scholarly journals Shortest Distance Between Multiple Orbits and Generalized Fractal Dimensions

2021 ◽  
Author(s):  
Vanessa Barros ◽  
Jérôme Rousseau
Keyword(s):  
Fractal Dimensions ◽  
Shortest Distance

Fractal dimensions of dynamically triangulated random surfaces

1992 ◽  
Vol 2 (12) ◽  
pp. 2181-2190 ◽  
Author(s):  
Christian Münkel ◽  
Dieter W. Heermann
Keyword(s):  
Fractal Dimensions ◽  
Random Surfaces

Structure characterization of ground calcium carbonate flocs by fractal analysis and their effects on handsheet properties

TAPPI Journal ◽  
2013 ◽  
Vol 12 (3) ◽  
pp. 17-23 ◽  
Author(s):  
WANHEE IM ◽  
HAK LAE LEE ◽  
HYE JUNG YOUN ◽  
DONGIL SEO
Keyword(s):  
Fractal Analysis ◽  
Structural Characteristics ◽  
Fractal Dimensions ◽  
Strength Loss ◽  
Structure Characterization ◽  
Uniform Size ◽  
Cross Sectional ◽  
Floc Size ◽  
Mass Fractal ◽  
Handsheet Properties

Preflocculation of filler particles before their addition to pulp stock provides the most viable and practical solution to increase filler content while minimizing strength loss. The characteristics of filler flocs, such as floc size and structure, have a strong influence on preflocculation efficiency. The influence of flocculant systems on the structural characteristics of filler flocs was examined using a mass fractal analysis method. Mass fractal dimensions of filler flocs under high shear conditions were obtained using light diffraction spectroscopy for three different flocculants. A single polymer (C-PAM), a dual cationic polymer (p-DADMAC/C-PAM) and a C-PAM/micropolymer system were used as flocculants, and their effects on handsheet properties were investigated. The C-PAM/micropolymer system gave the greatest improvement in tensile index. The mass fractal analysis showed that this can be attributed to the formation of highly dense and spherical flocs by this flocculant. A cross-sectional analysis of the handsheets showed that filler flocs with more uniform size were formed when a C-PAM/micropolymer was used. The results suggest that a better understanding of the characteristics of preflocculated fillers and their influence on the properties of paper can be gained based on a fractal analysis.

Path Planning of Mobile Robot Using Improved Artificial Bee Colony Algorithm

2020 ◽  
Vol 38 (9A) ◽  
pp. 1384-1395
Author(s):  
Rakaa T. Kamil ◽  
Mohamed J. Mohamed ◽  
Bashra K. Oleiwi
Keyword(s):  
Mobile Robot ◽  
Comparative Research ◽  
Artificial Bee Colony Algorithm ◽  
Artificial Bee Colony ◽  
Dynamic Control ◽  
Computational Time ◽  
Bee Colony ◽  
Shortest Distance ◽  
Minimum Number ◽  
Cubic Polynomial

A modified version of the artificial Bee Colony Algorithm (ABC) was suggested namely Adaptive Dimension Limit- Artificial Bee Colony Algorithm (ADL-ABC). To determine the optimum global path for mobile robot that satisfies the chosen criteria for shortest distance and collision–free with circular shaped static obstacles on robot environment. The cubic polynomial connects the start point to the end point through three via points used, so the generated paths are smooth and achievable by the robot. Two case studies (or scenarios) are presented in this task and comparative research (or study) is adopted between two algorithm’s results in order to evaluate the performance of the suggested algorithm. The results of the simulation showed that modified parameter (dynamic control limit) is avoiding static number of limit which excludes unnecessary Iteration, so it can find solution with minimum number of iterations and less computational time. From tables of result if there is an equal distance along the path such as in case A (14.490, 14.459) unit, there will be a reduction in time approximately to halve at percentage 5%.

