An Application of the Fractal Theory: The Determination of Fractal Structure of Flocs in coagulation-flocculation

A rapid method of determining the structure of aggregated particles using small angle laser light scattering is applied here to assemblages of bacteria from wastewater treatment systems. The structure information so obtained is suggestive of fractal behaviour as found by other methods. Strong dependencies are shown to exist between the fractal structure of the bacterial aggregates and the behaviour of the biosolids in zone settling and dewatering by both pressure filtration and centrifugation methods. More rapid settling and significantly higher solids contents are achievable for “looser” flocs characterised by lower fractal dimensions. The rapidity of determination of structural information and the strong dependencies of the effectiveness of a number of wastewater treatment processes on aggregate structure suggests that this method may be particularly useful as an on-line control tool.

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Research On The Fractal and Percolation Characteristics of Coal-Based Porous Media For Filtration and Impregnation

10.21203/rs.3.rs-948994/v1 ◽

2021 ◽

Author(s):

Qili Wang ◽

Jiarui Sun ◽

Yuehu Chen ◽

Yuyan Qian ◽

Shengcheng Fei ◽

...

Keyword(s):

Porous Media ◽

Fractal Structure ◽

Mercury Intrusion Porosimetry ◽

Fractal Theory ◽

Fractal Dimensions ◽

Infinite Cluster ◽

Porous Graphite ◽

Local Aggregation ◽

Gradual Expansion ◽

The Difference

Abstract In order to distinguish the difference in the heterogeneous fractal structure of porous graphite used for filtration and impregnation, the fractal dimensions obtained through the mercury intrusion porosimetry (MIP) along with the fractal theory were used to calculate the volumetric FD of the graphite samples. The FD expression of the tortuosity along with all parameters from MIP test was optimized to simplify the calculation. In addition, the percolation evolution process of mercury in the porous media was analyzed in combination with the experimental data. As indicated in the analysis, the FDs in the backbone formation regions of sample vary from 2.695 to 2.984, with 2.923 to 2.991 in the percolation regions and 1.224 to 1.544 in the tortuosity. According to the MIP test, the mercury distribution in porous graphite manifested a transitional process from local aggregation, gradual expansion, and infinite cluster connection to global connection.

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Determination of Clay Bound Water in Shales from NMR Signals: The Fractal Theory

Energy & Fuels ◽

10.1021/acs.energyfuels.1c02285 ◽

2021 ◽

Author(s):

Kouqi Liu ◽

Zhijun Jin ◽

Lianbo Zeng ◽

Yujie Yuan ◽

Mehdi Ostadhassan

Keyword(s):

Fractal Theory ◽

Bound Water ◽

Nmr Signals

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Complexity-Based Analysis of the Relation Between Fractal Visual Stimuli and Fractal Eye Movements

Fluctuation and Noise Letters ◽

10.1142/s0219477519500123 ◽

2019 ◽

Vol 18 (03) ◽

pp. 1950012 ◽

Cited By ~ 18

Author(s):

Hedieh Alipour ◽

Farzad Towhidkhah ◽

Sajad Jafari ◽

Avinash Menon ◽

Hamidreza Namazi

Keyword(s):

Eye Movements ◽

Eye Movement ◽

Fractal Structure ◽

Visual Target ◽

Fractal Theory ◽

Complex Structure ◽

Vision Science ◽

Human Eye ◽

Field Of Vision ◽

External Stimuli

Human eye movement is a key concept in the field of vision science. It has already been established that human eye movement responds to external stimuli. Hence, investigating the reaction of the human eye movement to various types of external stimuli is important in this field. There have been many researches on human eye movement that were previously done, but this is the first study to show a relation between the complex structure of human eye movement and the complex structure of static visual stimulus. Fractal theory was implemented and we showed that the fractal dynamics of the human eye movement is related to the fractal structure of visual target as stimulus. The outcome of this research provides new platforms to scientists to further investigate on the relation between eye movement and other applied stimuli.

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Culturomics meets random fractal theory: insights into long-range correlations of social and natural phenomena over the past two centuries

Journal of The Royal Society Interface ◽

10.1098/rsif.2011.0846 ◽

2012 ◽

Vol 9 (73) ◽

pp. 1956-1964 ◽

Cited By ~ 74

Author(s):

Jianbo Gao ◽

Jing Hu ◽

Xiang Mao ◽

Matjaž Perc

Keyword(s):

Long Range ◽

Driving Forces ◽

Fractal Theory ◽

Natural Phenomena ◽

Social Phenomena ◽

Long Range Correlations ◽

The Past ◽

Random Fractal ◽

Data Collection And Analysis

Culturomics was recently introduced as the application of high-throughput data collection and analysis to the study of human culture. Here, we make use of these data by investigating fluctuations in yearly usage frequencies of specific words that describe social and natural phenomena, as derived from books that were published over the course of the past two centuries. We show that the determination of the Hurst parameter by means of fractal analysis provides fundamental insights into the nature of long-range correlations contained in the culturomic trajectories, and by doing so offers new interpretations as to what might be the main driving forces behind the examined phenomena. Quite remarkably, we find that social and natural phenomena are governed by fundamentally different processes. While natural phenomena have properties that are typical for processes with persistent long-range correlations, social phenomena are better described as non-stationary, on–off intermittent or Lévy walk processes.

