scholarly journals Design of Regular One-Dimensional, Two-Dimensional, and Three-Dimensional Linkage-Based Tessellations

2020 ◽  
Vol 12 (2) ◽  
Author(s):  
Alden D. Yellowhorse ◽  
Nathan Brown ◽  
Larry L. Howell
Keyword(s):  
Three Dimensional ◽  
Finite Size ◽  
Three Dimensions ◽  
Two Dimensional ◽  
One Dimensional

Abstract Linkage origami is one effective approach for addressing stiffness and accommodating panels of finite size in origami models and tessellations. However, successfully implementing linkage origami in tessellations can be challenging. In this work, multiple theorems are presented that provide criteria for designing origami units or cells that can be assembled into arbitrarily large tessellations. The application of these theorems is demonstrated through examples of tessellations in two and three dimensions.

Mine Impact Burial Prediction From One to Three Dimensions

2008 ◽  
Vol 62 (1) ◽  
Author(s):  
Peter C. Chu
Keyword(s):  
Three Dimensional ◽  
Time History ◽  
Three Dimensions ◽  
Vertical Position ◽  
Burial Depth ◽  
Prediction Errors ◽  
Two Dimensional ◽  
Dimensional Model ◽  
One Dimensional ◽  
Dimensional Models

The Navy’s mine impact burial prediction model creates a time history of a cylindrical or a noncylindrical mine as it falls through air, water, and sediment. The output of the model is the predicted mine trajectory in air and water columns, burial depth/orientation in sediment, as well as height, area, and volume protruding. Model inputs consist of parameters of environment, mine characteristics, and initial release. This paper reviews near three decades’ effort on model development from one to three dimensions: (1) one-dimensional models predict the vertical position of the mine’s center of mass (COM) with the assumption of constant falling angle, (2) two-dimensional models predict the COM position in the (x,z) plane and the rotation around the y-axis, and (3) three-dimensional models predict the COM position in the (x,y,z) space and the rotation around the x-, y-, and z-axes. These models are verified using the data collected from mine impact burial experiments. The one-dimensional model only solves one momentum equation (in the z-direction). It cannot predict the mine trajectory and burial depth well. The two-dimensional model restricts the mine motion in the (x,z) plane (which requires motionless for the environmental fluids) and uses incorrect drag coefficients and inaccurate sediment dynamics. The prediction errors are large in the mine trajectory and burial depth prediction (six to ten times larger than the observed depth in sand bottom of the Monterey Bay). The three-dimensional model predicts the trajectory and burial depth relatively well for cylindrical, near-cylindrical mines, and operational mines such as Manta and Rockan mines.

scholarly journals Determination of load distribution in a given medium according to the values of the loads at certain points

2021 ◽  
pp. 167-175
Author(s):  
Oleksandr Mostovenko ◽  
Serhii Kovalov ◽  
Svitlana Botvinovska
Keyword(s):  
Boundary Conditions ◽  
Load Distribution ◽  
Numerical Solutions ◽  
Dimensional Space ◽  
Geometric Model ◽  
Three Dimensional ◽  
The Body ◽  
Three Dimensions ◽  
Two Dimensional ◽  
One Dimensional

Taking into account force, temperature and other loads, the stress and strain state calculations methods of spatial structures involve determining the distribution of the loads in the three-dimensional body of the structure [1, 2]. In many cases the output data for this distribution can be the values of loadings in separate points of the structure. The problem of load distribution in the body of the structure can be solved by three-dimensional discrete interpolation in four-dimensional space based on the method of finite differences, which has been widely used in solving various engineering problems in different fields. A discrete conception of the load distribution at points in the body or in the environment is also required for solving problems by the finite elements method [3-7]. From a geometrical point of view, the result of three-dimensional interpolation is a multivariate of the four-dimensional space [8], where the three dimensions are the coordinates of a three-dimensional body point, and the fourth is the loading at this point. Such interpolation provides for setting of the three coordinates of the point and determining the load at that point. The simplest three-dimensional grid in the three-dimensional space is the grid based on a single sided hypercube. The coordinates of the nodes of such a grid correspond to the numbering of nodes along the coordinate axes. Discrete interpolation of points by the finite difference method is directly related to the numerical solutions of differential equations with given boundary conditions and also requires the setting of boundary conditions. If we consider a three-dimensional grid included into a parallelepiped, the boundary conditions are divided into three types: 1) zero-dimensional (loads at points), where the three edges of the grid converge; 2) one-dimensional (loads at points of lines), where the four edges of the grid converge; 3) two-dimensional (loads at the points of faces), where the five edges of the grid converge. The zero-dimensional conditions are boundary conditions for one-dimensional interpolation of the one-dimensional conditions, which, in turn, are boundary conditions for two-dimensional conditions, and the two-dimensional conditions are boundary conditions for determining the load on the inner points of the grid. If a load is specified only at certain points of boundary conditions, then the interpolation problem is divided into three stages: one-dimensional load interpolation onto the line nodes, two-dimensional load interpolation onto the surface nodes and three-dimensional load interpolation onto internal grid nodes. The proposed method of discrete three-dimensional interpolation allows, according to the specified values of force, temperature or other loads at individual points of the three-dimensional body, to interpolate such loads on all nodes of a given regular three-dimensional grid with cubic cells. As a result of interpolation, a discrete point framework of the multivariate is obtained, which is a geometric model of the distribution of physical characteristics in a given medium according to the values of these characteristics at individual points.

