scholarly journals On the Structural Properties of Voronoi Diagrams

KoG ◽  
2021 ◽  
pp. 72-77
Author(s):  
Leonard Weydemann ◽  
Christian Clemenz ◽  
Clemens Preisinger
Keyword(s):  
Physical Properties ◽  
Structural Properties ◽  
Voronoi Diagram ◽  
Structural Engineering ◽  
Voronoi Tessellation ◽  
Voronoi Diagrams ◽  
Biological Processes ◽  
Voronoi Tessellations ◽  
Cell Tissue

A Voronoi diagram is a tessellation technique, which subdivides space into regions in proximity to a given set of objects called seeds. Patterns emerging naturally in biological processes (for example, in cell tissue) can be modelled in a biomimicry process via Voronoi diagrams. As they originate in nature, we investigate the physical properties of such patterns to determine whether they are optimal given the constraints imposed by surrounding geometry and natural forces. This paper describes under what circumstances the Voronoi tessellation has optimal (structural) properties by surveying recent studies that apply this tessellation technique across different scales. To investigate the properties of random and optimized Voronoi tessellations in comparison to a regular tessellation method, we additionally run and evaluate a simulation in Karamba3D, a parametric structural engineering tool for Rhinoceros3D. The novelty of this research lies in presenting a simple and straightforward simulation of Voronoi diagrams and highlighting how and where their advantages over regular tessellations can be exploited by surveying more advanced approaches as found in literature.

Grow in accessible directions, like Voronoi diagrams

2020 ◽  
pp. 15-18
Author(s):  
Susan D'Agostino
Keyword(s):  
Voronoi Diagram ◽  
Regional Planning ◽  
Voronoi Diagrams ◽  
Real Life ◽  
Two Dimensional ◽  
Mathematics Students ◽  
Voronoi Tessellations ◽  
Dimensional Plane ◽  
A Cell

“Grow in accessible directions, like Voronoi diagrams” offers an accessible introduction to the mathematics of Voronoi diagrams—a separation of a two-dimensional plane into regions known as “cells” based on “sites.” In a Voronoi diagram, any point inside a cell is closer to the site of its cell than the site of any other cell. The discussion includes numerous real-life examples of Voronoi diagrams—also known as a Voronoi tessellations—in nature and regional planning. The discussion is supplemented with numerous hand-drawn sketches to enhance understanding. Mathematics students and enthusiasts are encouraged to draw inspiration from Voronoi diagrams by growing in accessible directions in mathematical and life pursuits. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.

COLUMBIUM 15W-5Mo-1Zr

Alloy Digest ◽  
1969 ◽  
Vol 18 (12) ◽  
Keyword(s):  
High Temperature ◽  
Physical Properties ◽  
Tensile Properties ◽  
Structural Properties ◽  
Base Alloy ◽  
Heat Treating ◽  
Temperature Performance

Abstract Columbium 15W-5 Mo- 1Zr is a columbium-base alloy capable of retaining usuable structural properties up to 2500 F. This datasheet provides information on composition, physical properties, hardness, elasticity, and tensile properties as well as creep. It also includes information on high temperature performance as well as forming, heat treating, machining, and joining. Filing Code: Cb-17. Producer or source: Fansteel Metallurgical Corporation.

Optimizing Protocols for High-Quality RNA Extraction from Blood and Liver Tissues of the Broad-Snouted Caiman

2021 ◽  
Vol 28 (4) ◽  
pp. 197-204
Author(s):  
Evelyn Cecilia López González ◽  
Lucía Magdalena Odetti ◽  
Gisela Laura Poletta ◽  
Nancy Denslow ◽  
Kevin J. Kroll ◽  
...  
Keyword(s):  
Rna Extraction ◽  
Biological Processes ◽  
High Quality ◽  
Efficient Procedure ◽  
Physiological Conditions ◽  
Environmental Perturbation ◽  
Preservation Methods ◽  
Cell Tissue ◽  
And Storage ◽  
Liver Tissues

Transcriptomic information provides fundamental insights into biological processes and can be used to determine gene expression in cell, tissue, or organism under specific physiological conditions, or in response to any environmental perturbation. Extraction of high quality RNA is a challenging step mainly in non-traditional organisms, and protocols for preservation and isolation need to be adjusted in many cases. In the present work, we aimed to develop a protocol for preservation and isolation of high-quality and quantity of RNA from blood and liver tissues of Caiman latirostris. Three preservation methods were tested: 1) flash freezing (LN2) and storage at –80°C; 2) RNAlater® conservation with progressive cooling up to –80°C); 3) preservation in TRIzol® reagent, flash freezing in LN2 and storage at –80°C. Methods 1 and 2 were tested for liver, while 2 and 3 for blood. Our results showed that both preservation methods resulted in excellent outcomes for liver samples. For blood samples however, TRIzol® preservation was an efficient procedure for adequate RNA quality, quantity, and integrity, while conservation in RNAlater® solution was inadequate in both quality and quantity for an optimal RNA extraction. Appropriate protocols were established for each tissue and are being used now for transcriptomic studies in this sentinel organism.