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DECODING OF STEADY-STATE VISUAL EVOKED POTENTIALS BY FRACTAL ANALYSIS OF THE ELECTROENCEPHALOGRAPHIC (EEG) SIGNAL

Fractals ◽

10.1142/s0218348x18500925 ◽

2018 ◽

Vol 26 (06) ◽

pp. 1850092 ◽

Cited By ~ 29

Author(s):

HAMIDREZA NAMAZI ◽

TIRDAD SEIFI ALA ◽

HOVAGIM BAKARDJIAN

Keyword(s):

Steady State ◽

Evoked Potentials ◽

Visual Evoked Potentials ◽

Fractal Structure ◽

Visual Stimulation ◽

Fractal Theory ◽

Objective Assessment ◽

Eeg Signal ◽

Brain Response ◽

Visual Evoked

Analysis of the brain response to different types of external stimuli has always been one of the major research areas in behavioral neuroscience. The electroencephalography (EEG) technique combined with different signal analysis approaches has been especially successful in revealing the detailed dynamic properties of the neural response to exogenous stimulation. In this analysis, we evaluated the nonlinear structure of the EEG signal using fractal theory in rest and visual stimulation (checkerboard reversal at 8, 14 and 28[Formula: see text]Hz). Our analysis showed a significant influence of stimulation on the fractal structure of EEG signal. On comparison between different conditions, 14-Hz steady-state visual evoked potentials (SSVEPs), previously shown to trigger an optimal brain response, exhibited the greatest influence on the complexity of the EEG signal. On the other hand, we observed the lowest complexity of EEG signal in the post-stimulation rest period. Statistical analysis confirmed significant differences in the fractal structure of the EEG signal between rest and different stimulation conditions. These findings demonstrate for the first time a direct relationship between the efficiency of brain processing and the complexity of the measured EEG signal, which could be employed for objective assessment and classification in various experimental paradigms.

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FAST LASER SPECTROSCOPY FOR DETERMINATION OF ENERGY TRANSFER ON THE FRACTAL STRUCTURE OF SILICA-GELS

Le Journal de Physique Colloques ◽

10.1051/jphyscol:19877126 ◽

1987 ◽

Vol 48 (C7) ◽

pp. C7-529-C7-531

Author(s):

B. CHAMPAGNON ◽

J. L. ROUSSET ◽

A. MONTEIL ◽

M. FERRARI ◽

E. DUVAL ◽

...

Keyword(s):

Energy Transfer ◽

Laser Spectroscopy ◽

Fractal Structure ◽

Silica Gels

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Self-Affine Fractal Characterization of a TNT Fracture Surface

MRS Proceedings ◽

10.1557/proc-578-363 ◽

1999 ◽

Vol 578 ◽

Author(s):

L. V. Meisel ◽

R. D. Scanlon ◽

M. A. Johnson ◽

Y. D. Lanzerotti

Keyword(s):

Fracture Surface ◽

Fractal Structure ◽

Height Function ◽

Height Functions ◽

Atomic Force ◽

High Acceleration ◽

Surface Image ◽

Fracture Processes

AbstractA trinitrotoluene (TNT) fracture surface image is characterized in terms of a self-affine fractal structure. The fracture surface was produced by high acceleration in an ultracentrifuge when the TNT strength was exceeded. An atomic force microscope (AFM) captured the topography of a 4 micron square region on the fracture surface. The present analysis supports a self-affine description of the TNT fracture surface (wavelengths of 0.016 micron to 4.0 micron) and provides a new prespective on fracture processes in TNT. An essential step in self-affine fractal characterization of surfaces is the determination of reference surfaces. A self-affine fracture surface can be described in terms of a single-valued height function. In the TNT fracture surface, single-valued height functions, which describe surface texture can only be defined with respect to curved reference surfaces. By employing curved reference surfaces, we have demonstrated that self-affine fractal scaling can be used to characterize the TNT fracture surface. This provides important information that is not evident in the analysis of individual surface scans.

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