Micromorphological characterization of zinc/silver particle composite coatings

PubMed Central

Méndez, Alia; Reyes, Yolanda; Trejo, Gabriel; StĘpień, Krzysztof

2015-01-01

ABSTRACT The aim of this study was to evaluate the three‐dimensional (3D) surface micromorphology of zinc/silver particles (Zn/AgPs) composite coatings with antibacterial activity prepared using an electrodeposition technique. These 3D nanostructures were investigated over square areas of 5 μm × 5 μm by atomic force microscopy (AFM), fractal, and wavelet analysis. The fractal analysis of 3D surface roughness revealed that (Zn/AgPs) composite coatings have fractal geometry. Triangulation method, based on the linear interpolation type, applied for AFM data was employed in order to characterise the surfaces topographically (in amplitude, spatial distribution and pattern of surface characteristics). The surface fractal dimension D f, as well as height values distribution have been determined for the 3D nanostructure surfaces. Microsc. Res. Tech. 78:1082–1089, 2015. © 2015 The Authors published by Wiley Periodicals, Inc. PMID:26500164

Time Series Analysis OF SAR Image Fractal Maps: The Somma-Vesuvio Volcanic Complex Case Study

NASA Astrophysics Data System (ADS)

Pepe, Antonio; De Luca, Claudio; Di Martino, Gerardo; Iodice, Antonio; Manzo, Mariarosaria; Pepe, Susi; Riccio, Daniele; Ruello, Giuseppe; Sansosti, Eugenio; Zinno, Ivana

2016-04-01

The fractal dimension is a significant geophysical parameter describing natural surfaces representing the distribution of the roughness over different spatial scale; in case of volcanic structures, it has been related to the specific nature of materials and to the effects of active geodynamic processes. In this work, we present the analysis of the temporal behavior of the fractal dimension estimates generated from multi-pass SAR images relevant to the Somma-Vesuvio volcanic complex (South Italy). To this aim, we consider a Cosmo-SkyMed data-set of 42 stripmap images acquired from ascending orbits between October 2009 and December 2012. Starting from these images, we generate a three-dimensional stack composed by the corresponding fractal maps (ordered according to the acquisition dates), after a proper co-registration. The time-series of the pixel-by-pixel estimated fractal dimension values show that, over invariant natural areas, the fractal dimension values do not reveal significant changes; on the contrary, over urban areas, it correctly assumes values outside the natural surfaces fractality range and show strong fluctuations. As a final result of our analysis, we generate a fractal map that includes only the areas where the fractal dimension is considered reliable and stable (i.e., whose standard deviation computed over the time series is reasonably small). The so-obtained fractal dimension map is then used to identify areas that are homogeneous from a fractal viewpoint. Indeed, the analysis of this map reveals the presence of two distinctive landscape units corresponding to the Mt. Vesuvio and Gran Cono. The comparison with the (simplified) geological map clearly shows the presence in these two areas of volcanic products of different age. The presented fractal dimension map analysis demonstrates the ability to get a figure about the evolution degree of the monitored volcanic edifice and can be profitably extended in the future to other volcanic systems with very distinctive characteristics, with the aim to perform land classification, such as the identification of areas characterized by similar soil use, slopes and exposures.

The Impact of The Fractal Paradigm on Geography

NASA Astrophysics Data System (ADS)

De Cola, L.

2001-12-01

Being itself somewhat fractal, Benoit Mandelbrot's magnum opus THE FRACTAL GEOMETRY OF NATURE may be deconstructed in many ways, including geometrically, systematically, and epistemologically. Viewed as a work of geography it may be used to organize the major topics of interest to scientists preoccupied with the understanding of real-world space in astronomy, geology, meteorology, hydrology, and biology. We shall use it to highlight such recent geographic accomplishments as automated feature detection, understanding urban growth, and modeling the spread of disease in space and time. However, several key challenges remain unsolved, among them: 1. It is still not possible to move continuously from one map scale to another so that objects change their dimension smoothly. I.e. as a viewer zooms in on a map the zero-dimensional location of a city should gradually become a 2-dimensional polygon, then a network of 1-dimensional streets, then 3-dimensional buildings, etc. 2. Spatial autocorrelation continues to be regarded more as an econometric challenge than as a problem of scaling. Similarities of values among closely-spaced observation is not so much a problem to be overcome as a source of information about spatial structure. 3. Although the fractal paradigm is a powerful model for data analysis, its ideas and techniques need to be brought to bear on the problems of understanding such hierarchies as ecosystems (the flow networks of energy and matter), taxonomies (biological classification), and knowledge (hierarchies of bureaucratic information, networks of linked data, etc).

Fractal geometry in an expanding, one-dimensional, Newtonian universe.

PubMed

Miller, Bruce N; Rouet, Jean-Louis; Le Guirriec, Emmanuel

2007-09-01

Observations of galaxies over large distances reveal the possibility of a fractal distribution of their positions. The source of fractal behavior is the lack of a length scale in the two body gravitational interaction. However, even with new, larger, sample sizes from recent surveys, it is difficult to extract information concerning fractal properties with confidence. Similarly, three-dimensional N-body simulations with a billion particles only provide a thousand particles per dimension, far too small for accurate conclusions. With one-dimensional models these limitations can be overcome by carrying out simulations with on the order of a quarter of a million particles without compromising the computation of the gravitational force. Here the multifractal properties of two of these models that incorporate different features of the dynamical equations governing the evolution of a matter dominated universe are compared. For each model at least two scaling regions are identified. By employing criteria from dynamical systems theory it is shown that only one of them can be geometrically significant. The results share important similarities with galaxy observations, such as hierarchical clustering and apparent bifractal geometry. They also provide insights concerning possible constraints on length and time scales for fractal structure. They clearly demonstrate that fractal geometry evolves in the mu (position, velocity) space. The observed patterns are simply a shadow (projection) of higher-dimensional structure.

Fractal density modeling of crustal heterogeneity from the KTB deep hole

NASA Astrophysics Data System (ADS)

Chen, Guoxiong; Cheng, Qiuming

2017-03-01

Fractal or multifractal concepts have significantly enlightened our understanding of crustal heterogeneity. Much attention has focused on 1/f scaling natures of physicochemical heterogeneity of Earth crust from fractal increment perspective. In this study, fractal density model from fractal clustering point of view is used to characterize the scaling behaviors of heterogeneous sources recorded at German Continental Deep Drilling Program (KTB) main hole, and of special contribution is the local and global multifractal analysis revisited by using Haar wavelet transform (HWT). Fractal density modeling of mass accumulation generalizes the unit of rock density from integer (e.g., g/cm3) to real numbers (e.g., g/cmα), so that crustal heterogeneities with respect to source accumulation are quantified by singularity strength of fractal density in α-dimensional space. From that perspective, we found that the bulk densities of metamorphic rocks exhibit fractal properties but have a weak multifractality, decreasing with the depth. The multiscaling natures of chemical logs also have been evidenced, and the observed distinct fractal laws for mineral contents are related to their different geochemical behaviors within complex lithological context. Accordingly, scaling distributions of mineral contents have been recognized as a main contributor to the multifractal natures of heterogeneous density for low-porosity crystalline rocks. This finally allows us to use de Wijs cascade process to explain the mechanism of fractal density. In practice, the proposed local singularity analysis based on HWT is suggested as an attractive high-pass filtering to amplify weak signatures of well logs as well as to delineate microlithological changes.

Scale-free crystallization of two-dimensional complex plasmas: Domain analysis using Minkowski tensors

NASA Astrophysics Data System (ADS)

Böbel, A.; Knapek, C. A.; Räth, C.

2018-05-01

Experiments of the recrystallization processes in two-dimensional complex plasmas are analyzed to rigorously test a recently developed scale-free phase transition theory. The "fractal-domain-structure" (FDS) theory is based on the kinetic theory of Frenkel. It assumes the formation of homogeneous domains, separated by defect lines, during crystallization and a fractal relationship between domain area and boundary length. For the defect number fraction and system energy a scale-free power-law relation is predicted. The long-range scaling behavior of the bond-order correlation function shows clearly that the complex plasma phase transitions are not of the Kosterlitz, Thouless, Halperin, Nelson, and Young type. Previous preliminary results obtained by counting the number of dislocations and applying a bond-order metric for structural analysis are reproduced. These findings are supplemented by extending the use of the bond-order metric to measure the defect number fraction and furthermore applying state-of-the-art analysis methods, allowing a systematic testing of the FDS theory with unprecedented scrutiny: A morphological analysis of lattice structure is performed via Minkowski tensor methods. Minkowski tensors form a complete family of additive, motion covariant and continuous morphological measures that are sensitive to nonlinear properties. The FDS theory is rigorously confirmed and predictions of the theory are reproduced extremely well. The predicted scale-free power-law relation between defect fraction number and system energy is verified for one more order of magnitude at high energies compared to the inherently discontinuous bond-order metric. It is found that the fractal relation between crystalline domain area and circumference is independent of the experiment, the particular Minkowski tensor method, and the particular choice of parameters. Thus, the fractal relationship seems to be inherent to two-dimensional phase transitions in complex plasmas. Minkowski tensor analysis turns out to be a powerful tool for investigations of crystallization processes. It is capable of revealing nonlinear local topological properties, however, still provides easily interpretable results founded on a solid mathematical framework.

Experimental Study and Fractal Analysis on the Anisotropic Performance of Explosively Welded Interfaces of 304 Stainless Steel/245 Carbon Steel

NASA Astrophysics Data System (ADS)

Fu, Yanshu; Qiu, Yaohui; Li, Yulong

2018-03-01

The mechanical anisotropy of an explosive welding composite plate made of 304 stainless steel/245 steel was studied through shear experiments performed on explosively welded wavy interfaces along several orientation angles. The results indicated that the strength and the fracture energy of samples significantly varied with the orientation angles. The fracture surfaces of all samples were observed using a scanning electron microscope and through three-dimensional structure microscopy. The periodic features of all the fracture surfaces were clearly shown in different fracture modes. The fractal dimension of the fracture surfaces was calculated based on the fractal geometry by the box-counting method in MATLAB. The cohesive element model was used to analyze the fracture energy according to the physical dependence of the fractal dimension on thermodynamic entropy and interface separation energy. The fracture energy was an exponential function of the fractal dimension value, which was in good agreement with the experimental results. All results were validated for effective use in the application of anisotropy analysis to the welded interface and structural optimization of explosively welded composite plates.

Experimental Study and Fractal Analysis on the Anisotropic Performance of Explosively Welded Interfaces of 304 Stainless Steel/245 Carbon Steel

NASA Astrophysics Data System (ADS)

Fu, Yanshu; Qiu, Yaohui; Li, Yulong

2018-05-01

The mechanical anisotropy of an explosive welding composite plate made of 304 stainless steel/245 steel was studied through shear experiments performed on explosively welded wavy interfaces along several orientation angles. The results indicated that the strength and the fracture energy of samples significantly varied with the orientation angles. The fracture surfaces of all samples were observed using a scanning electron microscope and through three-dimensional structure microscopy. The periodic features of all the fracture surfaces were clearly shown in different fracture modes. The fractal dimension of the fracture surfaces was calculated based on the fractal geometry by the box-counting method in MATLAB. The cohesive element model was used to analyze the fracture energy according to the physical dependence of the fractal dimension on thermodynamic entropy and interface separation energy. The fracture energy was an exponential function of the fractal dimension value, which was in good agreement with the experimental results. All results were validated for effective use in the application of anisotropy analysis to the welded interface and structural optimization of explosively welded composite plates.

Applications of ICA and fractal dimension in sEMG signal processing for subtle movement analysis: a review.

PubMed

Naik, Ganesh R; Arjunan, Sridhar; Kumar, Dinesh

2011-06-01

The surface electromyography (sEMG) signal separation and decphompositions has always been an interesting research topic in the field of rehabilitation and medical research. Subtle myoelectric control is an advanced technique concerned with the detection, processing, classification, and application of myoelectric signals to control human-assisting robots or rehabilitation devices. This paper reviews recent research and development in independent component analysis and Fractal dimensional analysis for sEMG pattern recognition, and presents state-of-the-art achievements in terms of their type, structure, and potential application. Directions for future research are also briefly outlined.

Three-dimensional fractal analysis of 99mTc-MAA SPECT images in chronic thromboembolic pulmonary hypertension for evaluation of response to balloon pulmonary angioplasty: association with pulmonary arterial pressure.

