finite Element ◽  
Dimensional Models ◽  
Support Conditions ◽  
The One ◽  
Three Dimensional Finite Element

Computational studies of hull-superstructure interaction were carried out using one-, two-and three-dimensional finite element analyses. Simplification of the original three-dimensional cases to one- and two-dimensional ones was undertaken to reduce the data preparation and computer solution times in an extensive parametric study. Both the one- and two-dimensional models were evaluated from numerical and experimental studies of the three-dimensional arrangements of hull and superstructure. One-dimensional analysis used a simple beam finite element with appropriately changed sections properties at stations where superstructures existed. Two-dimensional analysis used a four node, first order quadrilateral, isoparametric plane elasticity finite element, with a corresponding increase in the grid domain where the superstructure existed. Changes in the thickness property reflected deck stiffness. This model was essentially a multi-flanged beam with the shear webs representing the hull and superstructure sides, and the flanges representing the decks One-dimensional models consistently and uniformly underestimated the three-dimensional behaviour, but were fast to create and run. Two-dimensional models were also consistent in their assessment, and considerably closer in predicting the actual behaviours. These models took longer to create than the one-dimensional, but ran in very much less time than the refined three-dimensional finite element models Parametric insights were accomplished quickly and effectively with the simplest model and processor, but two-dimensional analyses achieved closer absolute measure of the displacement behaviours. Although only static analysis with simple loading and support conditions were presented, it is believed that similar benefits would be found for other loadings and support conditions. Other engineering components and structures may benefit from similarly judged simplification using one- and two-dimensional models to reduce the time and cost of preliminary design.

scholarly journals The Biomechanics of Erections: Modeling the Penis as a One-Comparment Pressurized Vessel vs. Modeling it as a Two-Compartments Pressurized Vessel

2009 ◽  
Vol 3 (2) ◽  
Author(s):  
A. Mohamed ◽  
A. Erdman ◽  
G. Timm
Keyword(s):  
Structural Integrity ◽  
Tunica Albuginea ◽  
Three Dimensional ◽  
The Body ◽  
Physical Models ◽  
Von Mises Stress ◽  
Two Dimensional ◽  
Biomechanical Models ◽  
Significant Difference ◽  
The One

Previous biomechanical models of the penis that have attempted to simulate penile erections have either been limited to two-dimensional geometry, simplified three-dimensional geometry or made inaccurate assumptions altogether. Most models designed the shaft of the penis as a one-compartment pressurized vessel fixed at one end, when in reality it is a two-compartments pressurized vessel, in which the compartments diverge as they enter the body and are fixed at two separate points. This study began by designing simplified two-dimensional and three-dimensional models of the erect penis using Finite Element Analysis (FEA) methods with varying anatomical considerations for analyzing structural stresses, axial buckling and lateral deformation. The study then validated the results by building physical models replicating the computer models. Finally a more complex and anatomically accurate model of the penis was designed and analyzed. There was a significant difference in the peak von-Mises stress distribution between the one-compartment pressurized vessel and the more anatomically correct two-compartments pressurized vessel. Furthermore, the two-compartments diverging pressurized vessel was found to have more structural integrity when subject to external lateral forces than the one-compartment pressurized vessel. This study suggests that Mother Nature has favored an anatomy of two corporal cavernosal bodies separated by a perforated septum as opposed to one corporal body, due to better structural integrity of the tunica albuginea when subject to external forces.

