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 Synthesis of Cobalt Oxides Thin Films Fractal Structures by Laser Chemical Vapor Deposition

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
P. Haniam ◽  
C. Kunsombat ◽  
S. Chiangga ◽  
A. Songsasen
Keyword(s):  
Thin Films ◽  
Chemical Vapor Deposition ◽  
Vapor Deposition ◽  
Atmospheric Pressure ◽  
Chemical Vapor ◽  
Cobalt Oxides ◽  
Fractal Structures ◽  
Laser Chemical Vapor Deposition ◽  
Diffusion Limited Aggregation ◽  
Diffusion Limited

Thin films of cobalt oxides (CoO and Co3O4) fractal structures have been synthesized by using laser chemical vapor deposition at room temperature and atmospheric pressure. Various factors which affect the density and crystallization of cobalt oxides fractal shapes have been examined. We show that the fractal structures can be described by diffusion-limited aggregation model and discuss a new possibility to control the fractal structures.

Concentration Influence on Diffusion Limited Cluster Aggregation

1994 ◽  
Vol 367 ◽  
Author(s):  
ST.C. Pencea ◽  
M. Dumitrascu
Keyword(s):  
Brownian Motion ◽  
Fractal Dimensions ◽  
Simple Random Walk ◽  
Two Dimensional ◽  
Diffusion Limited Aggregation ◽  
Dimensional Lattice ◽  
Cluster Aggregation ◽  
Box Counting ◽  
Diffusion Limited ◽  
Diffusion Limited Cluster Aggregation

AbstractDiffusion-limited cluster aggregation has been simulated on a square two dimensional lattice. In order to simulate the brownian motion, we used both the algorithm proposed initially by Kolb et all. and a new algorithm intermediary between a simple random walk and the ballistic model.The simulation was performed for many values of the concentration, from 1 to 50%. By using a box-counting algorithm one has calculated the fractal dimensions of the obtained clusters. Its increasing vs. concentration has been pointed out. The results were compared with those of the classical diffusion-limited aggregation (DLA).

scholarly journals Model the structure of nano-modified aluminium alloy with the addition of boron carbide

2021 ◽  
Vol 2131 (5) ◽  
pp. 052084
Author(s):  
D N Bukharov ◽  
S M Arakelyan ◽  
E S Prusov ◽  
A A Panfilov ◽  
V D Samyshkin ◽  
...  
Keyword(s):  
Boron Carbide ◽  
Dendritic Structure ◽  
Fractal Dimensions ◽  
High Tech ◽  
Time Intervals ◽  
Diffusion Limited Aggregation ◽  
High Tech Industry ◽  
Diffusion Limited ◽  
Nanocomposite Thin Films ◽  
Model Structures

Abstract Nanocomposite thin films based on Al-Si alloy with the addition of boron carbide (B4C) particles are widely used in various fields of modern high-tech industry. For their synthesis, the method of laser nanomodification was used, which made it possible to obtain samples with a dendritic structure. The parameters of laser radiation were selected on the basis of preliminary modeling of the temperature field of the system. To describe the ensemble of nanodendrites on the surface, we used modeling of their structure in variable phase field and temperature for the initial stages, as well as the approximation of diffusion-limited aggregation and fractal Brownian motion for subsequent time intervals. The model showed satisfactory adequacy, estimated on the basis of the ratio of fractal dimensions of experimental and model structures. The proposed approach can be useful for predicting the structure of nanomodified aluminum alloys with various additions.

Simulation of Fractal-Like Crystal Growth

1991 ◽  
Vol 46 (1-2) ◽  
pp. 203-205
Author(s):  
Attila Felinger ◽  
Jänos Liszi
Keyword(s):  
Crystal Growth ◽  
Fractal Dimensions ◽  
Stochastic Method ◽  
Square Lattice ◽  
Two Dimensional ◽  
Diffusion Limited Aggregation ◽  
Equilibrium Crystallization ◽  
Diffusion Limited ◽  
Large Clusters ◽  
Small Clusters

AbstractNon-equilibrium crystallization was simulated on a two dimensional square lattice. Several clusters were grown simultaneously by using the model of diffusion limited aggregation. The growing process was reversible, i.e. dissolution of particles from the boundary of any cluster was made possible. The rate of growth and dissolution was determined by a stochastic method. The simulation resulted in an aggregate pattern having a few large and several small clusters. The fractal dimensions of the large clusters were found in the range of D = 1.62-1.72.