PubMed

Maruoka, Yasuhiro; Nagao, Michinobu; Baba, Shingo; Isoda, Takuro; Kitamura, Yoshiyuki; Yamazaki, Yuzo; Abe, Koichiro; Sasaki, Masayuki; Abe, Kohtaro; Honda, Hiroshi

2017-06-01

Balloon pulmonary angioplasty (BPA) is used for inoperable chronic thromboembolic pulmonary hypertension (CTEPH), but its effect cannot be evaluated noninvasively. We devised a noninvasive quantitative index of response to BPA using three-dimensional fractal analysis (3D-FA) of technetium-99m-macroaggregated albumin (Tc-MAA) single-photon emission computed tomography (SPECT). Forty CTEPH patients who underwent pulmonary perfusion scintigraphy and mean pulmonary arterial pressure (mPAP) measurement by right heart catheterization before and after BPA were studied. The total uptake volume (TUV) in bilateral lungs was determined from maximum intensity projection Tc-MAA SPECT images. Fractal dimension was assessed by 3D-FA. Parameters were compared before and after BPA, and between patients with post-BPA mPAP more than 30 mmHg and less than or equal to 30 mmHg. Receiver operating characteristic analysis was carried out. BPA significantly improved TUV (595±204-885±214 ml, P<0.001) and reduced the laterality of uptake (238±147-135±131 ml, P<0.001). Patients with poor therapeutic response (post-BPA mPAP≥30 mmHg, n=16) showed a significantly smaller TUV increase (P=0.044) and a significantly greater post-BPA fractal dimension (P<0.001) than the low-mPAP group. Fractal dimension correlated with mPAP values before and after BPA (P=0.013 and 0.001, respectively). A post-BPA fractal dimension threshold of 2.4 distinguished between BPA success and failure with 75% sensitivity, 79% specificity, 78% accuracy, and area under the curve of 0.85. 3D-FA using Tc-MAA SPECT pulmonary perfusion scintigraphy enables a noninvasive evaluation of the response of CTEPH patients to BPA.

Poiseuille equation for steady flow of fractal fluid

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2016-07-01

Fractal fluid is considered in the framework of continuous models with noninteger dimensional spaces (NIDS). A recently proposed vector calculus in NIDS is used to get a description of fractal fluid flow in pipes with circular cross-sections. The Navier-Stokes equations of fractal incompressible viscous fluids are used to derive a generalization of the Poiseuille equation of steady flow of fractal media in pipe.

Experimental criteria for the determination of fractal parameters of premixed turbulent flames

NASA Astrophysics Data System (ADS)

Shepherd, I. G.; Cheng, Robert K.; Talbot, L.

1992-10-01

The influence of spatial resolution, digitization noise, the number of records used for averaging, and the method of analysis on the determination of the fractal parameters of a high Damköhler number, methane/air, premixed, turbulent stagnation-point flame are investigated in this paper. The flow exit velocity was 5 m/s and the turbulent Reynolds number was 70 based on a integral scale of 3 mm and a turbulent intensity of 7%. The light source was a copper vapor laser which delivered 20 nsecs, 5 mJ pulses at 4 kHz and the tomographic cross-sections of the flame were recorded by a high speed movie camera. The spatial resolution of the images is 155 × 121 μm/pixel with a field of view of 50 × 65 mm. The stepping caliper technique for obtaining the fractal parameters is found to give the clearest indication of the cutoffs and the effects of noise. It is necessary to ensemble average the results from more than 25 statistically independent images to reduce sufficiently the scatter in the fractal parameters. The effects of reduced spatial resolution on fractal plots are estimated by artificial degradation of the resolution of the digitized flame boundaries. The effect of pixel resolution, an apparent increase in flame length below the inner scale rolloff, appears in the fractal plots when the measurent scale is less than approximately twice the pixel resolution. Although a clearer determination of fractal parameters is obtained by local averaging of the flame boundaries which removes digitization noise, at low spatial resolution this technique can reduce the fractal dimension. The degree of fractal isotropy of the flame surface can have a significant effect on the estimation of the flame surface area and hence burning rate from two-dimensional images. To estimate this isotropy a determination of the outer cutoff is required and three-dimensional measurements are probably also necessary.

Relevance of deterministic chaos theory to studies in functioning of dynamical systems

NASA Astrophysics Data System (ADS)

Glagolev, S. N.; Bukhonova, S. M.; Chikina, E. D.

2018-03-01

The paper considers chaotic behavior of dynamical systems typical for social and economic processes. Approaches to analysis and evaluation of system development processes are studies from the point of view of controllability and determinateness. Explanations are given for necessity to apply non-standard mathematical tools to explain states of dynamical social and economic systems on the basis of fractal theory. Features of fractal structures, such as non-regularity, self-similarity, dimensionality and fractionality are considered.

Fractality and the law of the wall

NASA Astrophysics Data System (ADS)

Xu, Haosen H. A.; Yang, X. I. A.

2018-05-01

Fluid motions in the inertial range of isotropic turbulence are fractal, with their space-filling capacity slightly below regular three-dimensional objects, which is a consequence of the energy cascade. Besides the energy cascade, the other often encountered cascading process is the momentum cascade in wall-bounded flows. Despite the long-existing analogy between the two processes, many of the thoroughly investigated aspects of the energy cascade have so far received little attention in studies of the momentum counterpart, e.g., the possibility of the momentum-transferring scales in the logarithmic region being fractal has not been considered. In this work, this possibility is pursued, and we discuss one of its implications. Following the same dimensional arguments that lead to the D =2.33 fractal dimension of wrinkled surfaces in isotropic turbulence, we show that the large-scale momentum-carrying eddies may also be fractal and non-space-filling, which then leads to the power-law scaling of the mean velocity profile. The logarithmic law of the wall, on the other hand, corresponds to space-filling eddies, as suggested by Townsend [The Structure of Turbulent Shear Flow (Cambridge University Press, Cambridge, 1980)]. Because the space-filling capacity is an integral geometric quantity, the analysis presented in this work provides us with a low-order quantity, with which, one would be able to distinguish between the logarithmic law and the power law.

Fractal tomography and its application in 3D vision

NASA Astrophysics Data System (ADS)

Trubochkina, N.

2018-01-01

A three-dimensional artistic fractal tomography method that implements a non-glasses 3D visualization of fractal worlds in layered media is proposed. It is designed for the glasses-free 3D vision of digital art objects and films containing fractal content. Prospects for the development of this method in art galleries and the film industry are considered.

GEOPHYSICS, ASTRONOMY AND ASTROPHYSICS: A two scale nonlinear fractal sea surface model in a one dimensional deep sea

NASA Astrophysics Data System (ADS)

Xie, Tao; Zou, Guang-Hui; William, Perrie; Kuang, Hai-Lan; Chen, Wei

2010-05-01

Using the theory of nonlinear interactions between long and short waves, a nonlinear fractal sea surface model is presented for a one dimensional deep sea. Numerical simulation results show that spectra intensity changes at different locations (in both the wave number domain and temporal-frequency domain), and the system obeys the energy conservation principle. Finally, a method to limit the fractal parameters is also presented to ensure that the model system does not become ill-posed.

Wavelet and Fractal Analysis of Remotely Sensed Surface Temperature with Applications to Estimation of Surface Sensible Heat Flux Density

NASA Technical Reports Server (NTRS)

Schieldge, John

2000-01-01

Wavelet and fractal analyses have been used successfully to analyze one-dimensional data sets such as time series of financial, physical, and biological parameters. These techniques have been applied to two-dimensional problems in some instances, including the analysis of remote sensing imagery. In this respect, these techniques have not been widely used by the remote sensing community, and their overall capabilities as analytical tools for use on satellite and aircraft data sets is not well known. Wavelet and fractal analyses have the potential to provide fresh insight into the characterization of surface properties such as temperature and emissivity distributions, and surface processes such as the heat and water vapor exchange between the surface and the lower atmosphere. In particular, the variation of sensible heat flux density as a function of the change In scale of surface properties Is difficult to estimate, but - in general - wavelets and fractals have proved useful in determining the way a parameter varies with changes in scale. We present the results of a limited study on the relationship between spatial variations in surface temperature distribution and sensible heat flux distribution as determined by separate wavelet and fractal analyses. We analyzed aircraft imagery obtained in the thermal infrared (IR) bands from the multispectral TIMS and hyperspectral MASTER airborne sensors. The thermal IR data allows us to estimate the surface kinetic temperature distribution for a number of sites in the Midwestern and Southwestern United States (viz., San Pedro River Basin, Arizona; El Reno, Oklahoma; Jornada, New Mexico). The ground spatial resolution of the aircraft data varied from 5 to 15 meters. All sites were instrumented with meteorological and hydrological equipment including surface layer flux measuring stations such as Bowen Ratio systems and sonic anemometers. The ground and aircraft data sets provided the inputs for the wavelet and fractal analyses, and the validation of the results.

Comparison of two fractal interpolation methods

NASA Astrophysics Data System (ADS)

Fu, Yang; Zheng, Zeyu; Xiao, Rui; Shi, Haibo

2017-03-01

As a tool for studying complex shapes and structures in nature, fractal theory plays a critical role in revealing the organizational structure of the complex phenomenon. Numerous fractal interpolation methods have been proposed over the past few decades, but they differ substantially in the form features and statistical properties. In this study, we simulated one- and two-dimensional fractal surfaces by using the midpoint displacement method and the Weierstrass-Mandelbrot fractal function method, and observed great differences between the two methods in the statistical characteristics and autocorrelation features. From the aspect of form features, the simulations of the midpoint displacement method showed a relatively flat surface which appears to have peaks with different height as the fractal dimension increases. While the simulations of the Weierstrass-Mandelbrot fractal function method showed a rough surface which appears to have dense and highly similar peaks as the fractal dimension increases. From the aspect of statistical properties, the peak heights from the Weierstrass-Mandelbrot simulations are greater than those of the middle point displacement method with the same fractal dimension, and the variances are approximately two times larger. When the fractal dimension equals to 1.2, 1.4, 1.6, and 1.8, the skewness is positive with the midpoint displacement method and the peaks are all convex, but for the Weierstrass-Mandelbrot fractal function method the skewness is both positive and negative with values fluctuating in the vicinity of zero. The kurtosis is less than one with the midpoint displacement method, and generally less than that of the Weierstrass-Mandelbrot fractal function method. The autocorrelation analysis indicated that the simulation of the midpoint displacement method is not periodic with prominent randomness, which is suitable for simulating aperiodic surface. While the simulation of the Weierstrass-Mandelbrot fractal function method has strong periodicity, which is suitable for simulating periodic surface.

Wavelet-based 3D reconstruction of microcalcification clusters from two mammographic views: new evidence that fractal tumors are malignant and Euclidean tumors are benign.

PubMed

Batchelder, Kendra A; Tanenbaum, Aaron B; Albert, Seth; Guimond, Lyne; Kestener, Pierre; Arneodo, Alain; Khalil, Andre

2014-01-01

The 2D Wavelet-Transform Modulus Maxima (WTMM) method was used to detect microcalcifications (MC) in human breast tissue seen in mammograms and to characterize the fractal geometry of benign and malignant MC clusters. This was done in the context of a preliminary analysis of a small dataset, via a novel way to partition the wavelet-transform space-scale skeleton. For the first time, the estimated 3D fractal structure of a breast lesion was inferred by pairing the information from two separate 2D projected mammographic views of the same breast, i.e. the cranial-caudal (CC) and mediolateral-oblique (MLO) views. As a novelty, we define the "CC-MLO fractal dimension plot", where a "fractal zone" and "Euclidean zones" (non-fractal) are defined. 118 images (59 cases, 25 malignant and 34 benign) obtained from a digital databank of mammograms with known radiologist diagnostics were analyzed to determine which cases would be plotted in the fractal zone and which cases would fall in the Euclidean zones. 92% of malignant breast lesions studied (23 out of 25 cases) were in the fractal zone while 88% of the benign lesions were in the Euclidean zones (30 out of 34 cases). Furthermore, a Bayesian statistical analysis shows that, with 95% credibility, the probability that fractal breast lesions are malignant is between 74% and 98%. Alternatively, with 95% credibility, the probability that Euclidean breast lesions are benign is between 76% and 96%. These results support the notion that the fractal structure of malignant tumors is more likely to be associated with an invasive behavior into the surrounding tissue compared to the less invasive, Euclidean structure of benign tumors. Finally, based on indirect 3D reconstructions from the 2D views, we conjecture that all breast tumors considered in this study, benign and malignant, fractal or Euclidean, restrict their growth to 2-dimensional manifolds within the breast tissue.

EUS elastography (strain ratio) and fractal-based quantitative analysis for the diagnosis of solid pancreatic lesions.

