Fractal structure of diffusion and invasion fronts in three-dimensional lattices through the gradient percolation approach

Three-dimensional data sets of kidney arterial vessels were obtained from resin casts by serial sectioning and by micro-NMR-tomography, and were analyzed by the mass-radius-relation both for global and local scaling properties. We present for the first time the spatial resolution of local scaling and thus the dispersion of the fractal dimension within the organs. The arterial system is characterized as a non-homogeneous fractal. We discuss and relate the fractal structure to the scaling and allometry of metabolic rates in living organisms.

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Fabrication of Functionally Porous Structures by the Sheet Lamination Method

Materials Science Forum ◽

10.4028/www.scientific.net/msf.561-565.1711 ◽

2007 ◽

Vol 561-565 ◽

pp. 1711-1714 ◽

Cited By ~ 1

Author(s):

K. Yamasaki ◽

S. Fukuda ◽

Takashi Murakami ◽

K. Maekawa

Keyword(s):

Porous Structure ◽

Cross Sections ◽

Fractal Structure ◽

Three Dimensional ◽

Tissue Growth ◽

Porous Structures ◽

Plasma Sintering ◽

Spark Plasma ◽

Recent Trends ◽

Materials Used

Recent trends in bio technology have resulted in the need for accurate fabrication of pore structure of sophisticated porous materials used in advanced applications such as substrates for tissue growth, and various kinds of implants. Control of pore size is important for promoting growth of blood vessels and adequate fluid flow. In the present study, an attempt has been made to fabricate functionally porous structures using titanium, including an internally controlled three-dimensional (3-D) fractal structure. A novel 3-D modeling method that combines rapid prototyping with spark plasma sintering (SPS) is proposed, which enables us to control the internal porous structure. Titanium powder-tape or sheet is sintered or cut by a pulsed Nd:YAG laser to form 2-D fractal cross-sections. These 2-D layers are temporarily laminated in a carbon mold, being then jointed by the SPS method to maintain the internal porous structure. Process parameters for the sheet lamination method have extensively been investigated.

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Bio-inspired plasmonic leaf for enhanced light-matter interactions

Nanophotonics ◽

10.1515/nanoph-2019-0104 ◽

2019 ◽

Vol 8 (7) ◽

pp. 1291-1298

Author(s):

Changxu Liu ◽

Peng Mao ◽

Qinghua Guo ◽

Min Han ◽

Shuang Zhang

Keyword(s):

Fractal Structure ◽

Near Field ◽

Three Dimensional ◽

Mathematical Concept ◽

Optical Antennas ◽

Hot Electron ◽

Self Similarity ◽

Enhanced Fluorescence ◽

Planar Structures ◽

Direct Laser

AbstractThe mathematical concept of fractals is widely applied to photonics as planar structures ranging from terahertz resonators, optical antennas, to photodetectors. Here, instead of a direct mathematical abstract, we design a plasmonic leaf with fractal geometry from the outline of a leaf from Wargrave Pink. The enhanced light-matter interactions are observed numerically from the improvement in both absorption and near-field intensification. To demonstrate the effect experimentally, a three-dimensional fractal structure is realised through direct laser writing, which significantly improves the photothermal conversion. By virtue of the self-similarity in geometry, the artificial leaf improves the absorption of a 10-nm-thick gold film with 14 × temperature increment compared to flat Au film. Not limited to the proof-of-concept photothermal experiment demonstrated here, the fractal structure with improved light-matter interactions can be utilised in a variety of applications ranging from non-linear harmonic generation, plasmonic-enhanced fluorescence, to hot electron generation for photocatalysis.