Fuzzy Three-Dimensional Voronoi Diagram and its Application to Geographical Data Analysis

2012 ◽  
Vol 16 (2) ◽  
pp. 191-198
Author(s):  
Mian Dai ◽  
◽  
Fangyan Dong ◽  
Kaoru Hirota
Keyword(s):  
Voronoi Diagram ◽  
Three Dimensional ◽  
Spatial Relation ◽  
Spatial Relations ◽  
Mountainous Area ◽  
Two Dimensional ◽  
Spatial Direction ◽  
Geographical Data ◽  
Direction Relations ◽  
Complex Boundaries

A concept of fuzzy three-dimensional Voronoi Diagram is presented for spatial relations analysis of real world three-dimensional geographical data, where it is an extension of well known two-dimensional Voronoi Diagram to three-dimensional representation with uncertain spatial relation information in terms of fuzzy set. It makes possible to analyze quantitatively complex boundaries of geographically intricate areas, to give human friendly fuzzy explanation of determining three-dimensional directions, and to express uncertain spatial relations by precise unified fuzzy description. It is applied to decide spatial direction relations of artificial geographicalmountain data, which includes 8 spatial directions with at most 60 relative direction relations, and it leads to detect threedimensional directions whereas the expression of traditional 4 directions and 12 relative directions indicate two-dimensional directions only. The proposed concept aims to discriminate neighbors’ class relations and spatial-temporal changes of specially appointed objects, and also aims to be a tool to achieve the intellective extraction and analysis of geographical data of a mountainous area located in northeast China.

A novel one-dimensional silver cylinder stabilized by mixed 2-mercaptobenzoic acid and ethylenediamine ligands

2012 ◽  
Vol 68 (8) ◽  
pp. m229-m232
Author(s):  
Di Sun ◽  
Zhi-Hao Yan
Keyword(s):  
Three Dimensional ◽  
Van Der Waals Interactions ◽  
Two Dimensional ◽  
Binding Modes ◽  
Supramolecular Framework ◽  
One Pot ◽  
Tetrahedral Geometry ◽  
Coordination Environment ◽  
One Dimensional ◽  
The One

A novel infinite one-dimensional silver cylinder, namely poly[μ-ethylenediamine-μ5-(2-sulfanidylbenzoato)-μ4-(2-sulfanidylbenzoato)-tetrasilver(I)], [Ag4(C7H4O2S)2(C2H8N2)]n, has been synthesized by one-pot reaction of equivalent molar silver nitrate and 2-mercaptobenzoic acid (H2mba) in the presence of ethylenediamine (eda). One Ag atom is located in an AgS2NO four-coordinated tetrahedral geometry, two other Ag atoms are in an AgS2O three-coordinated T-shaped geometry and the fourth Ag atom is in an AgSNO coordination environment. The two mba ligands show two different binding modes. The μ2-N:N′-eda ligand, acting as a bridge, combines with mba ligands to extend the AgIions into a one-dimensional silver cylinder incorporating abundant Ag...Ag interactions ranging from 2.9298 (11) to 3.2165 (13) Å. Interchain N—H...O hydrogen bonds extend the one-dimensional cylinder into an undulating two-dimensional sheet, which is further packed into a three-dimensional supramolecular framework by van der Waals interactions; no π–π interactions were observed in the crystal structure.

scholarly journals Optimal control of the two-dimensional Vlasov-Maxwell system

2020 ◽  
Author(s):  
Jörg Weber
Keyword(s):  
Adjoint Equation ◽  
Collisionless Plasma ◽  
Three Dimensional ◽  
Classical Solutions ◽  
Two Dimensional ◽  
Maxwell System ◽  
Global Classical Solutions ◽  
Global Existence Of Solutions ◽  
Dimensional Version ◽  
The One

The time evolution of a collisionless plasma is modeled by the Vlasov-Maxwell system which couples the Vlasov equation (the transport equation) with the Maxwell equations of electrodynamics. We only consider a two-dimensional version of the problem since existence of global, classical solutions of the full three-dimensional problem is not known. We add external currents to the system, in applications generated by coils, to control the plasma properly. After considering global existence of solutions to this system, differentiability of the control-to-state operator is proved. In applications, on the one hand, we want the shape of the plasma to be close to some desired shape. On the other hand, a cost term penalizing the external currents shall be as small as possible. These two aims lead to minimizing some objective function. We restrict ourselves to only such control currents that are realizable in applications. After that, we prove existence of a minimizer and deduce first order optimality conditions and the adjoint equation.