PubMed

Carrara, Silvia; Di Leo, Milena; Grizzi, Fabio; Correale, Loredana; Rahal, Daoud; Anderloni, Andrea; Auriemma, Francesco; Fugazza, Alessandro; Preatoni, Paoletta; Maselli, Roberta; Hassan, Cesare; Finati, Elena; Mangiavillano, Benedetto; Repici, Alessandro

2018-06-01

EUS elastography is useful in characterizing solid pancreatic lesions (SPLs), and fractal analysis-based technology has been used to evaluate geometric complexity in oncology. The aim of this study was to evaluate EUS elastography (strain ratio) and fractal analysis for the characterization of SPLs. Consecutive patients with SPLs were prospectively enrolled between December 2015 and February 2017. Elastographic evaluation included parenchymal strain ratio (pSR) and wall strain ratio (wSR) and was performed with a new compact US processor. Elastographic images were analyzed using a computer program to determine the 3-dimensional histogram fractal dimension. A composite cytology/histology/clinical reference standard was used to assess sensitivity, specificity, positive predictive value, negative predictive value, and area under the receiver operating curve. Overall, 102 SPLs from 100 patients were studied. At final diagnosis, 69 (68%) were malignant and 33 benign. At elastography, both pSR and wSR appeared to be significantly higher in malignant as compared with benign SPLs (pSR, 24.5 vs 6.4 [P < .001]; wSR, 56.6 vs 15.3 [P < .001]). When the best cut-off levels of pSR and wSR at 9.10 and 16.2, respectively, were used, sensitivity, specificity, positive predictive value, negative predictive value, and area under the receiver operating curve were 88.4%, 78.8%, 89.7%, 76.9%, and 86.7% and 91.3%, 69.7%, 86.5%, 80%, and 85.7%, respectively. Fractal analysis showed a significant statistical difference (P = .0087) between the mean surface fractal dimension of malignant lesions (D = 2.66 ± .01) versus neuroendocrine tumor (D = 2.73 ± .03) and a statistical difference for all 3 channels red, green, and blue (P < .0001). EUS elastography with pSR and fractal-based analysis are useful in characterizing SPLs. (Clinical trial registration number: NCT02855151.). Copyright © 2018 American Society for Gastrointestinal Endoscopy. Published by Elsevier Inc. All rights reserved.

Two-Dimensional Animal-Like Fractals in Thin Films

NASA Astrophysics Data System (ADS)

Gao, Hong-jun; Xue, Zeng-quan; Wu, Quan-de; Pang, Shi-jin

1996-02-01

We present a few unique animal-like fractal patterns in ionized-cluster-beam deposited fullerene-tetracyanoquinodimethane thin films. The fractal patterns consisting of animal-like aggregates such as "fishes" and "quasi-seahorses" have been characterized by transmission electron microscopy. The results indicate that the small aggregates of the animal-like body are composed of many single crystals whose crystalline directions are generally different. The formation of the fractal patterns can be attributed to the cluster-diffusion-limited aggregation.

Fractal Dimensionality of Pore and Grain Volume of a Siliciclastic Marine Sand

NASA Astrophysics Data System (ADS)

Reed, A. H.; Pandey, R. B.; Lavoie, D. L.

Three-dimensional (3D) spatial distributions of pore and grain volumes were determined from high-resolution computer tomography (CT) images of resin-impregnated marine sands. Using a linear gradient extrapolation method, cubic three-dimensional samples were constructed from two-dimensional CT images. Image porosity (0.37) was found to be consistent with the estimate of porosity by water weight loss technique (0.36). Scaling of the pore volume (Vp) with the linear size (L), V~LD provides the fractal dimensionalities of the pore volume (D=2.74+/-0.02) and grain volume (D=2.90+/-0.02) typical for sedimentary materials.

Self-interacting polymer chains terminally anchored to adsorbing surfaces of three-dimensional fractal lattices

NASA Astrophysics Data System (ADS)

Živić, I.; Elezović-Hadžić, S.; Milošević, S.

2018-01-01

We have studied the adsorption problem of self-attracting linear polymers, modeled by self-avoiding walks (SAWs), situated on three-dimensional fractal structures, exemplified by 3d Sierpinski gasket (SG) family of fractals as containers of a poor solvent. Members of SG family are enumerated by an integer b (b ≥ 2), and it is assumed that one side of each SG fractal is an impenetrable adsorbing surface. We calculate the critical exponents γ1 ,γ11, and γs, which are related to the numbers of all possible SAWs with one, both, and no ends anchored to the adsorbing boundary, respectively. By applying the exact renormalization group (RG) method (for the first three members of the SG fractal family, b = 2 , 3, and 4), we have obtained specific values of these exponents, for θ-chain and globular polymer phase. We discuss their mutual relations and relations with corresponding values pertinent to extended polymer chain phase.

A holistic approach to determine tree structural complexity based on laser scanning data and fractal analysis.

PubMed

Seidel, Dominik

2018-01-01

The three-dimensional forest structure affects many ecosystem functions and services provided by forests. As forests are made of trees it seems reasonable to approach their structure by investigating individual tree structure. Based on three-dimensional point clouds from laser scanning, a newly developed holistic approach is presented that enables to calculate the box dimension as a measure of structural complexity of individual trees using fractal analysis. It was found that the box dimension of trees was significantly different among the tested species, among trees belonging to the same species but exposed to different growing conditions (at gap vs. forest interior) or to different kinds of competition (intraspecific vs. interspecific). Furthermore, it was shown that the box dimension is positively related to the trees' growth rate. The box dimension was identified as an easy to calculate measure that integrates the effect of several external drivers of tree structure, such as competition strength and type, while simultaneously providing information on structure-related properties, like tree growth.

A new version of Visual tool for estimating the fractal dimension of images

NASA Astrophysics Data System (ADS)

Grossu, I. V.; Felea, D.; Besliu, C.; Jipa, Al.; Bordeianu, C. C.; Stan, E.; Esanu, T.

2010-04-01

This work presents a new version of a Visual Basic 6.0 application for estimating the fractal dimension of images (Grossu et al., 2009 [1]). The earlier version was limited to bi-dimensional sets of points, stored in bitmap files. The application was extended for working also with comma separated values files and three-dimensional images. New version program summaryProgram title: Fractal Analysis v02 Catalogue identifier: AEEG_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEG_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 9999 No. of bytes in distributed program, including test data, etc.: 4 366 783 Distribution format: tar.gz Programming language: MS Visual Basic 6.0 Computer: PC Operating system: MS Windows 98 or later RAM: 30 M Classification: 14 Catalogue identifier of previous version: AEEG_v1_0 Journal reference of previous version: Comput. Phys. Comm. 180 (2009) 1999 Does the new version supersede the previous version?: Yes Nature of problem: Estimating the fractal dimension of 2D and 3D images. Solution method: Optimized implementation of the box-counting algorithm. Reasons for new version:The previous version was limited to bitmap image files. The new application was extended in order to work with objects stored in comma separated values (csv) files. The main advantages are: Easier integration with other applications (csv is a widely used, simple text file format); Less resources consumed and improved performance (only the information of interest, the "black points", are stored); Higher resolution (the points coordinates are loaded into Visual Basic double variables [2]); Possibility of storing three-dimensional objects (e.g. the 3D Sierpinski gasket). In this version the optimized box-counting algorithm [1] was extended to the three-dimensional case. Summary of revisions:The application interface was changed from SDI (single document interface) to MDI (multi-document interface). One form was added in order to provide a graphical user interface for the new functionalities (fractal analysis of 2D and 3D images stored in csv files). Additional comments: User friendly graphical interface; Easy deployment mechanism. Running time: In the first approximation, the algorithm is linear. References:[1] I.V. Grossu, C. Besliu, M.V. Rusu, Al. Jipa, C.C. Bordeianu, D. Felea, Comput. Phys. Comm. 180 (2009) 1999-2001.[2] F. Balena, Programming Microsoft Visual Basic 6.0, Microsoft Press, US, 1999.

Three-Dimensional Surface Parameters and Multi-Fractal Spectrum of Corroded Steel

PubMed Central

Shanhua, Xu; Songbo, Ren; Youde, Wang

2015-01-01

To study multi-fractal behavior of corroded steel surface, a range of fractal surfaces of corroded surfaces of Q235 steel were constructed by using the Weierstrass-Mandelbrot method under a high total accuracy. The multi-fractal spectrum of fractal surface of corroded steel was calculated to study the multi-fractal characteristics of the W-M corroded surface. Based on the shape feature of the multi-fractal spectrum of corroded steel surface, the least squares method was applied to the quadratic fitting of the multi-fractal spectrum of corroded surface. The fitting function was quantitatively analyzed to simplify the calculation of multi-fractal characteristics of corroded surface. The results showed that the multi-fractal spectrum of corroded surface was fitted well with the method using quadratic curve fitting, and the evolution rules and trends were forecasted accurately. The findings can be applied to research on the mechanisms of corroded surface formation of steel and provide a new approach for the establishment of corrosion damage constitutive models of steel. PMID:26121468

Three-Dimensional Surface Parameters and Multi-Fractal Spectrum of Corroded Steel.

PubMed

Shanhua, Xu; Songbo, Ren; Youde, Wang

2015-01-01

To study multi-fractal behavior of corroded steel surface, a range of fractal surfaces of corroded surfaces of Q235 steel were constructed by using the Weierstrass-Mandelbrot method under a high total accuracy. The multi-fractal spectrum of fractal surface of corroded steel was calculated to study the multi-fractal characteristics of the W-M corroded surface. Based on the shape feature of the multi-fractal spectrum of corroded steel surface, the least squares method was applied to the quadratic fitting of the multi-fractal spectrum of corroded surface. The fitting function was quantitatively analyzed to simplify the calculation of multi-fractal characteristics of corroded surface. The results showed that the multi-fractal spectrum of corroded surface was fitted well with the method using quadratic curve fitting, and the evolution rules and trends were forecasted accurately. The findings can be applied to research on the mechanisms of corroded surface formation of steel and provide a new approach for the establishment of corrosion damage constitutive models of steel.

Shape-related characteristics of age-related differences in subcortical structures.

PubMed

Madan, Christopher R

2018-01-11

With an increasing aging population, it is important to understand biological markers of aging. Subcortical volume is known to differ with age; additionally considering shape-related characteristics may provide a better index of age-related differences. Fractal dimensionality is more sensitive to age-related differences, but is borne out of mathematical principles, rather than neurobiological relevance. We considered four distinct measures of shape and how they relate to aging and fractal dimensionality: surface-to-volume ratio, sphericity, long-axis curvature, and surface texture. Structural MRIs from a combined sample of over 600 healthy adults were used to measure age-related differences in the structure of the thalamus, putamen, caudate, and hippocampus. For each, volume and fractal dimensionality were calculated, as well as four distinct shape measures. These measures were examined for their utility in explaining age-related variability in brain structure. The four shape measures were able to account for 80%-90% of the variance in fractal dimensionality. Of the distinct shape measures, surface-to-volume ratio was the most sensitive biomarker. Though volume is often used to characterize inter-individual differences in subcortical structures, our results demonstrate that additional measures can be useful complements. Our results indicate that shape characteristics are useful biological markers of aging.

Fractal planetary rings: Energy inequalities and random field model

NASA Astrophysics Data System (ADS)

Malyarenko, Anatoliy; Ostoja-Starzewski, Martin

2017-12-01

This study is motivated by a recent observation, based on photographs from the Cassini mission, that Saturn’s rings have a fractal structure in radial direction. Accordingly, two questions are considered: (1) What Newtonian mechanics argument in support of such a fractal structure of planetary rings is possible? (2) What kinematics model of such fractal rings can be formulated? Both challenges are based on taking planetary rings’ spatial structure as being statistically stationary in time and statistically isotropic in space, but statistically nonstationary in space. An answer to the first challenge is given through an energy analysis of circular rings having a self-generated, noninteger-dimensional mass distribution [V. E. Tarasov, Int. J. Mod Phys. B 19, 4103 (2005)]. The second issue is approached by taking the random field of angular velocity vector of a rotating particle of the ring as a random section of a special vector bundle. Using the theory of group representations, we prove that such a field is completely determined by a sequence of continuous positive-definite matrix-valued functions defined on the Cartesian square F2 of the radial cross-section F of the rings, where F is a fat fractal.

[Recent progress of research and applications of fractal and its theories in medicine].

PubMed

Cai, Congbo; Wang, Ping

2014-10-01

Fractal, a mathematics concept, is used to describe an image of self-similarity and scale invariance. Some organisms have been discovered with the fractal characteristics, such as cerebral cortex surface, retinal vessel structure, cardiovascular network, and trabecular bone, etc. It has been preliminarily confirmed that the three-dimensional structure of cells cultured in vitro could be significantly enhanced by bionic fractal surface. Moreover, fractal theory in clinical research will help early diagnosis and treatment of diseases, reducing the patient's pain and suffering. The development process of diseases in the human body can be expressed by the fractal theories parameter. It is of considerable significance to retrospectively review the preparation and application of fractal surface and its diagnostic value in medicine. This paper gives an application of fractal and its theories in the medical science, based on the research achievements in our laboratory.

Definition of fractal topography to essential understanding of scale-invariance

NASA Astrophysics Data System (ADS)

Jin, Yi; Wu, Ying; Li, Hui; Zhao, Mengyu; Pan, Jienan

2017-04-01

Fractal behavior is scale-invariant and widely characterized by fractal dimension. However, the cor-respondence between them is that fractal behavior uniquely determines a fractal dimension while a fractal dimension can be related to many possible fractal behaviors. Therefore, fractal behavior is independent of the fractal generator and its geometries, spatial pattern, and statistical properties in addition to scale. To mathematically describe fractal behavior, we propose a novel concept of fractal topography defined by two scale-invariant parameters, scaling lacunarity (P) and scaling coverage (F). The scaling lacunarity is defined as the scale ratio between two successive fractal generators, whereas the scaling coverage is defined as the number ratio between them. Consequently, a strictly scale-invariant definition for self-similar fractals can be derived as D = log F /log P. To reflect the direction-dependence of fractal behaviors, we introduce another parameter Hxy, a general Hurst exponent, which is analytically expressed by Hxy = log Px/log Py where Px and Py are the scaling lacunarities in the x and y directions, respectively. Thus, a unified definition of fractal dimension is proposed for arbitrary self-similar and self-affine fractals by averaging the fractal dimensions of all directions in a d-dimensional space, which . Our definitions provide a theoretical, mechanistic basis for understanding the essentials of the scale-invariant property that reduces the complexity of modeling fractals.