Salts of 3,5-dinitrobenzoic acid with organic diamines: hydrogen-bonded supramolecular structures in one, two and three dimensions

2001 ◽  
Vol 57 (2) ◽  
pp. 201-212 ◽  
Author(s):  
Colin J. Burchell ◽  
Christopher Glidewell ◽  
Alan J. Lough ◽  
George Ferguson
Keyword(s):  
Carboxylic Acid ◽  
Hydrogen Bonds ◽  
Secondary Amine ◽  
Tertiary Amine ◽  
Primary Amine ◽  
Three Dimensional ◽  
Supramolecular Structures ◽  
Three Dimensions ◽  
Two Dimensional ◽  
One Dimensional

The trigonally trisubstituted carboxylic acid 3,5-dinitrobenzoic acid, (O2N)2C6H3COOH, forms 2:1 salts with a range of organic diamines L, with the general composition [LH2]2+·[{(O2N)2C6H3COO}−]2. When L is a bis-tertiary amine the hard N—H...O hydrogen bonds generate finite three-component aggregates, anion...cation...anion, and these aggregates are further linked by soft C—H...O hydrogen bonds to form one-dimensional molecular ladders when L is N,N,N′,N′′-tetramethyl-1,2-diaminoethane and chains of rings when L is 4,4′-dipyridylethane or 4,4′-dipyridylethene; two-dimensional sheets are formed when L is 1,4-diazabicyclo[2.2.2]octane and a three-dimensional framework is formed when L is N,N′-dimethylpiperazine. When L is the bis-secondary amine piperazine, the hard N—H...O and soft C—H...O hydrogen bonds each generate continuous motifs in the form of distinct chains of rings, the combination of which generates sheets, while when L is the bis-primary amine 1,2-diaminoethane the hard N—H...O hydrogen bonds alone generate a three-dimensional framework.

Ferrocene-1,1′-dicarboxylic acid as a building block in supramolecular chemistry: supramolecular structures in one, two and three dimensions

2002 ◽  
Vol 58 (5) ◽  
pp. 786-802 ◽  
Author(s):  
Choudhury M. Zakaria ◽  
George Ferguson ◽  
Alan J. Lough ◽  
Christopher Glidewell
Keyword(s):  
Hydrogen Bonds ◽  
Dicarboxylic Acid ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Supramolecular Structures ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Acid Molecule ◽  
One Dimensional ◽  
Partial Transfer

The supramolecular structures have been determined for nine adducts formed between organic diamines and ferrocene-1,1′-dicarboxylic acid. In the salt-like 1:1 adduct (1) formed with methylamine, the supramolecular structure is one-dimensional, whereas in the 1:1 adducts formed with 1,4-diazabicyclo[2.2.2]octane, (2), and 4,4′-bipyridyl, (4), and in the hydrated 2:1 adduct (3) formed with morpholine, the hard hydrogen bonds form one-dimensional structures, which are expanded to two dimensions by soft C—H...O hydrogen bonds. The hard hydrogen bonds generate two-dimensional structures in the 2:1 adduct (5) formed with octylamine, where the ferrocene component lies across a centre of inversion, in the 1:1 adduct (6) formed with piperidine and in the tetrahydrofuran-solvated 1:1 adduct (7) formed with di(cyclohexyl)amine. In the 2:3 adduct (8) formed by tris-(2-aminoethyl)amine, and in the 2:1 adduct (9) formed with 2-(4′-hydroxyphenyl)ethylamine (tyramine), where Z′ = 1.5 in space group P\bar{1}, the hard hydrogen bonds generate three-dimensional structures. No H transfer from O to N occurs in (4) and only partial transfer of H occurs in (2); in (1), (6) and (7), one H is transferred to N from each acid molecule, and in (3), (5), (8) and (9), two H are transferred from each acid molecule.

scholarly journals Topological correlators and surface defects from equivariant cohomology

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Rodolfo Panerai ◽  
Antonio Pittelli ◽  
Konstantina Polydorou
Keyword(s):  
Quantum Mechanics ◽  
Equivariant Cohomology ◽  
Surface Defects ◽  
Star Product ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Dimensional System ◽  
The Novel ◽  
One Dimensional ◽  
Dual Quantum