scholarly journals Volume degeneracy of the typical cell and the chord length distribution for Poisson-Voronoi tessellations in high dimensions

2008 ◽  
Vol 40 (04) ◽  
pp. 919-938 ◽  
Author(s):  
Kasra Alishahi ◽  
Mohsen Sharifitabar
Keyword(s):  
Space Dimension ◽  
Voronoi Tessellation ◽  
Length Distribution ◽  
Chord Length ◽  
Voronoi Tessellations ◽  
Constant Intensity ◽  
Chord Length Distribution ◽  
Typical Cell ◽  
Centered Ball ◽  
Contact Distribution

This paper is devoted to the study of some asymptotic behaviors of Poisson-Voronoi tessellation in the Euclidean space as the space dimension tends to ∞. We consider a family of homogeneous Poisson-Voronoi tessellations with constant intensity λ in Euclidean spaces of dimensions n = 1, 2, 3, …. First we use the Blaschke-Petkantschin formula to prove that the variance of the volume of the typical cell tends to 0 exponentially in dimension. It is also shown that the volume of intersection of the typical cell with the co-centered ball of volume u converges in distribution to the constant λ−1(1 − e−λu ). Next we consider the linear contact distribution function of the Poisson-Voronoi tessellation and compute the limit when the space dimension goes to ∞. As a by-product, the chord length distribution and the geometric covariogram of the typical cell are obtained in the limit.

CHEMICAL TESSELLATIONS — RESULTS OF BINARY AND TERTIARY REACTIONS BETWEEN METAL IONS AND FERRICYANIDE OR FERROCYANIDE LOADED GELS

2010 ◽  
Vol 20 (07) ◽  
pp. 2241-2252 ◽  
Author(s):  
B. P. J. DE LACY COSTELLO ◽  
I. JAHAN ◽  
P. HAMBIDGE ◽  
K. LOCKING ◽  
D. PATEL ◽  
...  
Keyword(s):  
Metal Ions ◽  
Voronoi Diagram ◽  
Metal Salt ◽  
Voronoi Diagrams ◽  
Reaction Rates ◽  
Cross Reactivity ◽  
Diffusion Reaction ◽  
Reactive Metal ◽  
Simple Chemical ◽  
Pattern Forming

In our recent letter [de Lacy Costello et al., 2009] we described the formation of spontaneous complex tessellations of the plane constructed in simple chemical reactions between drops of metal salts and ferricyanide or ferrocyanide loaded gels. In this paper, we provide more examples of binary tessellations and extend our analysis to tessellations constructed via tertiary mixtures of reactants. We also provide a classification system which describes the tessellation based on the reactivity of the metal salt with the substrate and also the cross-reactivity of the primary products. This results in balanced tessellations where both reactants have equal reactivity or unbalanced tessellations where one reactant has a lower reactivity with the gel. The products can also be partially or fully cross reactive which gives a highly complex tessellation. The tessellations are made up of colored cells (corresponding to different metal ferricyanides or ferrocyanides) separated by bisectors of low precipitate concentration. The tessellations constructed by these reactions constitute generalized Voronoi diagrams. In the case of certain binary or tertiary combinations of reactants where the diffusion/reaction rates differ, then multiplicatively weighted crystal growth Voronoi diagrams are constructed. Where one reactant has limited or no reactivity with the gel (or the products are cross reactive) then the fronts originating from the reactive metal ions cross the fronts originating from the partially reactive metal ions. The fronts can annihilate in the formation of a second Voronoi diagram relating to the relative positions of the reactive drops. Therefore, two or more generalised or weighted Voronoi diagrams can be calculated in parallel by these simple chemical systems. However when these reactions were used to calculate an additively weighted Voronoi diagram (the reaction was initiated at different time intervals) the diagram constructed did not correspond to the theoretical calculation. We use the failure of these reactions to construct an additively weighted Voronoi diagram to prove a mechanism of substrate competition for bisector formation. These tessellations are an important class of pattern forming reactions and are useful in modeling natural pattern forming phenomena in addition to being a great resource for scientific demonstrations.

scholarly journals Physical Properties and Consumer Evaluation of Cocoa Bean Shell-Functionalized Biscuits Adapted for Diabetic Consumers by the Replacement of Sucrose with Tagatose

Foods ◽  
2020 ◽  
Vol 9 (6) ◽  
pp. 814 ◽  
Author(s):  
Olga Rojo-Poveda ◽  
Letricia Barbosa-Pereira ◽  
David Orden ◽  
Caroline Stévigny ◽  
Giuseppe Zeppa ◽  
...  
Keyword(s):  
Physical Properties ◽  
Structural Properties ◽  
Water Retention ◽  
Consumer Acceptance ◽  
Cocoa Bean ◽  
Total Dietary Fiber ◽  
Consumer Evaluation ◽  
Lower Solubility ◽  
Interesting Possibility ◽  
Physicochemical And Structural Properties