Numerical study of electromagnetic scattering from one-dimensional nonlinear fractal sea surface

NASA Astrophysics Data System (ADS)

Xie, Tao; He, Chao; William, Perrie; Kuang, Hai-Lan; Zou, Guang-Hui; Chen, Wei

2010-02-01

In recent years, linear fractal sea surface models have been developed for the sea surface in order to establish an electromagnetic backscattering model. Unfortunately, the sea surface is always nonlinear, particularly at high sea states. We present a nonlinear fractal sea surface model and derive an electromagnetic backscattering model. Using this model, we numerically calculate the normalized radar cross section (NRCS) of a nonlinear sea surface. Comparing the averaged NRCS between linear and nonlinear fractal models, we show that the NRCS of a linear fractal sea surface underestimates the NRCS of the real sea surface, especially for sea states with high fractal dimensions, and for dominant ocean surface gravity waves that are either very short or extremely long.

Small-angle scattering from 3D Sierpinski tetrahedron generated using chaos game

NASA Astrophysics Data System (ADS)

Slyamov, Azat

2017-12-01

We approximate a three dimensional version of deterministic Sierpinski gasket (SG), also known as Sierpinski tetrahedron (ST), by using the chaos game representation (CGR). Structural properties of the fractal, generated by both deterministic and CGR algorithms are determined using small-angle scattering (SAS) technique. We calculate the corresponding monodisperse structure factor of ST, using an optimized Debye formula. We show that scattering from CGR of ST recovers basic fractal properties, such as fractal dimension, iteration number, scaling factor, overall size of the system and the number of units composing the fractal.

Path Complexity in Virtual Water Maze Navigation: Differential Associations with Age, Sex, and Regional Brain Volume.

PubMed

Daugherty, Ana M; Yuan, Peng; Dahle, Cheryl L; Bender, Andrew R; Yang, Yiqin; Raz, Naftali

2015-09-01

Studies of human navigation in virtual maze environments have consistently linked advanced age with greater distance traveled between the start and the goal and longer duration of the search. Observations of search path geometry suggest that routes taken by older adults may be unnecessarily complex and that excessive path complexity may be an indicator of cognitive difficulties experienced by older navigators. In a sample of healthy adults, we quantify search path complexity in a virtual Morris water maze with a novel method based on fractal dimensionality. In a two-level hierarchical linear model, we estimated improvement in navigation performance across trials by a decline in route length, shortening of search time, and reduction in fractal dimensionality of the path. While replicating commonly reported age and sex differences in time and distance indices, a reduction in fractal dimension of the path accounted for improvement across trials, independent of age or sex. The volumes of brain regions associated with the establishment of cognitive maps (parahippocampal gyrus and hippocampus) were related to path dimensionality, but not to the total distance and time. Thus, fractal dimensionality of a navigational path may present a useful complementary method of quantifying performance in navigation. © The Author 2014. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

A tale of two fractals: The Hofstadter butterfly and the integral Apollonian gaskets

NASA Astrophysics Data System (ADS)

Satija, Indubala I.

2016-11-01

This paper unveils a mapping between a quantum fractal that describes a physical phenomena, and an abstract geometrical fractal. The quantum fractal is the Hofstadter butterfly discovered in 1976 in an iconic condensed matter problem of electrons moving in a two-dimensional lattice in a transverse magnetic field. The geometric fractal is the integer Apollonian gasket characterized in terms of a 300 BC problem of mutually tangent circles. Both of these fractals are made up of integers. In the Hofstadter butterfly, these integers encode the topological quantum numbers of quantum Hall conductivity. In the Apollonian gaskets an infinite number of mutually tangent circles are nested inside each other, where each circle has integer curvature. The mapping between these two fractals reveals a hidden D3 symmetry embedded in the kaleidoscopic images that describe the asymptotic scaling properties of the butterfly. This paper also serves as a mini review of these fractals, emphasizing their hierarchical aspects in terms of Farey fractions.

Robust estimation of fractal measures for characterizing the structural complexity of the human brain: optimization and reproducibility

PubMed Central

Goñi, Joaquín; Sporns, Olaf; Cheng, Hu; Aznárez-Sanado, Maite; Wang, Yang; Josa, Santiago; Arrondo, Gonzalo; Mathews, Vincent P; Hummer, Tom A; Kronenberger, William G; Avena-Koenigsberger, Andrea; Saykin, Andrew J.; Pastor, María A.

2013-01-01

High-resolution isotropic three-dimensional reconstructions of human brain gray and white matter structures can be characterized to quantify aspects of their shape, volume and topological complexity. In particular, methods based on fractal analysis have been applied in neuroimaging studies to quantify the structural complexity of the brain in both healthy and impaired conditions. The usefulness of such measures for characterizing individual differences in brain structure critically depends on their within-subject reproducibility in order to allow the robust detection of between-subject differences. This study analyzes key analytic parameters of three fractal-based methods that rely on the box-counting algorithm with the aim to maximize within-subject reproducibility of the fractal characterizations of different brain objects, including the pial surface, the cortical ribbon volume, the white matter volume and the grey matter/white matter boundary. Two separate datasets originating from different imaging centers were analyzed, comprising, 50 subjects with three and 24 subjects with four successive scanning sessions per subject, respectively. The reproducibility of fractal measures was statistically assessed by computing their intra-class correlations. Results reveal differences between different fractal estimators and allow the identification of several parameters that are critical for high reproducibility. Highest reproducibility with intra-class correlations in the range of 0.9–0.95 is achieved with the correlation dimension. Further analyses of the fractal dimensions of parcellated cortical and subcortical gray matter regions suggest robustly estimated and region-specific patterns of individual variability. These results are valuable for defining appropriate parameter configurations when studying changes in fractal descriptors of human brain structure, for instance in studies of neurological diseases that do not allow repeated measurements or for disease-course longitudinal studies. PMID:23831414

Improving the signal subtle feature extraction performance based on dual improved fractal box dimension eigenvectors

NASA Astrophysics Data System (ADS)

Chen, Xiang; Li, Jingchao; Han, Hui; Ying, Yulong

2018-05-01

Because of the limitations of the traditional fractal box-counting dimension algorithm in subtle feature extraction of radiation source signals, a dual improved generalized fractal box-counting dimension eigenvector algorithm is proposed. First, the radiation source signal was preprocessed, and a Hilbert transform was performed to obtain the instantaneous amplitude of the signal. Then, the improved fractal box-counting dimension of the signal instantaneous amplitude was extracted as the first eigenvector. At the same time, the improved fractal box-counting dimension of the signal without the Hilbert transform was extracted as the second eigenvector. Finally, the dual improved fractal box-counting dimension eigenvectors formed the multi-dimensional eigenvectors as signal subtle features, which were used for radiation source signal recognition by the grey relation algorithm. The experimental results show that, compared with the traditional fractal box-counting dimension algorithm and the single improved fractal box-counting dimension algorithm, the proposed dual improved fractal box-counting dimension algorithm can better extract the signal subtle distribution characteristics under different reconstruction phase space, and has a better recognition effect with good real-time performance.

Multifractal Approach to the Analysis of Crime Dynamics: Results for Burglary in San Francisco

NASA Astrophysics Data System (ADS)

Melgarejo, Miguel; Obregon, Nelson

This paper provides evidence of fractal, multifractal and chaotic behaviors in urban crime by computing key statistical attributes over a long data register of criminal activity. Fractal and multifractal analyses based on power spectrum, Hurst exponent computation, hierarchical power law detection and multifractal spectrum are considered ways to characterize and quantify the footprint of complexity of criminal activity. Moreover, observed chaos analysis is considered a second step to pinpoint the nature of the underlying crime dynamics. This approach is carried out on a long database of burglary activity reported by 10 police districts of San Francisco city. In general, interarrival time processes of criminal activity in San Francisco exhibit fractal and multifractal patterns. The behavior of some of these processes is close to 1/f noise. Therefore, a characterization as deterministic, high-dimensional, chaotic phenomena is viable. Thus, the nature of crime dynamics can be studied from geometric and chaotic perspectives. Our findings support that crime dynamics may be understood from complex systems theories like self-organized criticality or highly optimized tolerance.

LETTER TO THE EDITOR: Fractal diffusion coefficient from dynamical zeta functions

NASA Astrophysics Data System (ADS)

Cristadoro, Giampaolo

2006-03-01

Dynamical zeta functions provide a powerful method to analyse low-dimensional dynamical systems when the underlying symbolic dynamics is under control. On the other hand, even simple one-dimensional maps can show an intricate structure of the grammar rules that may lead to a non-smooth dependence of global observables on parameters changes. A paradigmatic example is the fractal diffusion coefficient arising in a simple piecewise linear one-dimensional map of the real line. Using the Baladi-Ruelle generalization of the Milnor-Thurnston kneading determinant, we provide the exact dynamical zeta function for such a map and compute the diffusion coefficient from its smallest zero.

A Fractal Excursion.

ERIC Educational Resources Information Center

Camp, Dane R.

1991-01-01

After introducing the two-dimensional Koch curve, which is generated by simple recursions on an equilateral triangle, the process is extended to three dimensions with simple recursions on a regular tetrahedron. Included, for both fractal sequences, are iterative formulae, illustrations of the first several iterations, and a sample PASCAL program.…

Monte carlo simulations of enzyme reactions in two dimensions: fractal kinetics and spatial segregation.

PubMed

Berry, Hugues

2002-10-01

Conventional equations for enzyme kinetics are based on mass-action laws, that may fail in low-dimensional and disordered media such as biological membranes. We present Monte Carlo simulations of an isolated Michaelis-Menten enzyme reaction on two-dimensional lattices with varying obstacle densities, as models of biological membranes. The model predicts that, as a result of anomalous diffusion on these low-dimensional media, the kinetics are of the fractal type. Consequently, the conventional equations for enzyme kinetics fail to describe the reaction. In particular, we show that the quasi-stationary-state assumption can hardly be retained in these conditions. Moreover, the fractal characteristics of the kinetics are increasingly pronounced as obstacle density and initial substrate concentration increase. The simulations indicate that these two influences are mainly additive. Finally, the simulations show pronounced S-P segregation over the lattice at obstacle densities compatible with in vivo conditions. This phenomenon could be a source of spatial self organization in biological membranes.

Monte carlo simulations of enzyme reactions in two dimensions: fractal kinetics and spatial segregation.

PubMed Central

Berry, Hugues

2002-01-01

Conventional equations for enzyme kinetics are based on mass-action laws, that may fail in low-dimensional and disordered media such as biological membranes. We present Monte Carlo simulations of an isolated Michaelis-Menten enzyme reaction on two-dimensional lattices with varying obstacle densities, as models of biological membranes. The model predicts that, as a result of anomalous diffusion on these low-dimensional media, the kinetics are of the fractal type. Consequently, the conventional equations for enzyme kinetics fail to describe the reaction. In particular, we show that the quasi-stationary-state assumption can hardly be retained in these conditions. Moreover, the fractal characteristics of the kinetics are increasingly pronounced as obstacle density and initial substrate concentration increase. The simulations indicate that these two influences are mainly additive. Finally, the simulations show pronounced S-P segregation over the lattice at obstacle densities compatible with in vivo conditions. This phenomenon could be a source of spatial self organization in biological membranes. PMID:12324410

Condition of Mechanical Equilibrium at the Phase Interface with Arbitrary Geometry

NASA Astrophysics Data System (ADS)

Zubkov, V. V.; Zubkova, A. V.

2017-09-01

The authors produced an expression for the mechanical equilibrium condition at the phase interface within the force definition of surface tension. This equilibrium condition is the most general one from the mathematical standpoint and takes into account the three-dimensional aspect of surface tension. Furthermore, the formula produced allows describing equilibrium on the fractal surface of the interface. The authors used the fractional integral model of fractal distribution and took the fractional order integrals over Euclidean space instead of integrating over the fractal set.

Bak-Tang-Wiesenfeld model in the upper critical dimension: Induced criticality in lower-dimensional subsystems

NASA Astrophysics Data System (ADS)

Dashti-Naserabadi, H.; Najafi, M. N.

2017-10-01

We present extensive numerical simulations of Bak-Tang-Wiesenfeld (BTW) sandpile model on the hypercubic lattice in the upper critical dimension Du=4 . After re-extracting the critical exponents of avalanches, we concentrate on the three- and two-dimensional (2D) cross sections seeking for the induced criticality which are reflected in the geometrical and local exponents. Various features of finite-size scaling (FSS) theory have been tested and confirmed for all dimensions. The hyperscaling relations between the exponents of the distribution functions and the fractal dimensions are shown to be valid for all dimensions. We found that the exponent of the distribution function of avalanche mass is the same for the d -dimensional cross sections and the d -dimensional BTW model for d =2 and 3. The geometrical quantities, however, have completely different behaviors with respect to the same-dimensional BTW model. By analyzing the FSS theory for the geometrical exponents of the two-dimensional cross sections, we propose that the 2D induced models have degrees of similarity with the Gaussian free field (GFF). Although some local exponents are slightly different, this similarity is excellent for the fractal dimensions. The most important one showing this feature is the fractal dimension of loops df, which is found to be 1.50 ±0.02 ≈3/2 =dfGFF .