Abstract We find a one-dimensional protected subsector of $$ \mathcal{N} $$ N = 4 matter theories on a general class of three-dimensional manifolds. By means of equivariant localization we identify a dual quantum mechanics computing BPS correlators of the original model in three dimensions. Specifically, applying the Atiyah-Bott-Berline-Vergne formula to the original action demonstrates that this localizes on a one-dimensional action with support on the fixed-point submanifold of suitable isometries. We first show that our approach reproduces previous results obtained on S3. Then, we apply it to the novel case of S2× S1 and show that the theory localizes on two noninteracting quantum mechanics with disjoint support. We prove that the BPS operators of such models are naturally associated with a noncom- mutative star product, while their correlation functions are essentially topological. Finally, we couple the three-dimensional theory to general $$ \mathcal{N} $$ N = (2, 2) surface defects and extend the localization computation to capture the full partition function and BPS correlators of the mixed-dimensional system.

Transformations of two-dimensional layered zinc phosphates to three-dimensional and one-dimensional structures

2002 ◽  
Vol 12 (4) ◽  
pp. 1044-1052 ◽  
Author(s):  
Amitava Choudhury ◽  
S. Neeraj ◽  
Srinivasan Natarajan ◽  
C. N. R. Rao
Keyword(s):  
Three Dimensional ◽  
Two Dimensional ◽  
One Dimensional ◽  
Zinc Phosphates

Theory of ultrasonic attenuation in one and two dimensional metals

1976 ◽  
Vol 54 (14) ◽  
pp. 1454-1460 ◽  
Author(s):  
T. Tiedje ◽  
R. R. Haering
Keyword(s):  
Ultrasonic Attenuation ◽  
Three Dimensional ◽  
Electronic Systems ◽  
Two Dimensional ◽  
Temperature Dependent ◽  
One Dimensional ◽  
The Difference

The theory of ultrasonic attenuation in metals is extended so that it applies to quasi one and two dimensional electronic systems. It is shown that the attenuation in such systems differs significantly from the well-known results for three dimensional systems. The difference is particularly marked for one dimensional systems, for which the attenuation is shown to be strongly temperature dependent.

Monkey superior colliculus represents rapid eye movements in a two-dimensional motor map

1993 ◽  
Vol 69 (3) ◽  
pp. 965-979 ◽  
Author(s):  
K. Hepp ◽  
A. J. Van Opstal ◽  
D. Straumann ◽  
B. J. Hess ◽  
V. Henn
Keyword(s):  
Eye Movements ◽  
Superior Colliculus ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Eye Position ◽  
Two Dimensional ◽  
Vestibular Nystagmus ◽  
Rapid Eye Movements ◽  
Q Model

1. Although the eye has three rotational degrees of freedom, eye positions, during fixations, saccades, and smooth pursuit, with the head stationary and upright, are constrained to a plane by ListingR's law. We investigated whether Listing's law for rapid eye movements is implemented at the level of the deeper layers of the superior colliculus (SC). 2. In three alert rhesus monkeys we tested whether the saccadic motor map of the SC is two dimensional, representing oculocentric target vectors (the vector or V-model), or three dimensional, representing the coordinates of the rotation of the eye from initial to final position (the quaternion or Q-model). 3. Monkeys made spontaneous saccadic eye movements both in the light and in the dark. They were also rotated about various axes to evoke quick phases of vestibular nystagmus, which have three degrees of freedom. Eye positions were measured in three dimensions with the magnetic search coil technique. 4. While the monkey made spontaneous eye movements, we electrically stimulated the deeper layers of the SC and elicited saccades from a wide range of initial positions. According to the Q-model, the torsional component of eye position after stimulation should be uniquely related to saccade onset position. However, stimulation at 110 sites induced no eye torsion, in line with the prediction of the V-model. 5. Activity of saccade-related burst neurons in the deeper layers of the SC was analyzed during rapid eye movements in three dimensions. No systematic eye-position dependence of the movement fields, as predicted by the Q-model, could be detected for these cells. Instead, the data fitted closely the predictions made by the V-model. 6. In two monkeys, both SC were reversibly inactivated by symmetrical bilateral injections of muscimol. The frequency of spontaneous saccades in the light decreased dramatically. Although the remaining spontaneous saccades were slow, Listing's law was still obeyed, both during fixations and saccadic gaze shifts. In the dark, vestibularly elicited fast phases of nystagmus could still be generated in three dimensions. Although the fastest quick phases of horizontal and vertical nystagmus were slower by about a factor of 1.5, those of torsional quick phases were unaffected. 7. On the basis of the electrical stimulation data and the properties revealed by the movement field analysis, we conclude that the collicular motor map is two dimensional. The reversible inactivation results suggest that the SC is not the site where three-dimensional fast phases of vestibular nystagmus are generated.(ABSTRACT TRUNCATED AT 400 WORDS)

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