Rapid determination of fractal structure of bacterial assemblages in wastewater treatment: implications to process optimisation

1998 ◽  
Vol 38 (2) ◽  
pp. 9-15 ◽  
Author(s):  
J. Guan ◽  
T. D. Waite ◽  
R. Amal ◽  
H. Bustamante ◽  
R. Wukasch
Keyword(s):  
Wastewater Treatment ◽  
Fractal Structure ◽  
Structural Information ◽  
Rapid Determination ◽  
Fractal Dimensions ◽  
Structure Information ◽  
Treatment Processes ◽  
On Line ◽  
Bacterial Aggregates

A rapid method of determining the structure of aggregated particles using small angle laser light scattering is applied here to assemblages of bacteria from wastewater treatment systems. The structure information so obtained is suggestive of fractal behaviour as found by other methods. Strong dependencies are shown to exist between the fractal structure of the bacterial aggregates and the behaviour of the biosolids in zone settling and dewatering by both pressure filtration and centrifugation methods. More rapid settling and significantly higher solids contents are achievable for “looser” flocs characterised by lower fractal dimensions. The rapidity of determination of structural information and the strong dependencies of the effectiveness of a number of wastewater treatment processes on aggregate structure suggests that this method may be particularly useful as an on-line control tool.

scholarly journals Impact of Coseismic Frictional Melting on Particle Size, Shape Distribution and Chemistry of Experimentally-Generated Pseudotachylite

2020 ◽  
Vol 8 ◽  
Author(s):  
Leny Montheil ◽  
Virginia G. Toy ◽  
James M. Scott ◽  
Thomas M. Mitchell ◽  
David P. Dobson
Keyword(s):  
Particle Size ◽  
Host Rock ◽  
Fractal Dimensions ◽  
Rock Composition ◽  
Slip Rates ◽  
Shape Distribution ◽  
Frictional Behavior ◽  
Particle Size And Shape ◽  
Frictional Melting ◽  
Glass Compositions

In natural friction melts, or pseudotachylites, clast textures and glass compositions can influence the frictional behavior of faults hosting pseudotachylites, and are, in turn, sensitive to the processes involved in pseudotachylite formation. Quantification of these parameters in situations where the host rock composition and formation conditions are well-constrained, such as analogue experiments, may yield calibrations that can be employed in analysis of natural pseudotachylites. In this paper, we experimentally-generated pseudotachylites in granitoid rocks (tonalite and Westerly granite) at Pconf = 40 MPa and slip rates of ∼0.1 m s−1, comparable to the conditions under which natural pseudotachylite is known to form in Earth’s upper crust. We find variations in both clast textures and glass compositions that reflect formation processes, and probably influence the frictional behavior of similar natural faults hosting pseudotachylite. Quantification of particle size and shape distribution with a semi-automatic image analysis method, combined with analysis of glass and host-rock composition of these experimentally generated pseudotachylites, reveals that the textures of pseudotachylite material evolved by combinations of 1) comminution, 2) heterogeneous frictional flash melting, and 3) homogeneous (diffusive) clast melting and/or marginal decrepitation. Fractal dimensions of pseudotachylite-hosted clasts (D ∼ 3) that are greater than those of marginal fragmented host rock particles (gouge, D ∼ 2.4), reflect an increase of the intensity of comminution by slip localisation during a pre-melting phase. Chemical analyses demonstrate that these pseudotachylite glasses were generated by frictional flash melting, where host rock phases melt individually. Biotite is the least resistant to melting, feldspar intermediate, and quartz is the most resistant. The peudotachylite glass generated in these experiments has an alkaline composition, is depleted in SiO2 compared to the bulk host-rock, and shows heterogeneous compositions in a single sample related to proximity to host-rock minerals. The percentage contributions of host rock phases to the melt, calculated by a mixing model, shows that glass compositions are dominated by plagioclase and biotite. Within the melt, margins of clasts were dissolved uniformly by diffusion and/or affected by marginal decrepitation, resulting in convex and round shapes with convexities averaging ∼0.8 and circularities averaging ∼0.65.

FRACTAL DIMENSION, PRIMES, AND THE PERSISTENCE OF MEMORY

2003 ◽  
Vol 06 (02) ◽  
pp. 241-249
Author(s):  
JOSEPH L. PE
Keyword(s):  
Number Theory ◽  
Fractal Dimension ◽  
Fractal Dimensions ◽  
Distinguishing Characteristic ◽  
Local Behavior ◽  
Remarkable Similarity ◽  
Recursive Procedures

Many sequences from number theory, such as the primes, are defined by recursive procedures, often leading to complex local behavior, but also to graphical similarity on different scales — a property that can be analyzed by fractal dimension. This paper computes sample fractal dimensions from the graphs of some number-theoretic functions. It argues for the usefulness of empirical fractal dimension as a distinguishing characteristic of the graph. Also, it notes a remarkable similarity between two apparently unrelated sequences: the persistence of a number, and the memory of a prime. This similarity is quantified using fractal dimension.