Bak-Tang-Wiesenfeld model in the upper critical dimension: Induced criticality in lower-dimensional subsystems.

PubMed

Dashti-Naserabadi, H; Najafi, M N

2017-10-01

We present extensive numerical simulations of Bak-Tang-Wiesenfeld (BTW) sandpile model on the hypercubic lattice in the upper critical dimension D_{u}=4. After re-extracting the critical exponents of avalanches, we concentrate on the three- and two-dimensional (2D) cross sections seeking for the induced criticality which are reflected in the geometrical and local exponents. Various features of finite-size scaling (FSS) theory have been tested and confirmed for all dimensions. The hyperscaling relations between the exponents of the distribution functions and the fractal dimensions are shown to be valid for all dimensions. We found that the exponent of the distribution function of avalanche mass is the same for the d-dimensional cross sections and the d-dimensional BTW model for d=2 and 3. The geometrical quantities, however, have completely different behaviors with respect to the same-dimensional BTW model. By analyzing the FSS theory for the geometrical exponents of the two-dimensional cross sections, we propose that the 2D induced models have degrees of similarity with the Gaussian free field (GFF). Although some local exponents are slightly different, this similarity is excellent for the fractal dimensions. The most important one showing this feature is the fractal dimension of loops d_{f}, which is found to be 1.50±0.02≈3/2=d_{f}^{GFF}.

Fractal dimension of trabecular bone projection texture is related to three-dimensional microarchitecture.

PubMed

Pothuaud, L; Benhamou, C L; Porion, P; Lespessailles, E; Harba, R; Levitz, P

2000-04-01

The purpose of this work was to understand how fractal dimension of two-dimensional (2D) trabecular bone projection images could be related to three-dimensional (3D) trabecular bone properties such as porosity or connectivity. Two alteration processes were applied to trabecular bone images obtained by magnetic resonance imaging: a trabeculae dilation process and a trabeculae removal process. The trabeculae dilation process was applied from the 3D skeleton graph to the 3D initial structure with constant connectivity. The trabeculae removal process was applied from the initial structure to an altered structure having 99% of porosity, in which both porosity and connectivity were modified during this second process. Gray-level projection images of each of the altered structures were simply obtained by summation of voxels, and fractal dimension (Df) was calculated. Porosity (phi) and connectivity per unit volume (Cv) were calculated from the 3D structure. Significant relationships were found between Df, phi, and Cv. Df values increased when porosity increased (dilation and removal processes) and when connectivity decreased (only removal process). These variations were in accordance with all previous clinical studies, suggesting that fractal evaluation of trabecular bone projection has real meaning in terms of porosity and connectivity of the 3D architecture. Furthermore, there was a statistically significant linear dependence between Df and Cv when phi remained constant. Porosity is directly related to bone mineral density and fractal dimension can be easily evaluated in clinical routine. These two parameters could be associated to evaluate the connectivity of the structure.

Electromagnetism on anisotropic fractal media

NASA Astrophysics Data System (ADS)

Ostoja-Starzewski, Martin

2013-04-01

Basic equations of electromagnetic fields in anisotropic fractal media are obtained using a dimensional regularization approach. First, a formulation based on product measures is shown to satisfy the four basic identities of the vector calculus. This allows a generalization of the Green-Gauss and Stokes theorems as well as the charge conservation equation on anisotropic fractals. Then, pursuing the conceptual approach, we derive the Faraday and Ampère laws for such fractal media, which, along with two auxiliary null-divergence conditions, effectively give the modified Maxwell equations. Proceeding on a separate track, we employ a variational principle for electromagnetic fields, appropriately adapted to fractal media, so as to independently derive the same forms of these two laws. It is next found that the parabolic (for a conducting medium) and the hyperbolic (for a dielectric medium) equations involve modified gradient operators, while the Poynting vector has the same form as in the non-fractal case. Finally, Maxwell's electromagnetic stress tensor is reformulated for fractal systems. In all the cases, the derived equations for fractal media depend explicitly on fractal dimensions in three different directions and reduce to conventional forms for continuous media with Euclidean geometries upon setting these each of dimensions equal to unity.

The Fractal Patterns of Words in a Text: A Method for Automatic Keyword Extraction.

PubMed

Najafi, Elham; Darooneh, Amir H

2015-01-01

A text can be considered as a one dimensional array of words. The locations of each word type in this array form a fractal pattern with certain fractal dimension. We observe that important words responsible for conveying the meaning of a text have dimensions considerably different from one, while the fractal dimensions of unimportant words are close to one. We introduce an index quantifying the importance of the words in a given text using their fractal dimensions and then ranking them according to their importance. This index measures the difference between the fractal pattern of a word in the original text relative to a shuffled version. Because the shuffled text is meaningless (i.e., words have no importance), the difference between the original and shuffled text can be used to ascertain degree of fractality. The degree of fractality may be used for automatic keyword detection. Words with the degree of fractality higher than a threshold value are assumed to be the retrieved keywords of the text. We measure the efficiency of our method for keywords extraction, making a comparison between our proposed method and two other well-known methods of automatic keyword extraction.

The Fractal Patterns of Words in a Text: A Method for Automatic Keyword Extraction

PubMed Central

Najafi, Elham; Darooneh, Amir H.

2015-01-01

A text can be considered as a one dimensional array of words. The locations of each word type in this array form a fractal pattern with certain fractal dimension. We observe that important words responsible for conveying the meaning of a text have dimensions considerably different from one, while the fractal dimensions of unimportant words are close to one. We introduce an index quantifying the importance of the words in a given text using their fractal dimensions and then ranking them according to their importance. This index measures the difference between the fractal pattern of a word in the original text relative to a shuffled version. Because the shuffled text is meaningless (i.e., words have no importance), the difference between the original and shuffled text can be used to ascertain degree of fractality. The degree of fractality may be used for automatic keyword detection. Words with the degree of fractality higher than a threshold value are assumed to be the retrieved keywords of the text. We measure the efficiency of our method for keywords extraction, making a comparison between our proposed method and two other well-known methods of automatic keyword extraction. PMID:26091207

Plasmon confinement in fractal quantum systems

NASA Astrophysics Data System (ADS)

Westerhout, Tom; van Veen, Edo; Katsnelson, Mikhail I.; Yuan, Shengjun

2018-05-01

Recent progress in the fabrication of materials has made it possible to create arbitrary nonperiodic two-dimensional structures in the quantum plasmon regime. This paves the way for exploring the quantum plasmonic properties of electron gases in complex geometries. In this work we study systems with a fractal dimension. We calculate the full dielectric functions of two prototypical fractals with different ramification numbers, namely the Sierpinski carpet and gasket. We show that the Sierpinski carpet has a dispersion comparable to a square lattice, but the Sierpinski gasket features highly localized plasmon modes with a flat dispersion. This strong plasmon confinement in finitely ramified fractals can provide a novel setting for manipulating light at the quantum level.

Influence of Landscape Coverage on Measuring Spatial and Length Properties of Rock Fracture Networks: Insights from Numerical Simulation

NASA Astrophysics Data System (ADS)

Cao, Wenzhuo; Lei, Qinghua

2018-01-01

Natural fractures are ubiquitous in the Earth's crust and often deeply buried in the subsurface. Due to the difficulty in accessing to their three-dimensional structures, the study of fracture network geometry is usually achieved by sampling two-dimensional (2D) exposures at the Earth's surface through outcrop mapping or aerial photograph techniques. However, the measurement results can be considerably affected by the coverage of forests and other plant species over the exposed fracture patterns. We quantitatively study such effects using numerical simulation. We consider the scenario of nominally isotropic natural fracture systems and represent them using 2D discrete fracture network models governed by fractal and length scaling parameters. The groundcover is modelled as random patches superimposing onto the 2D fracture patterns. The effects of localisation and total coverage of landscape patches are further investigated. The fractal dimension and length exponent of the covered fracture networks are measured and compared with those of the original non-covered patterns. The results show that the measured length exponent increases with the reduced localisation and increased coverage of landscape patches, which is more evident for networks dominated by very large fractures (i.e. small underlying length exponent). However, the landscape coverage seems to have a minor impact on the fractal dimension measurement. The research findings of this paper have important implications for field survey and statistical analysis of geological systems.

Fractal universe and quantum gravity.

PubMed

Calcagni, Gianluca

2010-06-25

We propose a field theory which lives in fractal spacetime and is argued to be Lorentz invariant, power-counting renormalizable, ultraviolet finite, and causal. The system flows from an ultraviolet fixed point, where spacetime has Hausdorff dimension 2, to an infrared limit coinciding with a standard four-dimensional field theory. Classically, the fractal world where fields live exchanges energy momentum with the bulk with integer topological dimension. However, the total energy momentum is conserved. We consider the dynamics and the propagator of a scalar field. Implications for quantum gravity, cosmology, and the cosmological constant are discussed.

The N-Simplex and Its Generalizations towards Fractals

ERIC Educational Resources Information Center

Kosi-Ulbl, Irena; Pagon, Dusan

2002-01-01

Nature is full of different crystals and many of them have shapes of regular geometric objects. Those in which the fractal structure of a geometric object can be recognized are especially unusual. In this paper a generalization of one of these shapes is described: a formation, based on an n-dimensional simplex. The construction of an n-dimensional…

Fractal and topological sustainable methods of overcoming expected uncertainty in the radiolocation of low-contrast targets and in the processing of weak multi-dimensional signals on the background of high-intensity noise: A new direction in the statistical decision theory

NASA Astrophysics Data System (ADS)

Potapov, A. A.

2017-11-01

The main purpose of this work is to interpret the main directions of radio physics, radio engineering and radio location in “fractal” language that makes new ways and generalizations on future promising radio systems. We introduce a new kind and approach of up-to-date radiolocation: fractal-scaling or scale-invariant radiolocation. The new topologic signs and methods of detecting the low-contrast objects against the high-intensity noise background are presented. It leads to basic changes in the theoretical radiolocation structure itself and also in its mathematical apparatus. The fractal radio systems conception, sampling topology, global fractal-scaling approach and the fractal paradigm underlie the scientific direction established by the author in Russia and all over the world for the first time ever.

Two Dimensional Drug Diffusion Between Nanoparticles and Fractal Tumors

NASA Astrophysics Data System (ADS)

Samioti, S. E.; Karamanos, K.; Tsiantis, A.; Papathanasiou, A.; Sarris, I.

2017-11-01

Drug delivery methods based on nanoparticles are some of the most promising medical applications in nanotechnology to treat cancer. It is observed that drug released by nanoparticles to the cancer tumors may be driven by diffusion. A fractal tumor boundary of triangular Von Koch shape is considered here and the diffusion mechanism is studied for different drug concentrations and increased fractality. A high order Finite Elements method based on the Fenics library is incorporated in fine meshes to fully resolve these irregular boundaries. Drug concentration, its transfer rates and entropy production are calculated in an up to forth order fractal iteration boundaries. We observed that diffusion rate diminishes for successive prefractal generations. Also, the entropy production around the system changes greatly as the order of the fractal curve increases. Results indicate with precision where the active sites are, in which most of the diffusion takes place and thus drug arrives to the tumor.

A 3D model for rain-induced landslides based on molecular dynamics with fractal and fractional water diffusion

NASA Astrophysics Data System (ADS)

Martelloni, Gianluca; Bagnoli, Franco; Guarino, Alessio

2017-09-01

We present a three-dimensional model of rain-induced landslides, based on cohesive spherical particles. The rainwater infiltration into the soil follows either the fractional or the fractal diffusion equations. We analytically solve the fractal partial differential equation (PDE) for diffusion with particular boundary conditions to simulate a rainfall event. We developed a numerical integration scheme for the PDE, compared with the analytical solution. We adapt the fractal diffusion equation obtaining the gravimetric water content that we use as input of a triggering scheme based on Mohr-Coulomb limit-equilibrium criterion. This triggering is then complemented by a standard molecular dynamics algorithm, with an interaction force inspired by the Lennard-Jones potential, to update the positions and velocities of particles. We present our results for homogeneous and heterogeneous systems, i.e., systems composed by particles with same or different radius, respectively. Interestingly, in the heterogeneous case, we observe segregation effects due to the different volume of the particles. Finally, we analyze the parameter sensibility both for the triggering and the propagation phases. Our simulations confirm the results of a previous two-dimensional model and therefore the feasible applicability to real cases.

Aesthetic Responses to Exact Fractals Driven by Physical Complexity

PubMed Central

Bies, Alexander J.; Blanc-Goldhammer, Daryn R.; Boydston, Cooper R.; Taylor, Richard P.; Sereno, Margaret E.

