CHARACTERIZATION OF FRACTAL STRUCTURES THROUGH A HAUSDORFF MEASURE BASED METHOD

2004 ◽  
Author(s):  
FAHIMA NEKKA ◽  
JUN LI
Keyword(s):  
Hausdorff Measure ◽  
Fractal Structures

Morphogenesis of the bone marrow: fractal structures and diffusion- limited growth

Blood ◽  
1996 ◽  
Vol 87 (12) ◽  
pp. 5027-5031 ◽  
Author(s):  
F Naeim ◽  
F Moatamed ◽  
M Sahimi
Keyword(s):  
Bone Marrow ◽  
Spatial Organization ◽  
Fractal Dimensions ◽  
Fractal Structures ◽  
Diffusion Limited Aggregation ◽  
Diffusion Limited ◽  
Morphometric Analyses ◽  
Cellular Area ◽  
Pathologic Processes

Bone marrow (BM) provides a particular spatial organization that allows interaction between its various components. Characterization of the spatial patterns in the BM and understanding the mechanisms that give rise to them may play a role in better understanding of the BM pathologic processes. Morphometric analyses were performed in BM biopsy samples from 30 patients (16 men and 14 women) with an average age of 46 years, ranging from 17 to 77 years. The biopsies were obtained during the course of patient care to rule out BM involvement in a variety of hematologic disorders before or after therapy. Three different, but structurally interrelated, parameters were measured: (A) cellular area, (B) nuclear area, and (C) cell numbers. All three methods, in all cases, showed that the spatial structure of the BM is fractal. The average values of the fractal dimensions (Df) were 1.7 +/- 0.08, 1.64 +/- 0.1, and 1.69 +/- 0.04 for categories A, B, and C, respectively. The overall value of Df for the cellularity in the range of 40% to 60% was about 1.67 +/- 0.09. Fractal dimensions of 1.6 to 1.7 represent configurations that correspond to two-dimensional diffusion limited aggregation structures, suggesting that the structural configuration of hematopoietic cells is dependent on the diffusion of regulatory cytokines in the BM.

scholarly journals Dynamical characterization of mixed fractal structures

2011 ◽  
Vol 6 (1-4) ◽  
pp. 51-69 ◽  
Author(s):  
Luiz Bevilacqua ◽  
Marcelo Barros
Keyword(s):  
Fractal Structures

scholarly journals Inducing Nematic Ordering of Cellulose Nanofibers using Osmotic Dehydration

2018 ◽  
Author(s):  
Valentina Guccini ◽  
Shun Yu ◽  
Michael Agthe ◽  
Korneliya Gordeyeva ◽  
Yulia Trushkina ◽  
...  
Keyword(s):  
Osmotic Dehydration ◽  
Cellulose Nanofibers ◽  
Gel Formation ◽  
Fractal Structures ◽  
Maximum Order ◽  
X Ray ◽  
Nematic Ordering ◽  
X Ray Scattering ◽  
Wide Range

<div><div><p>The formation and characterization of nematically-ordered CNF materials (maximum order parameter f ≈ 0.8) has been studied by polarized optical microscopy, small angle x-ray scattering (SAXS), and rheological measurements as a function of CNF concentration. The wide range of CNF concentrations, from 0.5 wt% to 4.9 wt%, is obtained using osmotic dehydration with PEG. At concentrations >1.05 wt% the CNF suspension crosses an isotropic-anisotropic transition that is accompanied by a dramatic increase of the optical birefringence. The resulting nanostructures are depicted by a hierarchical model with mass fractal structures that converge into co-existing nematically-ordered regions and network-like regions, in which the correlation distances decrease upon increasing concentration. The use of rapid, upscaleble osmotic dehydration is an effective method to increase the concentration of CNF suspensions while partly circumventing the gel formation. The facile formation of highly ordered fibers can result in materials with interesting macroscopic properties.</p></div></div>

Projected Measures: A Simple Way to Characterize Fractal Structures and Interfaces

Fractals ◽  
1997 ◽  
Vol 05 (02) ◽  
pp. 295-308
Author(s):  
Massimiliano Giona ◽  
Manuela Giustiniani ◽  
Oreste Patierno
Keyword(s):  
Closed Form ◽  
Fourier Transforms ◽  
Fractal Structures ◽  
Multifractal Spectra ◽  
Self Similar ◽  
The Moment ◽  
Dynamic Phenomena

The properties of projected measures of fractal objects are investigated in detail. In general, projected measures display multifractal features which play a role in the evolution of dynamic phenomena on/through fractal structures. Closed-form results are obtained for the moment hierarchy of model fractal interfaces. The distinction between self-similar and self-affine interfaces is discussed by considering the properties of multifractal spectra, the orientational effects in the behavior of the moment hierarchies, and the scaling of the corresponding Fourier transforms. The implications of the properties of projected measures in the characterization of transfer phenomena across fractal interfaces are briefly analyzed.

