Cytoskeleton as a Fractal Percolation Cluster: Some Biological Remarks

Author(s):  
Silvano Traverso
2021 ◽  
Vol 11 (15) ◽  
pp. 6808
Author(s):  
Gengbiao Chen ◽  
Zhiwen Liu

A colloidal damper (CD) can dissipate a significant amount of vibrations and impact energy owing to the interface power that is generated when it is used. It is of great practical significance to study the influence of the nanochannel structure of hydrophobic silica gel in the CD damping medium on the running speed of the CD. The fractal theory was applied to observe the characteristics of the micropore structure of the hydrophobic silica gel by scanning electron microscopy (SEM), the primary particles were selected to carry out fractal analysis, and the two-dimensional fractal dimension of the pore area and the tortuous fractal dimension of the hydrophobic silica gel pore structure were calculated. The fractal percolation model of water in hydrophobic silica nanochannels based on the slip theory could thus be obtained. This model revealed the relationship between the micropore structure parameters of the silica gel and the running speed of the CD. The CD running speed increases with the addition of grafted molecules and the reduction in pore size of the silica gel particles. Continuous loading velocity testing of the CD loaded with hydrophobic silica gels with different pore structures was conducted. By comparing the experimental results with the calculation results of the fractal percolation model, it was determined that the fractal percolation model can better characterize the change trend of the CD running velocity for the first loading, but the fractal dimension was changed from the second loading, caused by the small amount of water retained in the nanochannel, leading to the failure of fractal characterization.


1999 ◽  
Vol 121 (5) ◽  
pp. 480-486 ◽  
Author(s):  
O. I. Craciunescu ◽  
S. K. Das ◽  
S. T. Clegg

Dynamic contrast-enhanced magnetic resonance imaging (DE-MRI) of the tumor blood pool is used to study tumor tissue perfusion. The results are then analyzed using percolation models. Percolation cluster geometry is depicted using the wash-in component of MRI contrast signal intensity. Fractal characteristics are determined for each two-dimensional cluster. The invasion percolation model is used to describe the evolution of the tumor perfusion front. Although tumor perfusion can be depicted rigorously only in three dimensions, two-dimensional cases are used to validate the methodology. It is concluded that the blood perfusion in a two-dimensional tumor vessel network has a fractal structure and that the evolution of the perfusion front can be characterized using invasion percolation. For all the cases studied, the front starts to grow from the periphery of the tumor (where the feeding vessel was assumed to lie) and continues to grow toward the center of the tumor, accounting for the well-documented perfused periphery and necrotic core of the tumor tissue.


1997 ◽  
Vol 240 (3) ◽  
pp. 242-253 ◽  
Author(s):  
A.M. Glukhov ◽  
A.S. Pokhila ◽  
I.M. Dmitrenko ◽  
A.E. Kolinko ◽  
A.P. Panchekha

1991 ◽  
Vol 24 (3) ◽  
pp. 735-740
Author(s):  
Jae Woo Lee ◽  
Ho Chui Kim ◽  
Jong-Jean Kim

1992 ◽  
Vol 03 (01) ◽  
pp. 213-219 ◽  
Author(s):  
ULLI WOLFF

Percolation cluster Monte Carlo algorithms for nonlinear σ-models on the lattice are reviewed with special emphasis on their possible generalizations. While they have been found to practically eliminate critical slowing down for the standard O(n) invariant vector models, their extension to other physically similar models — like RPn−1 and SU(n)×SU(n) chiral models — is less straight forward than one might have thought. I outline the present situation in this area of research. In the second part of my talk I described a numerical calculation of a physical running coupling constant in the O(3) model. This represents an application of the cluster technique in a preparatory study for a later lattice gauge theory calculation. This material can be found in Ref. 11.


1989 ◽  
Vol 03 (10) ◽  
pp. 765-770
Author(s):  
C.S. KIM ◽  
MIN-HO LEE

We studied two subjects related to anisotropy: random walk on percolation cluster having anisotropy (RWAC) and direction dependent (anisotropic) random walk on percolation cluster (AWIC). We find that the anisotropy of the cluster has only time-delaying effect on asymptotic convergence of the spectral dimensionality ds and fractal dimensionality of walk dw, however, the anisotropy of the walk results in lower spectral dimensionality and higher fractal dimensionality, as anisotropy grows larger.


JETP Letters ◽  
1999 ◽  
Vol 69 (12) ◽  
pp. 954-958
Author(s):  
Yu. V. Pakharukov ◽  
T. E. Shevnina

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