2016-01-01

Fractals are physically complex due to their repetition of patterns at multiple size scales. Whereas the statistical characteristics of the patterns repeat for fractals found in natural objects, computers can generate patterns that repeat exactly. Are these exact fractals processed differently, visually and aesthetically, than their statistical counterparts? We investigated the human aesthetic response to the complexity of exact fractals by manipulating fractal dimensionality, symmetry, recursion, and the number of segments in the generator. Across two studies, a variety of fractal patterns were visually presented to human participants to determine the typical response to exact fractals. In the first study, we found that preference ratings for exact midpoint displacement fractals can be described by a linear trend with preference increasing as fractal dimension increases. For the majority of individuals, preference increased with dimension. We replicated these results for other exact fractal patterns in a second study. In the second study, we also tested the effects of symmetry and recursion by presenting asymmetric dragon fractals, symmetric dragon fractals, and Sierpinski carpets and Koch snowflakes, which have radial and mirror symmetry. We found a strong interaction among recursion, symmetry and fractal dimension. Specifically, at low levels of recursion, the presence of symmetry was enough to drive high preference ratings for patterns with moderate to high levels of fractal dimension. Most individuals required a much higher level of recursion to recover this level of preference in a pattern that lacked mirror or radial symmetry, while others were less discriminating. This suggests that exact fractals are processed differently than their statistical counterparts. We propose a set of four factors that influence complexity and preference judgments in fractals that may extend to other patterns: fractal dimension, recursion, symmetry and the number of segments in a pattern. Conceptualizations such as Berlyne’s and Redies’ theories of aesthetics also provide a suitable framework for interpretation of our data with respect to the individual differences that we detect. Future studies that incorporate physiological methods to measure the human aesthetic response to exact fractal patterns would further elucidate our responses to such timeless patterns. PMID:27242475

Pore-wall roughness as a fractal surface and theoretical simulation of mercury intrusion/retraction in porous media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tsakiroglou, C.D.; Payatakes, A.C.

The mercury intrusion/retraction curves of many types of porous materials (e.g., sandstones) have sections of finite slope in the region of high and very high pressure. This feature is attributed to the existence of microroughness on the pore walls. In the present work pore-wall roughness features are added to a three-dimensional primary network of chambers-and-throats using ideas of fractal geometry. The roughness of the throats is modeled with a finite number of self-similar triangular prisms of progressively smaller sizes. The roughness of the chambers is modeled in a similar way using right circular cones instead of prisms. Three parameters sufficemore » for the complete characterization of the model of fractal roughness, namely, the number of features per unit length, the common angle of sharpness, and the number of layers (which is taken to be the same for throats and chambers). Analytical relations that give the surface area, pore volume, and mercury saturation of the pore network as functions of the fractal roughness parameters are developed for monolayer and multilayer arrangements. The chamber-and-throat network with fractal pore-wall roughness is used to develop an extended version of the computer-aided simulator of mercury porosimetry that has been reported in previous publications. This new simulator is used to investigate the effects of the roughness features on the form of mercury intrusion/retraction curves. It turns out that the fractal model of the porewall roughness gives an adequate representation of real porous media, and capillary pressure curves which are similar to the experimental ones for many typical porous materials such as sandstones. The method is demonstrated with the analysis of a Greek sandstone.« less

Multifractal analysis with the probability density function at the three-dimensional anderson transition.

PubMed

Rodriguez, Alberto; Vasquez, Louella J; Römer, Rudolf A

2009-03-13

The probability density function (PDF) for critical wave function amplitudes is studied in the three-dimensional Anderson model. We present a formal expression between the PDF and the multifractal spectrum f(alpha) in which the role of finite-size corrections is properly analyzed. We show the non-Gaussian nature and the existence of a symmetry relation in the PDF. From the PDF, we extract information about f(alpha) at criticality such as the presence of negative fractal dimensions and the possible existence of termination points. A PDF-based multifractal analysis is shown to be a valid alternative to the standard approach based on the scaling of inverse participation ratios.

An Evaluation of Fractal Surface Measurement Methods for Characterizing Landscape Complexity from Remote-Sensing Imagery

NASA Technical Reports Server (NTRS)

Lam, Nina Siu-Ngan; Qiu, Hong-Lie; Quattrochi, Dale A.; Emerson, Charles W.; Arnold, James E. (Technical Monitor)

2001-01-01

The rapid increase in digital data volumes from new and existing sensors necessitates the need for efficient analytical tools for extracting information. We developed an integrated software package called ICAMS (Image Characterization and Modeling System) to provide specialized spatial analytical functions for interpreting remote sensing data. This paper evaluates the three fractal dimension measurement methods: isarithm, variogram, and triangular prism, along with the spatial autocorrelation measurement methods Moran's I and Geary's C, that have been implemented in ICAMS. A modified triangular prism method was proposed and implemented. Results from analyzing 25 simulated surfaces having known fractal dimensions show that both the isarithm and triangular prism methods can accurately measure a range of fractal surfaces. The triangular prism method is most accurate at estimating the fractal dimension of higher spatial complexity, but it is sensitive to contrast stretching. The variogram method is a comparatively poor estimator for all of the surfaces, particularly those with higher fractal dimensions. Similar to the fractal techniques, the spatial autocorrelation techniques are found to be useful to measure complex images but not images with low dimensionality. These fractal measurement methods can be applied directly to unclassified images and could serve as a tool for change detection and data mining.

The fractal geometry of life.

PubMed

Losa, Gabriele A

2009-01-01

The extension of the concepts of Fractal Geometry (Mandelbrot [1983]) toward the life sciences has led to significant progress in understanding complex functional properties and architectural / morphological / structural features characterising cells and tissues during ontogenesis and both normal and pathological development processes. It has even been argued that fractal geometry could provide a coherent description of the design principles underlying living organisms (Weibel [1991]). Fractals fulfil a certain number of theoretical and methodological criteria including a high level of organization, shape irregularity, functional and morphological self-similarity, scale invariance, iterative pathways and a peculiar non-integer fractal dimension [FD]. Whereas mathematical objects are deterministic invariant or self-similar over an unlimited range of scales, biological components are statistically self-similar only within a fractal domain defined by upper and lower limits, called scaling window, in which the relationship between the scale of observation and the measured size or length of the object can be established (Losa and Nonnenmacher [1996]). Selected examples will contribute to depict complex biological shapes and structures as fractal entities, and also to show why the application of the fractal principle is valuable for measuring dimensional, geometrical and functional parameters of cells, tissues and organs occurring within the vegetal and animal realms. If the criteria for a strict description of natural fractals are met, then it follows that a Fractal Geometry of Life may be envisaged and all natural objects and biological systems exhibiting self-similar patterns and scaling properties may be considered as belonging to the new subdiscipline of "fractalomics".

Fractal analysis of scatter imaging signatures to distinguish breast pathologies

NASA Astrophysics Data System (ADS)

Eguizabal, Alma; Laughney, Ashley M.; Krishnaswamy, Venkataramanan; Wells, Wendy A.; Paulsen, Keith D.; Pogue, Brian W.; López-Higuera, José M.; Conde, Olga M.

2013-02-01

Fractal analysis combined with a label-free scattering technique is proposed for describing the pathological architecture of tumors. Clinicians and pathologists are conventionally trained to classify abnormal features such as structural irregularities or high indices of mitosis. The potential of fractal analysis lies in the fact of being a morphometric measure of the irregular structures providing a measure of the object's complexity and self-similarity. As cancer is characterized by disorder and irregularity in tissues, this measure could be related to tumor growth. Fractal analysis has been probed in the understanding of the tumor vasculature network. This work addresses the feasibility of applying fractal analysis to the scattering power map (as a physical modeling) and principal components (as a statistical modeling) provided by a localized reflectance spectroscopic system. Disorder, irregularity and cell size variation in tissue samples is translated into the scattering power and principal components magnitude and its fractal dimension is correlated with the pathologist assessment of the samples. The fractal dimension is computed applying the box-counting technique. Results show that fractal analysis of ex-vivo fresh tissue samples exhibits separated ranges of fractal dimension that could help classifier combining the fractal results with other morphological features. This contrast trend would help in the discrimination of tissues in the intraoperative context and may serve as a useful adjunct to surgeons.

Optimal spinneret layout in Von Koch curves of fractal theory based needleless electrospinning process

NASA Astrophysics Data System (ADS)

Yang, Wenxiu; Liu, Yanbo; Zhang, Ligai; Cao, Hong; Wang, Yang; Yao, Jinbo

2016-06-01

Needleless electrospinning technology is considered as a better avenue to produce nanofibrous materials at large scale, and electric field intensity and its distribution play an important role in controlling nanofiber diameter and quality of the nanofibrous web during electrospinning. In the current study, a novel needleless electrospinning method was proposed based on Von Koch curves of Fractal configuration, simulation and analysis on electric field intensity and distribution in the new electrospinning process were performed with Finite element analysis software, Comsol Multiphysics 4.4, based on linear and nonlinear Von Koch fractal curves (hereafter called fractal models). The result of simulation and analysis indicated that Second level fractal structure is the optimal linear electrospinning spinneret in terms of field intensity and uniformity. Further simulation and analysis showed that the circular type of Fractal spinneret has better field intensity and distribution compared to spiral type of Fractal spinneret in the nonlinear Fractal electrospinning technology. The electrospinning apparatus with the optimal Von Koch fractal spinneret was set up to verify the theoretical analysis results from Comsol simulation, achieving more uniform electric field distribution and lower energy cost, compared to the current needle and needleless electrospinning technologies.

Electromagnetic backscattering from one-dimensional drifting fractal sea surface I: Wave-current coupled model

NASA Astrophysics Data System (ADS)

Tao, Xie; Shang-Zhuo, Zhao; William, Perrie; He, Fang; Wen-Jin, Yu; Yi-Jun, He

2016-06-01

To study the electromagnetic backscattering from a one-dimensional drifting fractal sea surface, a fractal sea surface wave-current model is derived, based on the mechanism of wave-current interactions. The numerical results show the effect of the ocean current on the wave. Wave amplitude decreases, wavelength and kurtosis of wave height increase, spectrum intensity decreases and shifts towards lower frequencies when the current occurs parallel to the direction of the ocean wave. By comparison, wave amplitude increases, wavelength and kurtosis of wave height decrease, spectrum intensity increases and shifts towards higher frequencies if the current is in the opposite direction to the direction of ocean wave. The wave-current interaction effect of the ocean current is much stronger than that of the nonlinear wave-wave interaction. The kurtosis of the nonlinear fractal ocean surface is larger than that of linear fractal ocean surface. The effect of the current on skewness of the probability distribution function is negligible. Therefore, the ocean wave spectrum is notably changed by the surface current and the change should be detectable in the electromagnetic backscattering signal. Project supported by the National Natural Science Foundation of China (Grant No. 41276187), the Global Change Research Program of China (Grant No. 2015CB953901), the Priority Academic Development Program of Jiangsu Higher Education Institutions (PAPD), Program for the Innovation Research and Entrepreneurship Team in Jiangsu Province, China, the Canadian Program on Energy Research and Development, and the Canadian World Class Tanker Safety Service.

Higuchi Dimension of Digital Images

PubMed Central

Ahammer, Helmut

2011-01-01

There exist several methods for calculating the fractal dimension of objects represented as 2D digital images. For example, Box counting, Minkowski dilation or Fourier analysis can be employed. However, there appear to be some limitations. It is not possible to calculate only the fractal dimension of an irregular region of interest in an image or to perform the calculations in a particular direction along a line on an arbitrary angle through the image. The calculations must be made for the whole image. In this paper, a new method to overcome these limitations is proposed. 2D images are appropriately prepared in order to apply 1D signal analyses, originally developed to investigate nonlinear time series. The Higuchi dimension of these 1D signals is calculated using Higuchi's algorithm, and it is shown that both regions of interests and directional dependencies can be evaluated independently of the whole picture. A thorough validation of the proposed technique and a comparison of the new method to the Fourier dimension, a common two dimensional method for digital images, are given. The main result is that Higuchi's algorithm allows a direction dependent as well as direction independent analysis. Actual values for the fractal dimensions are reliable and an effective treatment of regions of interests is possible. Moreover, the proposed method is not restricted to Higuchi's algorithm, as any 1D method of analysis, can be applied. PMID:21931854

Contour fractal analysis of grains

NASA Astrophysics Data System (ADS)

Guida, Giulia; Casini, Francesca; Viggiani, Giulia MB

2017-06-01

Fractal analysis has been shown to be useful in image processing to characterise the shape and the grey-scale complexity in different applications spanning from electronic to medical engineering (e.g. [1]). Fractal analysis consists of several methods to assign a dimension and other fractal characteristics to a dataset describing geometric objects. Limited studies have been conducted on the application of fractal analysis to the classification of the shape characteristics of soil grains. The main objective of the work described in this paper is to obtain, from the results of systematic fractal analysis of artificial simple shapes, the characterization of the particle morphology at different scales. The long term objective of the research is to link the microscopic features of granular media with the mechanical behaviour observed in the laboratory and in situ.

Fractal-Based Image Analysis In Radiological Applications

NASA Astrophysics Data System (ADS)

Dellepiane, S.; Serpico, S. B.; Vernazza, G.; Viviani, R.