The cocoa bean shell (CBS), a by-product of the cocoa industry, has been reported to be rich in fiber and polyphenols, which could contribute to reducing the metabolism of sugars and glucose adsorption. The production of CBS-based biscuits in which sucrose is replaced with tagatose (a low-glycemic sugar with prebiotic properties), benefiting diabetic consumers, is proposed. Six prototype biscuits were produced using sucrose, tagatose, and CBS powder at 0%, 10%, and 20% as a wheat flour replacement. Biscuits were studied in terms of fiber content, and those with 10% and 20% CBS showed to contain 5.66% and 8.70–8.71% of total dietary fiber, respectively. Moreover, the physicochemical and structural properties of the biscuits were studied to evaluate their differences due to the use of sucrose and tagatose combined with CBS. Significant effects mainly caused by the reducing nature and lower solubility of tagatose with respect to sugar, and the water retention capacities of CBS were observed. Finally, the biscuits were evaluated by performing a consumer acceptance evaluation, and their perceptible sensorial differences were studied by performing a Napping® sensory characterization. CBS-based biscuits represent an interesting possibility for cocoa by-product revalorization, although an optimized recipe is recommended, especially when employing tagatose.

Moisture Effective Diffusivity in Porous Media with Different Physical Properties

2006 ◽  
Vol 258-260 ◽  
pp. 207-212
Author(s):  
Miranda M.N.N. ◽  
M.A. Silva
Keyword(s):  
Porous Media ◽  
Diffusion Coefficient ◽  
Moisture Content ◽  
Mass Transport ◽  
Physical Properties ◽  
Pore Size ◽  
Structural Properties ◽  
Effective Diffusivity ◽  
Nay Zeolite ◽  
Moisture Effective Diffusivity

In the drying of porous media, the mass transport occurs in the pores as well as on the surface of the solid. The mechanisms involved can take place simultaneously, influenced by the predominant one and can change depending on the moisture content. In this work, the moisture effective diffusivity was estimated in solids with distinct structural properties in order to verify the predominant mechanisms according to the moisture content, analyzing the influence of the physical properties. The materials studied were NaY Zeolite, Kaolin, Silica and Alumina. The results of diffusion coefficient present a minimum at low moisture content that can be related to pore size.

Contact and chord length distribution of a stationary Voronoi tessellation

1998 ◽  
Vol 30 (03) ◽  
pp. 603-618 ◽  
Author(s):  
Lothar Heinrich
Keyword(s):  
Point Process ◽  
Voronoi Tessellation ◽  
Pair Correlation ◽  
Length Distribution ◽  
Distribution Functions ◽  
Chord Length ◽  
Closed Form Expression ◽  
Voronoi Tessellations ◽  
Chord Length Distribution ◽  
Contact Distribution

We give formulae for different types of contact distribution functions for stationary (not necessarily Poisson) Voronoi tessellations in ℝ d in terms of the Palm void probabilities of the generating point process. Moreover, using the well-known relationship between the linear contact distribution and the chord length distribution we derive a closed form expression for the mean chord length in terms of the two-point Palm distribution and the pair correlation function of the generating point process. The results obtained are specified for Voronoi tessellations generated by Poisson cluster and Gibbsian processes, respectively.

Contact and chord length distribution of a stationary Voronoi tessellation

1998 ◽  
Vol 30 (3) ◽  
pp. 603-618 ◽  
Author(s):  
Lothar Heinrich
Keyword(s):  
Point Process ◽  
Voronoi Tessellation ◽  
Pair Correlation ◽  
Length Distribution ◽  
Distribution Functions ◽  
Chord Length ◽  
Closed Form Expression ◽  
Voronoi Tessellations ◽  
Chord Length Distribution ◽  
Contact Distribution

We give formulae for different types of contact distribution functions for stationary (not necessarily Poisson) Voronoi tessellations in ℝd in terms of the Palm void probabilities of the generating point process. Moreover, using the well-known relationship between the linear contact distribution and the chord length distribution we derive a closed form expression for the mean chord length in terms of the two-point Palm distribution and the pair correlation function of the generating point process. The results obtained are specified for Voronoi tessellations generated by Poisson cluster and Gibbsian processes, respectively.

Discrete Construction of Compoundly Weighted Voronoi Diagram

2013 ◽  
Vol 467 ◽  
pp. 545-548
Author(s):  
Hui Wang
Keyword(s):  
Production Process ◽  
Voronoi Diagram ◽  
Voronoi Diagrams ◽  
High Potential ◽  
Graphic Display ◽  
Potential Value ◽  
Discrete Algorithms ◽  
Traditional Algorithm ◽  
Definition Of

Compoundly weighted Voronoi diagram is difficult to construct because the bisector is fairly complex. In traditional algorithm, production process is always extremely complex and it is more difficult to graphic display because of the complex definition of mathematic formula. In this paper, discrete algorithms are used to construct compoundly weighted Voronoi diagrams. The algorithm can get over all kinds of shortcomings that we have just mentioned. So it is more useful and effective than the traditional algorithm. The results show that the algorithm is both simple and useful, and it is of high potential value in practice.

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