On the total number of distinct self-interacting self-avoiding walks on three-dimensional fractal structures

2004 ◽  
Vol 38 (3) ◽  
pp. 555-565 ◽  
Author(s):  
I Živić ◽  
S Milošević ◽  
B Djordjević
Keyword(s):  
Three Dimensional ◽  
Fractal Structures ◽  
Self Avoiding Walks

scholarly journals Monte Carlo results for three-dimensional self-avoiding walks

1998 ◽  
Vol 63 (1-3) ◽  
pp. 652-654 ◽  
Author(s):  
S. Caracciolo ◽  
M.S. Causo ◽  
A. Pelissetto
Keyword(s):  
Monte Carlo ◽  
Three Dimensional ◽  
Self Avoiding Walks

scholarly journals Three-dimensional Hausdorff derivative diffusion model for isotropic/anisotropic fractal porous media

2018 ◽  
Vol 22 (Suppl. 1) ◽  
pp. 1-6 ◽  
Author(s):  
Wei Cai ◽  
Wen Chen ◽  
Fajie Wang
Keyword(s):  
Porous Media ◽  
Fundamental Solution ◽  
Diffusion Equation ◽  
Diffusion Model ◽  
Anomalous Diffusion ◽  
Three Dimensional ◽  
Fractal Structures ◽  
Anisotropic Porous Media ◽  
Convection Diffusion Equation ◽  
Time Space

The anomalous diffusion in fractal isotropic/anisotropic porous media is characterized by the Hausdorff derivative diffusion model with the varying fractal orders representing the fractal structures in different directions. This paper presents a comprehensive understanding of the Hausdorff derivative diffusion model on the basis of the physical interpretation, the Hausdorff fractal distance and the fundamental solution. The concept of the Hausdorff fractal distance is introduced, which converges to the classical Euclidean distance with the varying orders tending to 1. The fundamental solution of the 3-D Hausdorff fractal derivative diffusion equation is proposed on the basis of the Hausdorff fractal distance. With the help of the properties of the Hausdorff derivative, the Huasdorff diffusion model is also found to be a kind of time-space dependent convection-diffusion equation underlying the anomalous diffusion behavior.

AUTOSTEREOSCOPIC STAIRCASE FRACTAL STRUCTURES WITH CSL-PARALLAX

Fractals ◽  
2007 ◽  
Vol 15 (04) ◽  
pp. 337-350
Author(s):  
BORIS P. BULAEV
Keyword(s):  
High Frequency ◽  
Three Dimensional ◽  
Design Guidelines ◽  
Laser Printer ◽  
Digital Printing ◽  
Depth Information ◽  
Fractal Structures ◽  
New Approach ◽  
Moiré Fringes ◽  
Standard Laser

We offer a new approach to the fabrication of remarkable autostereoscopic double-layer computer generated images or autostereoscopic staircase fractal structures (ASFSs) based on staircase fractals and moiré methods. Besides, we have found that the unwanted moiré fringes or moiré noises in the ASFSs will markedly decrease if high frequency fractal noises are employed. These ASFSs were observed to be similar in some sense to Denishuk or reflection holograms. Analyzing the geometry and parallax of the circle of skew lines (CSL-parallax) at the presentation of stereo depth information in ASFSs, we hope to provide design guidelines for autostereoscopic digital printing and so on and so forth. A far more important example is a computer synthesis of three-dimensional graphic symbols, a standard laser printer and this CSL-parallax being employed.

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