1987-10-01

We present some preliminary results of a study aimed to assess the actual effectiveness of fractal theory and to define its limitations in the area of medical image analysis for texture description, in particular, in radiological applications. A general analysis to select appropriate parameters (mask size, tolerance on fractal dimension estimation, etc.) has been performed on synthetically generated images of known fractal dimensions. Moreover, we analyzed some radiological images of human organs in which pathological areas can be observed. Input images were subdivided into blocks of 6x6 pixels; then, for each block, the fractal dimension was computed in order to create fractal images whose intensity was related to the D value, i.e., texture behaviour. Results revealed that the fractal images could point out the differences between normal and pathological tissues. By applying histogram-splitting segmentation to the fractal images, pathological areas were isolated. Two different techniques (i.e., the method developed by Pentland and the "blanket" method) were employed to obtain fractal dimension values, and the results were compared; in both cases, the appropriateness of the fractal description of the original images was verified.

Percolation Laws of a Fractal Fracture-Pore Double Medium

NASA Astrophysics Data System (ADS)

Zhao, Yangsheng; Feng, Zengchao; Lv, Zhaoxing; Zhao, Dong; Liang, Weiguo

2016-12-01

The fracture-pore double porosity medium is one of the most common media in nature, for example, rock mass in strata. Fracture has a more significant effect on fluid flow than a pore in a fracture-pore double porosity medium. Hence, the fracture effect on percolation should be considered when studying the percolation phenomenon in porous media. In this paper, based on the fractal distribution law, three-dimensional (3D) fracture surfaces, and two-dimensional (2D) fracture traces in rock mass, the locations of fracture surfaces or traces are determined using a random function of uniform distribution. Pores are superimposed to build a fractal fracture-pore double medium. Numerical experiments were performed to show percolation phenomena in the fracture-pore double medium. The percolation threshold can be determined from three independent variables (porosity n, fracture fractal dimension D, and initial value of fracture number N0). Once any two are determined, the percolation probability exists at a critical point with the remaining parameter changing. When the initial value of the fracture number is greater than zero, the percolation threshold in the fracture-pore medium is much smaller than that in a pore medium. When the fracture number equals zero, the fracture-pore medium degenerates to a pore medium, and both percolation thresholds are the same.

Fractal dimension of turbulent black holes

NASA Astrophysics Data System (ADS)

Westernacher-Schneider, John Ryan

2017-11-01

We present measurements of the fractal dimension of a turbulent asymptotically anti-de Sitter black brane reconstructed from simulated boundary fluid data at the perfect fluid order using the fluid-gravity duality. We argue that the boundary fluid energy spectrum scaling as E (k )˜k-2 is a more natural setting for the fluid-gravity duality than the Kraichnan-Kolmogorov scaling of E (k )˜k-5 /3, but we obtain fractal dimensions D for spatial sections of the horizon H ∩Σ in both cases: D =2.584 (1 ) and D =2.645 (4 ), respectively. These results are consistent with the upper bound of D =3 , thereby resolving the tension with the recent claim in Adams et al. [Phys. Rev. Lett. 112, 151602 (2014), 10.1103/PhysRevLett.112.151602] that D =3 +1 /3 . We offer a critical examination of the calculation which led to their result, and show that their proposed definition of the fractal dimension performs poorly as a fractal dimension estimator on one-dimensional curves with known fractal dimension. Finally, we describe how to define and in principle calculate the fractal dimension of spatial sections of the horizon H ∩Σ in a covariant manner, and we speculate on assigning a "bootstrapped" value of fractal dimension to the entire horizon H when it is in a statistically quasisteady turbulent state.

Fractal analysis of time varying data

DOEpatents

Vo-Dinh, Tuan; Sadana, Ajit

2002-01-01

Characteristics of time varying data, such as an electrical signal, are analyzed by converting the data from a temporal domain into a spatial domain pattern. Fractal analysis is performed on the spatial domain pattern, thereby producing a fractal dimension D.sub.F. The fractal dimension indicates the regularity of the time varying data.

Anomalous relaxation in fractal structures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fujiwara, S.; Yonezawa, F.

1995-03-01

For the purpose of studying some interesting properties of anomalous relaxation in fractal structures, we carry out Monte Carlo simulations of random walks on two-dimensional fractal structures (Sierpinski carpets with different cutouts and site-percolation clusters in a square lattice at the critical concentration). We find that the relaxation is of the Cole-Cole type [J. Chem. Phys. 9, 341 (1941)], which is one of the empirical laws of anomalous relaxation. Scaling properties are found in the relaxation function as well as in the particle density. We also find that, in strucures with almost the same fractal dimension, relaxation in structures withmore » dead ends is slower than that in structures without them. This paper ascertains that the essential aspects of the anomalous relaxation due to many-body effects can be explained in the framework of the one-body model.« less

Fractal Characteristics of the Pore Network in Diatomites Using Mercury Porosimetry and Image Analysis

NASA Astrophysics Data System (ADS)

Stańczak, Grażyna; Rembiś, Marek; Figarska-Warchoł, Beata; Toboła, Tomasz

The complex pore space considerably affects the unique properties of diatomite and its significant potential for many industrial applications. The pore network in the diatomite from the Lower Miocene strata of the Skole nappe (the Jawornik deposit, SE Poland) has been investigated using a fractal approach. The fractal dimension of the pore-space volume was calculated using the Menger sponge as a model of a porous body and the mercury porosimetry data in a pore-throat diameter range between 10,000 and 10 nm. Based on the digital analyses of the two-dimensional images from thin sections taken under a scanning electron microscope at the backscattered electron mode at different magnifications, the authors tried to quantify the pore spaces of the diatomites using the box counting method. The results derived from the analyses of the pore-throat diameter distribution using mercury porosimetry have revealed that the pore space of the diatomite has the bifractal structure in two separated ranges of the pore-throat diameters considerably smaller than the pore-throat sizes corresponding to threshold pressures. Assuming that the fractal dimensions identified for the ranges of the smaller pore-throat diameters characterize the overall pore-throat network in the Jawornik diatomite, we can set apart the distribution of the pore-throat volume (necks) and the pore volume from the distribution of the pore-space volume (pores and necks together).

Archaeon and archaeal virus diversity classification via sequence entropy and fractal dimension

NASA Astrophysics Data System (ADS)

Tremberger, George, Jr.; Gallardo, Victor; Espinoza, Carola; Holden, Todd; Gadura, N.; Cheung, E.; Schneider, P.; Lieberman, D.; Cheung, T.

2010-09-01

Archaea are important potential candidates in astrobiology as their metabolism includes solar, inorganic and organic energy sources. Archaeal viruses would also be expected to be present in a sustainable archaeal exobiological community. Genetic sequence Shannon entropy and fractal dimension can be used to establish a two-dimensional measure for classification and phylogenetic study of these organisms. A sequence fractal dimension can be calculated from a numerical series consisting of the atomic numbers of each nucleotide. Archaeal 16S and 23S ribosomal RNA sequences were studied. Outliers in the 16S rRNA fractal dimension and entropy plot were found to be halophilic archaea. Positive correlation (R-square ~ 0.75, N = 18) was observed between fractal dimension and entropy across the studied species. The 16S ribosomal RNA sequence entropy correlates with the 23S ribosomal RNA sequence entropy across species with R-square 0.93, N = 18. Entropy values correspond positively with branch lengths of a published phylogeny. The studied archaeal virus sequences have high fractal dimensions of 2.02 or more. A comparison of selected extremophile sequences with archaeal sequences from the Humboldt Marine Ecosystem database (Wood-Hull Oceanography Institute, MIT) suggests the presence of continuous sequence expression as inferred from distributions of entropy and fractal dimension, consistent with the diversity expected in an exobiological archaeal community.

Microtopographic Inspection and Fractal Analysis of Skin Neoplasia

NASA Astrophysics Data System (ADS)

Costa, Manuel F. M.; Hipolito, Alberto Valencia; Gutierrez, Gustavo Fidel; Chanona, Jorge; Gallegos, Eva Ramón

2008-04-01

Early detection of skin cancer is fundamental to a successful treatment. Changes in the shape, including the relief, of skin lesions are an indicator of a possible malignity. Optical microtopographic inspection of skin lesions can be used to identify diagnostic patterns of benign and malign skin' lesions. Statistical parameters like the mean roughness (Ra) may allow the discrimination between different types of lesions and degree of malignity. Fractal analysis of bi-dimensional and 3D images of skin lesions can validate or complement that assessment by calculation of its fractal dimensions (FD). On the study herein reported the microtopographic inspection of the skin lesions were performed using the optical triangulation based microtopographer developed at the Physics Department of the University of Minho, MICROTOP.03.MFC. The patients that participated in this research work were men and women older than 15 years with the clinical and histopathology diagnoses of: melanoma, basocellular carcinoma, epidermoide carcinoma, actinic keratosis, keratoacantosis and benign nevus. Latex impressions of the lesions were taken and microtopographically analyzed. Characteristic information for each type of studied lesion was obtained. For melanoma it was observed that on the average these tumors present an increased roughness of around 67 percent compared to the roughness of the healthy skin. This feature allows the distinction from other tumors as basocellular carcinoma (were the roughness increase was in the average of 49 percent) and benign lesions as the epidermoide cyst (37 percent) or the seborrhea keratosis (4 percent). Tumor size and roughness are directly proportional to the grade of malignality. The characterization of the fractal geometry of 2D (histological slides) and 3D images of skin lesions was performed by obtaining its FD evaluated by means of the Box counting method. Results obtained showed that the average fractal dimension of histological slide images (FDh) corresponding to some neoplasia is higher (1.334+/-0.072) than those for healthy skin (1.091+/-0.082). A significant difference between the fractal dimensions of neoplasia and healhty skin (>0.001) was registered. The FD of microtopography maps (FDm) can also distinguish between healthy and malignant tissue in general (2.277+/-0.070 to 2.309+/-0.040), but not discriminate the different types of skin neoplasias. The combination of the rugometric evaluation and fractal geometry characterization provides valuable information about the malignity of skin lesions and type of lesion.

Fractal analysis: A new tool in transient volcanic ash plume characterization.

NASA Astrophysics Data System (ADS)

Tournigand, Pierre-Yves; Peña Fernandez, Juan Jose; Taddeucci, Jacopo; Perugini, Diego; Sesterhenn, Jörn

2017-04-01

Transient volcanic plumes are time-dependent features generated by unstable eruptive sources. They represent a threat to human health and infrastructures, and a challenge to characterize due to their intrinsic instability. Plumes have been investigated through physical (e.g. visible, thermal, UV, radar imagery), experimental and numerical studies in order to provide new insights about their dynamics and better anticipate their behavior. It has been shown experimentally that plume dynamics is strongly dependent to source conditions and that plume shape evolution holds key to retrieve these conditions. In this study, a shape evolution analysis is performed on thermal high-speed videos of volcanic plumes from three different volcanoes Sakurajima (Japan), Stromboli (Italy) and Fuego (Guatemala), recorded with a FLIR SC655 thermal camera during several field campaigns between 2012 and 2016. To complete this dataset, three numerical gas-jet simulations at different Reynolds number (2000, 5000 and 10000) have been used in order to set reference values to the natural cases. Turbulent flow shapes are well known to feature scale-invariant structures and a high degree of complexity. For this reason we characterized the bi-dimensional shape of natural and synthetic plumes by using a fractal descriptor. Such method has been applied in other studies on experimental turbulent jets as well as on atmospheric clouds and have shown promising results. At each time-step plume contour has been manually outlined and measured using the box-counting method. This method consists in covering the image with squares of variable sizes and counting the number of squares containing the plume outline. The negative slope of the number of squares in function of their size in a log-log plot gives the fractal dimension of the plume at a given time. Preliminary results show an increase over time of the fractal dimension for natural volcanic plume as well as for the numerically simulated ones, but at varying rates. Increasing fractal dimension correspond to an increase in the overall complexity of plume shape and thus to an increase in flow turbulence over time. Accordingly, numerical simulations show that, fractal dimension increases faster with increasing Reynolds number. However, other parameters seem to play a role in volcanic plumes evolution. The features of the eruption source (e.g. vent number, size and shape, ejection duration, number and time interval between the different ejection pulses that characterize unsteady eruptions) seem also to have an effect on this time evolution with for example a single vent source generating a faster increase of the fractal dimension than in the case of a plume fed by several vents over time. This first attempt to use fractal analysis on volcanic plume could be the starting point towards a new kind of tools for volcanic plume characterization potentially giving an access to parameters so far unreachable by only using more traditional techniques. Fractal dimension analysis applied on volcanic plumes could directly link a shape evolution to source conditions and thus help to constrain uncertainties existing on such parameters.

Changes in Dimensionality and Fractal Scaling Suggest Soft-Assembled Dynamics in Human EEG

PubMed Central

Wiltshire, Travis J.; Euler, Matthew J.; McKinney, Ty L.; Butner, Jonathan E.