scholarly journals Characterization of tandem aerosol classifiers for selecting particles: implication for eliminating multiple charging effect

2022 ◽  
Author(s):  
Yao Song ◽  
Xiangyu Pei ◽  
Huichao Liu ◽  
Jiajia Zhou ◽  
Zhibin Wang
Keyword(s):  
Transfer Functions ◽  
Particle Morphology ◽  
Vital Role ◽  
Mass Analyzer ◽  
Fractal Structures ◽  
Multiply Charged ◽  
Lab Experiments ◽  
Multiple Charging ◽  
Charging Effect

Abstract. Accurate particle classification plays a vital role in aerosol studies. Differential mobility analyzer (DMA), centrifugal particle mass analyzer (CPMA) and aerodynamic aerosol classifier (AAC) are commonly used to select particles with a specific size or mass. However, multiple charging effect cannot be entirely avoided either using individual technique or using tandem system such as DMA-CPMA, especially when selecting soot particles with fractal structures. In this study, we demonstrate the transfer functions of DMA-CPMA and DMA-AAC systems, as well as the potential multiple charging effect. Our results show that the ability to remove multiply charged particles mainly depends on particles morphology and instruments setups of DMA-CPMA system. Using measurements from soot experiments and literature data, a general trend in the appearance of multiple charging effect with decreasing size when selecting aspherical particles was observed. Otherwise, our results indicated that the ability of DMA-AAC to resolve particles with multiple charges is mainly related to the resolutions of classifiers. In most cases, DMA-AAC can eliminate multiple charging effect regardless of the particle morphology, while particles with multiple charges can be selected when decreasing resolutions of DMA and AAC. We propose that the multiple charging effect should be reconsidered when using DMA-CPMA or DMA-AAC system in estimating size and mass resolved optical properties in the field and lab experiments.

scholarly journals On strong summability and convergence

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3095-3123
Author(s):  
Eberhard Malkowsky
Keyword(s):  
Hausdorff Measure ◽  
Measure Of Noncompactness ◽  
Compact Operators ◽  
Strong Summability ◽  
Linear Operators ◽  
Topological Properties ◽  
Hausdorff Measure Of Noncompactness ◽  
Bounded Sequences ◽  
Convergent Sequences

We give a survey of the recent results concerning the fundamental topological properties of spaces of stronly summable and convergent sequences, their ?- and continuous duals, and the characterizations of classes of linear operators between them. Furthermore we demonstrate how the Hausdorff measure of noncompactness can be used in the characterization of classes of compact operators between the spaces of strongly summable and bounded sequences.

scholarly journals Necessary Condition for Rectifiability Involving Wasserstein Distance W2

2020 ◽  
Author(s):  
Damian Dąbrowski
Keyword(s):  
Hausdorff Measure ◽  
Radon Measure ◽  
Recent Article ◽  
Wasserstein Distance ◽  
Necessary Condition ◽  
Absolutely Continuous ◽  
Dimensional Hausdorff Measure ◽  
Almost All

Abstract A Radon measure $\mu $ is $n$-rectifiable if it is absolutely continuous with respect to $n$-dimensional Hausdorff measure and $\mu $-almost all of ${\operatorname{supp}}\mu $ can be covered by Lipschitz images of $\mathbb{R}^n$. In this paper, we give a necessary condition for rectifiability in terms of the so-called $\alpha _2$ numbers — coefficients quantifying flatness using Wasserstein distance $W_2$. In a recent article, we showed that the same condition is also sufficient for rectifiability, and so we get a new characterization of rectifiable measures.

scholarly journals Characterization of some classes of compact operators between certain matrix domains of triangles

Filomat ◽  
2016 ◽  
Vol 30 (5) ◽  
pp. 1327-1337
Author(s):  
Ivana Djolovic ◽  
Eberhard Malkowsky
Keyword(s):  
Hausdorff Measure ◽  
Measure Of Noncompactness ◽  
Sufficient Conditions ◽  
Compact Operators ◽  
Fredholm Operators ◽  
Hausdorff Measure Of Noncompactness ◽  
Matrix Domains ◽  
Matrix Operators

In this paper, we characterize the classes ((?1)T, (?1)?T ) and (cT, c?T) where T = (tnk)?n,k=0 and ?T=(?tnk)?n,k=0 are arbitrary triangles. We establish identities or estimates for the Hausdorff measure of noncompactness of operators given by matrices in the classes ((?1)T, (?1)?T ) and (cT, c?T). Furthermore we give sufficient conditions for such matrix operators to be Fredholm operators on (?1)T and cT. As an application of our results, we consider the class (bv, bv) and the corresponding classes of matrix operators. Our results are complementary to those in [2] and some of them are generalization for those in [3].

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