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The Coexistence of Invariant Tori and Topological Horseshoe in a Generalized Nosé–Hoover Oscillator

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127417501115 ◽

2017 ◽

Vol 27 (07) ◽

pp. 1750111 ◽

Cited By ~ 4

Author(s):

Lei Wang ◽

Xiao-Song Yang

Keyword(s):

Cross Section ◽

Fractal Structure ◽

Polynomial System ◽

Invariant Tori ◽

Three Dimensional ◽

Topological Horseshoe ◽

Periodic Trajectories ◽

Dynamical Complexity ◽

Chaotic Region ◽

Stable Periodic

This paper is devoted to the study of dynamical complexity of a generalized Nosé–Hoover oscillator which is a three-dimensional quadratic polynomial system. Precisely, a lot of moderately conservative regions are found, each of which is filled with different sequences of nested tori with various knot types and is embedded in the “chaotic region”. This shows that the generalized Nosé–Hoover oscillator may possess so-called “fat fractal” structure in phase space. In addition, horseshoe chaos can be demonstrated by applying the topological horseshoe theory to a Poincaré map defined in a proper cross-section, which further shows the coexistence of infinitely stable periodic trajectories and infinite saddle periodic trajectories.

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On the Use of Fractal Concepts in Analysis of Distributions of Galaxies

Symposium - International Astronomical Union ◽

10.1017/s007418090011040x ◽

1996 ◽

Vol 168 ◽

pp. 473-475

Author(s):

I.B. Vavilova

Keyword(s):

Fractal Structure ◽

Three Dimensional ◽

Fractal Pattern ◽

Galaxy Distribution ◽

Low Surface Brightness ◽

The Galaxy ◽

Good Review ◽

Dimensional Distribution ◽

The Universe ◽

Scaling Index

The well- grounded polemics about the fractal structure of the Universe and a new cosmological picture which appears in connection with this, in first instance the absence of any evidence for homogenization up to present observational limits 200h−1Mpc, have been detailed at the work by Coleman, Pietronero (1992). Two versions on nature of fractal pattern of the galaxy distribution in the observed universe also are now: it behaves like a simple homogeneous fractal (Pietronero 1987; Coleman et al. 1988) and as a multifractal - fractal having more than one scaling index (Jones et al. 1988; Martinez, Jones 1990; Martinez et al. 1990; Borgani et al. 1993 (with the good review for matter of above)).This work does not play decisively into hands of these versions so the fractal concepts, exactly a selfsimilarity and multifractal, were applied here for the analysis oftwo - dimensionaldistribution of thebrightgalaxies and dwarf galaxies of the low surface brightness (LSBD) belonging to the Local Supercluster (LS). But if the observed universe holds the fractal structure, so it is useful to trace over the lower fractal pattern on the small scales of clustering of galaxies within the framework of the known superclusters and, in the first instance, within the local overdensity of galaxies. This work is a preliminary before preparing one with the same analysis of three- dimensional distribution of galaxies of LS.

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Three-dimensional reconstruction and quantification of cervical carcinoma invasion fronts from histological serial sections

IEEE Transactions on Medical Imaging ◽

10.1109/tmi.2005.855437 ◽

2005 ◽

Vol 24 (10) ◽

pp. 1286-1307 ◽

Cited By ~ 44

Author(s):

U.-D. Braumann ◽

J.-P. Kuska ◽

J. Einenkel ◽

L.-C. Horn ◽

M. Loffler ◽

...

Keyword(s):

Cervical Carcinoma ◽

Three Dimensional ◽

Serial Sections ◽

Three Dimensional Reconstruction ◽

Invasion Fronts ◽

Dimensional Reconstruction

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Development of Flow Behind Three-Dimensional Fractal Structure

ASME-JSME-KSME 2011 Joint Fluids Engineering Conference: Volume 1, Symposia – Parts A, B, C, and D ◽

10.1115/ajk2011-21022 ◽

2011 ◽

Cited By ~ 1

Author(s):

Toshimasa Hiramatsu ◽

Yuuki Kato ◽

Tatsuo Ushijima ◽

Osami Kitoh

Keyword(s):

Wind Tunnel ◽

Cross Section ◽

High Reynolds Number ◽

Fractal Structure ◽

Three Dimensional ◽

Small Scale ◽

Blockage Ratio ◽

Flow Development ◽

High Reynolds ◽

Dimensional Object

Flow development of wake behind Sierpinski tetrahedron has been investigated. The Sierpinski tetrahedron is a three dimensional object of which fractal dimension is 2. Blockage ratio of the Sierpinski tetrahedron over cross section of wind tunnel is 100%. It is found that the fractal object can has an ability to generate relatively high Reynolds number based on turbulent intensity and Taylor microscale (Reλ = 155) even with the small scale wind tunnel of the present study.

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