Combined Effects of 2D and 3D Inhomogeneities on the Dynamic Susceptibility of Superlattices

2010 ◽  
Vol 168-169 ◽  
pp. 97-100
Author(s):  
V.A. Ignatchenko ◽  
D.S. Tsikalov
Keyword(s):  
Density Of States ◽  
Three Dimensional ◽  
Wave Number ◽  
Dynamic Susceptibility ◽  
Combined Effects ◽  
Two Dimensional ◽  
Simultaneous Presence ◽  
One Dimensional ◽  
The One ◽  
2D And 3D

The dynamic susceptibility and the one-dimensional density of states (DOS) of an initially sinusoidal superlattice (SL) with simultaneous presence of two-dimensional (2D) phase inhomogeneities that simulate the deformations of the interfaces between the SL’s layers and three-dimensional (3D) amplitude inhomogeneities of the layer material of the SL were investigated. An analytical expression for the averaged Green’s function of the sinusoidal SL with 2D phase inhomogeneities was obtained in the Bourret approximation. It was shown that the effect of increasing asymmetry of heights of the dynamic susceptibility peaks at the edge of the Brillouin zone of the SL, which was found in [6] at increasing the rms fluctuations of 2D inhomogeneities, also takes place at increasing the correlation wave number of such inhomogeneities. It was also shown that the increase of the rms fluctuations of 3D amplitude inhomogeneities in the superlattice with 2D phase inhomogeneities leads to the suppression of the asymmetry effect and to the decrease of the depth of the DOS gap.

scholarly journals The Lagrangian and Hamiltonian for the Two-Dimensional Mathews-Lakshmanan Oscillator

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Wang Guangbao ◽  
Ding Guangtao
Keyword(s):  
Lagrange Function ◽  
Three Dimensional ◽  
Hamiltonian Function ◽  
First Integral ◽  
Dimensional Case ◽  
Analytical Mechanics ◽  
Two Dimensional ◽  
Rectangular Coordinates ◽  
Polar Coordinate ◽  
The One

The purpose of this paper is to illustrate the theory and methods of analytical mechanics that can be effectively applied to the research of some nonlinear nonconservative systems through the case study of two-dimensionally coupled Mathews-Lakshmanan oscillator (abbreviated as M-L oscillator). (1) According to the inverse problem method of Lagrangian mechanics, the Lagrangian and Hamiltonian function in the form of rectangular coordinates of the two-dimensional M-L oscillator is directly constructed from an integral of the two-dimensional M-L oscillators. (2) The Lagrange and Hamiltonian function in the form of polar coordinate was rewritten by using coordinate transformation. (3) By introducing the vector form variables, the two-dimensional M-L oscillator motion differential equation, the first integral, and the Lagrange function are written. Therefore, the two-dimensional M-L oscillator is directly extended to the three-dimensional case, and it is proved that the three-dimensional M-L oscillator can be reduced to the two-dimensional case. (4) The two direct integration methods were provided to solve the two-dimensional M-L oscillator by using polar coordinate Lagrangian and pointed out that the one-dimensional M-L oscillator is a special case of the two-dimensional M-L oscillator.

Complex Order from Disorder and from Simple Order in Coarse-Graining Invariant Orbits of Certain Two-Dimensional Linear Cellular Automata

1997 ◽  
Vol 07 (07) ◽  
pp. 1451-1496 ◽  
Author(s):  
André Barbé
Keyword(s):  
Cellular Automata ◽  
Three Dimensional ◽  
Coarse Graining ◽  
Dimensional Case ◽  
Two Dimensional ◽  
One Dimensional ◽  
Complex Order ◽  
Simple Order ◽  
Problems And Solutions ◽  
The One

This paper considers three-dimensional coarse-graining invariant orbits for two-dimensional linear cellular automata over a finite field, as a nontrivial extension of the two-dimensional coarse-graining invariant orbits for one-dimensional CA that were studied in an earlier paper. These orbits can be found by solving a particular kind of recursive equations (renormalizing equations with rescaling term). The solution starts from some seed that has to be determined first. In contrast with the one-dimensional case, the seed has infinite support in most cases. The way for solving these equations is discussed by means of some examples. Three categories of problems (and solutions) can be distinguished (as opposed to only one in the one-dimensional case). Finally, the morphology of a few coarse-graining invariant orbits is discussed: Complex order (of quasiperiodic type) seems to emerge from random seeds as well as from seeds of simple order (for example, constant or periodic seeds).