The Angular Distribution of Scattering Intensity and Polarization for Nano-Graphite Aggregates

2013 ◽  
Vol 432 ◽  
pp. 78-81
Author(s):  
Hong Xia Wang ◽  
Hong Hui Sun ◽  
Dai Zhi Liu ◽  
Zi Biao Song
Keyword(s):  
Light Scattering ◽  
Near Infrared ◽  
Three Dimensional ◽  
Dipole Approximation ◽  
Angle Distribution ◽  
Fractal Structures ◽  
Diffusion Limited Aggregation ◽  
Scattering Intensity ◽  
Diffusion Limited ◽  
Spherical Complex

The light scattering characteristics of nanographite aggregates are analyzed in this paper. Three dimensional fractal structures of aggregates were simulated based on the diffusion-limited aggregation model (DLA). For the incident wave of different wavelength, the method of discrete dipole approximation (DDA) was used to compute the light scattering intensity of nanographite aggregates and the changes of polarization along with the scattering angles, and the light scattering characteristics of nanographite aggregates were compared with the equal volume spherical nanographite particles. The computing results show that the non-spherical complex shape of nanographite aggregates has great effect on the scattering characteristics in the visible and near-infrared, and the angle distribution of scattering intensity and polarization have many complex changes. The forward scattering intensity of nanographite aggregates is obviously stronger than the equal volume spherical nanographite particles.

Two-Length-Scale Structure in Some Computer-Generated Aggregates Grown by Diffusion-Limited Aggregation

1994 ◽  
Vol 367 ◽  
Author(s):  
Paul W. Schmidt ◽  
Giuseppe Pipitone ◽  
M. A. Floriano ◽  
E. Caponetri ◽  
R. Triolo
Keyword(s):  
Neutron Scattering ◽  
Small Angle ◽  
Large Scale ◽  
Characteristic Length ◽  
Fractal Dimensions ◽  
Scale Structure ◽  
Length Scale ◽  
Diffusion Limited Aggregation ◽  
X Ray ◽  
Diffusion Limited

AbstractThe properties of some aggregates “grown” on a computer by diffusion-limited aggregation have been investigated. Calculations showed that the intensity of the small-angle x-ray and neutron scattering from the aggregates was proportional to q−D for qL ≫ 1, where D > 0, L is a length that characterizes the large-scale structure of the aggregate, q = 4πλ−1 sin(θ/2), γ is the wavelength, and θ is the scattering angle. The magnitude of the exponent D was appreciably smaller than the fractal dimensions that many simulations have shown to be typical of the mass fractal aggregates grown by diffusion-limited aggregation. The calculations suggest that the aggregates have structure on two different characteristic-length scales.

SCALING IN THE FREQUENCY-DEPENDENT ADMITTANCE OF ELECTRODEPOSITED FRACTAL ELECTRODES

Fractals ◽  
1994 ◽  
Vol 02 (02) ◽  
pp. 191-199 ◽  
Author(s):  
AMY E. LARSEN ◽  
DAVID G. GRIER ◽  
THOMAS C. HALSEY
Keyword(s):  
Aqueous Solution ◽  
Computer Simulations ◽  
Phase Angle ◽  
Fractal Dimensions ◽  
Frequency Range ◽  
Diffusion Limited Aggregation ◽  
Frequency Dependent ◽  
Aggregation Model ◽  
Diffusion Limited ◽  
Complex Admittance

We describe measurements of the complex admittance of the interface between a class of fractal electrodes and electrolytic solutions over the frequency range 100 Hz to 40 kHz. The electrodes are grown by the diffusion-limited electrodeposition of copper from aqueous solution and have fractal dimensions comparable to those obtained for computer simulations of the diffusion-limited aggregation model, Df = 2.5. The admittance measured at various stages of the electrodeposit's growth displays constant phase angle (CPA) scaling with frequency. This behavior appears to have its origins in the disordered geometry of the system, although our measurements do not agree with the scaling predictions of theories for fractal blocking electrodes.

Nonuniversal diffusion-limited aggregation and exact fractal dimensions

1994 ◽  
Vol 49 (3) ◽  
pp. R1788-R1791 ◽  
Author(s):  
P. Ossadnik ◽  
Chi-Hang Lam ◽  
Leonard M. Sander
Keyword(s):  
Fractal Dimensions ◽  
Diffusion Limited Aggregation ◽  
Diffusion Limited

The Simulation of the Two-Dimensional Ising Model on the Creutz Cellular Automaton for the Fractals Obtained by Using the Model of Diffusion-Limited Aggregation

2010 ◽  
Vol 65 (8-9) ◽  
pp. 705-710 ◽  
Author(s):  
Ziya Merdan ◽  
Mehmet Bayirli ◽  
Mustafa Kemal Ozturk
Keyword(s):  
Cellular Automaton ◽  
Finite Size ◽  
Fractal Dimensions ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Diffusion Limited Aggregation ◽  
Diffusion Limited ◽  
Linear Dimensions ◽  
Creutz Cellular Automaton ◽  
Good Agreement

The fractals are obtained by using the model of diffusion-limited aggregation (DLA) for the lattice with L = 80, 120, and 160. The values of the fractal dimensions are compared with the results of former studies. As increasing the linear dimensions they are in good agreement with those. The fractals obtained by using the model of DLA are simulated on the Creutz cellular automaton by using a two-bit demon. The values computed for the critical temperature and the static critical exponents within the framework of the finite-size scaling theory are in agreement with the results of other simulations and theoretical values

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