scholarly journals Initial Clinical Experience With a New Conformable Abdominal Aortic Endograft: Aortic Neck Coverage and Curvature Analysis in Challenging Aortic Necks

2021 ◽  
pp. 152660282199672
Author(s):  
Alice Finotello ◽  
Richte Schuurmann ◽  
Sara Di Gregorio ◽  
Gian Antonio Boschetti ◽  
Nabil Chakfé ◽  
...  
Keyword(s):  
Aortic Wall ◽  
Surface Coverage ◽  
Infrarenal Aorta ◽  
Technical Success ◽  
Curvature Analysis ◽  
Average Curvature ◽  
Aortic Neck ◽  
Abdominal Aortic ◽  
Shortest Distance ◽  
New Generation

Objectives: Aim of this work was to investigate precision of deployment and conformability of a new generation GORE EXCLUDER Conformable Endoprosthesis with active control system (CEXC Device, W.L. Gore and Associates, Flagstaff, AZ, USA) by analyzing aortic neck coverage and curvature. Methods: All consecutive elective patients affected by abdominal aortic aneurysm or aortoiliac aneurysm treated at our institution between November 2018 and June 2019 with the new CEXC Device were enrolled. Validated software was adopted to determine the available apposition surface area into the aortic neck, apposition of the endograft to the aortic wall, shortest apposition length (SAL), shortest distance between the endograft fabric and the lowest renal arteries (SFD) and between the endograft fabric and the contralateral renal artery (CFD). Pointwise centerline curvature was also computed. Results: Twelve patients (10 men, median age 78 years (71.75, 81.0)) with available pre- and postoperative computed tomography angiography (CTA) were included. Technical success was obtained in all the cases. Preoperative median length of the proximal aortic neck was 16.1 mm (10.7, 21.7) and suprarenal (α) and infrarenal (β) neck angulation were, respectively, 28.9° (15.7°, 47.5°) and 75.0° (66.9°, 81.4°). Postoperative median apposition surface coverage was 79% (69.25%, 90.75%) of the available apposition surface. SFD and CFD were 1.5 mm (0.75, 5.25) and 7 mm (4.5, 21.5), respectively. Average curvature over the infrarenal aorta decreased from 25 m−1 (21.75, 29.0) to 22.5 m−1 (18.75, 24.5) postoperatively (p=0.02). Maximum curvature did not decrease significantly from 64.5 m−1 (54.25, 92.0) to 62 m−1 (41.75, 71.5) (p=0.1). Conclusions: Our early experience showed that deployment of the CEXC Device is safe and effective for patients with challenging proximal aortic necks. Absence of significant changes between pre- and postoperative proximal aortic neck angulations and curvature confirms the high conformability of this endograft.

scholarly journals Supramolecular Fractal Growth of Self-Assembled Fibrillar Networks

Gels ◽  
2021 ◽  
Vol 7 (2) ◽  
pp. 46
Author(s):  
Pedram Nasr ◽  
Hannah Leung ◽  
France-Isabelle Auzanneau ◽  
Michael A. Rogers
Keyword(s):  
Fractal Dimension ◽  
Crystallization Temperature ◽  
Cayley Tree ◽  
Fractal Dimensions ◽  
Self Similarity ◽  
Avrami Model ◽  
Cluster Aggregation ◽  
Box Counting ◽  
Self Assembled ◽  
Limited Diffusion

Complex morphologies, as is the case in self-assembled fibrillar networks (SAFiNs) of 1,3:2,4-Dibenzylidene sorbitol (DBS), are often characterized by their Fractal dimension and not Euclidean. Self-similarity presents for DBS-polyethylene glycol (PEG) SAFiNs in the Cayley Tree branching pattern, similar box-counting fractal dimensions across length scales, and fractals derived from the Avrami model. Irrespective of the crystallization temperature, fractal values corresponded to limited diffusion aggregation and not ballistic particle–cluster aggregation. Additionally, the fractal dimension of the SAFiN was affected more by changes in solvent viscosity (e.g., PEG200 compared to PEG600) than crystallization temperature. Most surprising was the evidence of Cayley branching not only for the radial fibers within the spherulitic but also on the fiber surfaces.

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