Unsteady flow of gas at high pressure into a closed volume filled with liquid

2020 ◽  
Vol 6 (4) ◽  
pp. 127-140
Author(s):  
Maksim V. Alekseev ◽  
Ivan S. Vozhakov ◽  
Sergey I. Lezhnin
Keyword(s):  
Numerical Study ◽  
Three Dimensional ◽  
Water System ◽  
Liquid Lead ◽  
Asymptotic Model ◽  
Closed Volume ◽  
Two Dimensional ◽  
Open Platform ◽  
Significant Difference ◽  
The One

Within the framework of 2D (two-dimensional, axisymmetric) and 3D (three-dimensional) formulations of the problem, this article presents a numerical simulation of the process of gas outflow under pressure into a closed container partially filled with liquid. The authors have performed the numerical modeling using the open platform OpenFOAM with the help of a solver based on the method of liquid volumes (VOF method) with a standard k-e turbulence model. A comparison is made with the one-dimensional (1D) asymptotic model, in which the oscillations of the fluid as a whole are determined by the enthalpy balance. A numerical study of the evolution of pressure during gas outflow is carried out. The results show that the physical properties of the fluid used affect the amplitude and frequency of the pulsations. The modeling has shown that gas flows into water in the form of a jet, and a projectile forms in liquid lead near the hole through which it flows out. The significant influence of three-dimensional effects on the evolution of gas outflow into liquid is demonstrated. Satisfactory agreement was obtained for both two-dimensional and three-dimensional calculations and the results obtained using the asymptotic model. For the “gas — water” system, the results of calculations by the asymptotic model give a significant difference from the results of numerical calculations.

The role of the Internal courtyard in organizing the function and shaping architecture

2020 ◽  
Vol 27 (2) ◽  
pp. 135-146
Author(s):  
Basim Hasan Almajidi ◽  
Tuqa Mahmood Hameed
Keyword(s):  
Spatial Structure ◽  
Interior Design ◽  
Spatial Organization ◽  
Three Dimensional ◽  
Spatial Relations ◽  
Architectural Form ◽  
Formation Function ◽  
The One ◽  
Architectural Characteristics

Despite the development of architecture, the courtyard remained one of the most important methods of preserving the privacy and suitability of the environmental and social aspects as well as its role in the process of regulating the spatial relations between the mass and the vacuum, highlighting the importance, especially in light of the increasing seriousness of slums in the design and neglect of its role in the architectural form and reflections of the shape of the courtyard In the form of the composition of the building, thus the problem of the search was (Lack of cognitive perception available on the role of the internal courtyard in the organization of the function of architecture and its implications at the level of bilateral and three-dimensional mass configuration). And the approach of research to clarify the architectural characteristics of the structured internal courtyard and its functions and strategy as well as the patterns of spatial structure through the construction of knowledge framework, and then a comprehensive theoretical framework of the internal courtyard structured derived from the architectural proposals to reflect the final in four main words: The architectural characteristics of the structured inner courtyard, the spatial structure patterns of the structured inner courtyard, the functions of the organized inner courtyard, and the structured interior design strategy. It has been applied to selected projects to clarify the extent to which these indicators are achieved and to reach conclusions, which showed the existence of a relationship between the two (vacuum and mass) on the one hand and between the two (vacuum, and spatial organization of the spaces) on the other hand, and three aspects: Mass formation, function formation, and movement configuration", reflecting the internal courtyard structure in terms of simplicity or complexity.

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