2017-01-01

Humans are high-dimensional, complex systems consisting of many components that must coordinate in order to perform even the simplest of activities. Many behavioral studies, especially in the movement sciences, have advanced the notion of soft-assembly to describe how systems with many components coordinate to perform specific functions while also exhibiting the potential to re-structure and then perform other functions as task demands change. Consistent with this notion, within cognitive neuroscience it is increasingly accepted that the brain flexibly coordinates the networks needed to cope with changing task demands. However, evaluation of various indices of soft-assembly has so far been absent from neurophysiological research. To begin addressing this gap, we investigated task-related changes in two distinct indices of soft-assembly using the established phenomenon of EEG repetition suppression. In a repetition priming task, we assessed evidence for changes in the correlation dimension and fractal scaling exponents during stimulus-locked event-related potentials, as a function of stimulus onset and familiarity, and relative to spontaneous non-task-related activity. Consistent with predictions derived from soft-assembly, results indicated decreases in dimensionality and increases in fractal scaling exponents from resting to pre-stimulus states and following stimulus onset. However, contrary to predictions, familiarity tended to increase dimensionality estimates. Overall, the findings support the view from soft-assembly that neural dynamics should become increasingly ordered as external task demands increase, and support the broader application of soft-assembly logic in understanding human behavior and electrophysiology. PMID:28919862

Theory and discretization of ideal magnetohydrodynamic equilibria with fractal pressure profiles

NASA Astrophysics Data System (ADS)

Kraus, B. F.; Hudson, S. R.

2017-09-01

In three-dimensional ideal magnetohydrodynamics, closed flux surfaces cannot maintain both rational rotational-transform and pressure gradients, as these features together produce unphysical, infinite currents. A proposed set of equilibria nullifies these currents by flattening the pressure on sufficiently wide intervals around each rational surface. Such rational surfaces exist at every scale, which characterizes the pressure profile as self-similar and thus fractal. The pressure profile is approximated numerically by considering a finite number of rational regions and analyzed mathematically by classifying the irrational numbers that support gradients into subsets. Applying these results to a given rotational-transform profile in cylindrical geometry, we find magnetic field and current density profiles compatible with the fractal pressure.

Fuzzy fractals, chaos, and noise

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zardecki, A.

1997-05-01

To distinguish between chaotic and noisy processes, the authors analyze one- and two-dimensional chaotic mappings, supplemented by the additive noise terms. The predictive power of a fuzzy rule-based system allows one to distinguish ergodic and chaotic time series: in an ergodic series the likelihood of finding large numbers is small compared to the likelihood of finding them in a chaotic series. In the case of two dimensions, they consider the fractal fuzzy sets whose {alpha}-cuts are fractals, arising in the context of a quadratic mapping in the extended complex plane. In an example provided by the Julia set, the conceptmore » of Hausdorff dimension enables one to decide in favor of chaotic or noisy evolution.« less

Fractal dendrite-based electrically conductive composites for laser-scribed flexible circuits

PubMed Central

Yang, Cheng; Cui, Xiaoya; Zhang, Zhexu; Chiang, Sum Wai; Lin, Wei; Duan, Huan; Li, Jia; Kang, Feiyu; Wong, Ching-Ping

2015-01-01

Fractal metallic dendrites have been drawing more attentions recently, yet they have rarely been explored in electronic printing or packaging applications because of the great challenges in large-scale synthesis and limited understanding in such applications. Here we demonstrate a controllable synthesis of fractal Ag micro-dendrites at the hundred-gram scale. When used as the fillers for isotropically electrically conductive composites (ECCs), the unique three-dimensional fractal geometrical configuration and low-temperature sintering characteristic render the Ag micro dendrites with an ultra-low electrical percolation threshold of 0.97 vol% (8 wt%). The ultra-low percolation threshold and self-limited fusing ability may address some critical challenges in current interconnect technology for microelectronics. For example, only half of the laser-scribe energy is needed to pattern fine circuit lines printed using the present ECCs, showing great potential for wiring ultrathin circuits for high performance flexible electronics. PMID:26333352

THE GENERALIZATION OF SIERPINSKI CARPET AND MENGER SPONGE IN n-DIMENSIONAL SPACE

NASA Astrophysics Data System (ADS)

Yang, Yun; Feng, Yuting; Yu, Yanhua

In this paper, we generalize Sierpinski carpet and Menger sponge in n-dimensional space, by using the generations and characterizations of affinely-equivalent Sierpinski carpet and Menger sponge. Exactly, Menger sponge in 4-dimensional space could be drawn out clearly under an affine transformation. Furthermore, the method could be used to a much broader class in fractals.

Pre-Service Teachers' Concept Images on Fractal Dimension

ERIC Educational Resources Information Center

Karakus, Fatih

2016-01-01

The analysis of pre-service teachers' concept images can provide information about their mental schema of fractal dimension. There is limited research on students' understanding of fractal and fractal dimension. Therefore, this study aimed to investigate the pre-service teachers' understandings of fractal dimension based on concept image. The…

Renormalization Analysis of a Composite Ultrasonic Transducer with a Fractal Architecture

NASA Astrophysics Data System (ADS)

Algehyne, Ebrahem A.; Mulholland, Anthony J.

To ensure the safe operation of many safety critical structures such as nuclear plants, aircraft and oil pipelines, non-destructive imaging is employed using piezoelectric ultrasonic transducers. These sensors typically operate at a single frequency due to the restrictions imposed on their resonant behavior by the use of a single length scale in the design. To allow these transducers to transmit and receive more complex signals it would seem logical to use a range of length scales in the design so that a wide range of resonating frequencies will result. In this paper, we derive a mathematical model to predict the dynamics of an ultrasound transducer that achieves this range of length scales by adopting a fractal architecture. In fact, the device is modeled as a graph where the nodes represent segments of the piezoelectric and polymer materials. The electrical and mechanical fields that are contained within this graph are then expressed in terms of a finite element basis. The structure of the resulting discretized equations yields to a renormalization methodology which is used to derive expressions for the non-dimensionalized electrical impedance and the transmission and reception sensitivities. A comparison with a standard design shows some benefits of these fractal designs.

Flat bands in fractal-like geometry

NASA Astrophysics Data System (ADS)

Pal, Biplab; Saha, Kush

2018-05-01

We report the presence of multiple flat bands in a class of two-dimensional lattices formed by Sierpinski gasket (SPG) fractal geometries as the basic unit cells. Solving the tight-binding Hamiltonian for such lattices with different generations of a SPG network, we find multiple degenerate and nondegenerate completely flat bands, depending on the configuration of parameters of the Hamiltonian. Moreover, we establish a generic formula to determine the number of such bands as a function of the generation index ℓ of the fractal geometry. We show that the flat bands and their neighboring dispersive bands have remarkable features, the most interesting one being the spin-1 conical-type spectrum at the band center without any staggered magnetic flux, in contrast to the kagome lattice. We furthermore investigate the effect of magnetic flux in these lattice settings and show that different combinations of fluxes through such fractal unit cells lead to a richer spectrum with a single isolated flat band or gapless electron- or holelike flat bands. Finally, we discuss a possible experimental setup to engineer such a fractal flat-band network using single-mode laser-induced photonic waveguides.

Space-coiling fractal metamaterial with multi-bandgaps on subwavelength scale

NASA Astrophysics Data System (ADS)

Man, Xianfeng; Liu, Tingting; Xia, Baizhan; Luo, Zhen; Xie, Longxiang; Liu, Jian

2018-06-01

Acoustic metamaterials are remarkably different from conventional materials, as they can flexibly manipulate and control the propagation of sound waves. Unlike the locally resonant metamaterials introduced in earlier studies, we designed an ultraslow artificial structure with a sound speed much lower than that in air. In this paper, the space-coiling approach is proposed for achieving artificial metamaterial for extremely low-frequency airborne sound. In addition, the self-similar fractal technique is utilized for designing space-coiling Mie-resonance-based metamaterials (MRMMs) to obtain a band-dispersive spectrum. The band structures of two-dimensional (2D) acoustic metamaterials with different fractal levels are illustrated using the finite element method. The low-frequency bandgap can easily be formed, and multi-bandgap properties are observed in high-level fractals. Furthermore, the designed MRMMs with higher order fractal space coiling shows a good robustness against irregular arrangement. Besides, the proposed artificial structure was found to modify and control the radiation field arbitrarily. Thus, this work provides useful guidelines for the design of acoustic filtering devices and acoustic wavefront shaping applications on the subwavelength scale.

Electromagnetic backscattering from one-dimensional drifting fractal sea surface II: Electromagnetic backscattering model

NASA Astrophysics Data System (ADS)

Tao, Xie; William, Perrie; Shang-Zhuo, Zhao; He, Fang; Wen-Jin, Yu; Yi-Jun, He

2016-07-01

Sea surface current has a significant influence on electromagnetic (EM) backscattering signals and may constitute a dominant synthetic aperture radar (SAR) imaging mechanism. An effective EM backscattering model for a one-dimensional drifting fractal sea surface is presented in this paper. This model is used to simulate EM backscattering signals from the drifting sea surface. Numerical results show that ocean currents have a significant influence on EM backscattering signals from the sea surface. The normalized radar cross section (NRCS) discrepancies between the model for a coupled wave-current fractal sea surface and the model for an uncoupled fractal sea surface increase with the increase of incidence angle, as well as with increasing ocean currents. Ocean currents that are parallel to the direction of the wave can weaken the EM backscattering signal intensity, while the EM backscattering signal is intensified by ocean currents propagating oppositely to the wave direction. The model presented in this paper can be used to study the SAR imaging mechanism for a drifting sea surface. Project supported by the National Natural Science Foundation of China (Grant No. 41276187), the Global Change Research Program of China (Grant No. 2015CB953901), the Priority Academic Program Development of Jiangsu Higher Education Institutions, China, the Program for the Innovation Research and Entrepreneurship Team in Jiangsu Province, China, the Canadian Program on Energy Research and Development, and the Canadian World Class Tanker Safety Service Program.

Quantitative assessment of early diabetic retinopathy using fractal analysis.

PubMed

Cheung, Ning; Donaghue, Kim C; Liew, Gerald; Rogers, Sophie L; Wang, Jie Jin; Lim, Shueh-Wen; Jenkins, Alicia J; Hsu, Wynne; Li Lee, Mong; Wong, Tien Y

2009-01-01

Fractal analysis can quantify the geometric complexity of the retinal vascular branching pattern and may therefore offer a new method to quantify early diabetic microvascular damage. In this study, we examined the relationship between retinal fractal dimension and retinopathy in young individuals with type 1 diabetes. We conducted a cross-sectional study of 729 patients with type 1 diabetes (aged 12-20 years) who had seven-field stereoscopic retinal photographs taken of both eyes. From these photographs, retinopathy was graded according to the modified Airlie House classification, and fractal dimension was quantified using a computer-based program following a standardized protocol. In this study, 137 patients (18.8%) had diabetic retinopathy signs; of these, 105 had mild retinopathy. Median (interquartile range) retinal fractal dimension was 1.46214 (1.45023-1.47217). After adjustment for age, sex, diabetes duration, A1C, blood pressure, and total cholesterol, increasing retinal vascular fractal dimension was significantly associated with increasing odds of retinopathy (odds ratio 3.92 [95% CI 2.02-7.61] for fourth versus first quartile of fractal dimension). In multivariate analysis, each 0.01 increase in retinal vascular fractal dimension was associated with a nearly 40% increased odds of retinopathy (1.37 [1.21-1.56]). This association remained after additional adjustment for retinal vascular caliber. Greater retinal fractal dimension, representing increased geometric complexity of the retinal vasculature, is independently associated with early diabetic retinopathy signs in type 1 diabetes. Fractal analysis of fundus photographs may allow quantitative measurement of early diabetic microvascular damage.

The Effect of Impeller Type on Floc Size and Structure during Shear-Induced Flocculation

PubMed

Spicer; Keller; Pratsinis

1996-12-01

The effect of impeller type and shear rate on the evolution of floc size and structure during shear-induced flocculation of polystyrene particles with aluminum sulfate is investigated by image analysis. One radial flow (six-blade Rushton turbine) and two axial flow (three-blade fluid foil, four-blade 45° pitch) impeller configurations are examined. The steady state average floc size is shown to depend on the frequency of recirculation to the impeller zone and its characteristic velocity gradient. The concepts of fractal geometry are used to characterize the floc structure. For all impellers, the two-dimensional floc fractal dimension, Dpf, increases during floc growth, indicating formation of more open structures. Later on, Dpf levels off at a steady state value as breakage becomes significant and the floc size distribution approaches steady state. The shear rate does not affect the steady state Dpf of the flocs within experimental uncertainty.

Passenger flow analysis of Beijing urban rail transit network using fractal approach

NASA Astrophysics Data System (ADS)

Li, Xiaohong; Chen, Peiwen; Chen, Feng; Wang, Zijia

2018-04-01

To quantify the spatiotemporal distribution of passenger flow and the characteristics of an urban rail transit network, we introduce four radius fractal dimensions and two branch fractal dimensions by combining a fractal approach with passenger flow assignment model. These fractal dimensions can numerically describe the complexity of passenger flow in the urban rail transit network and its change characteristics. Based on it, we establish a fractal quantification method to measure the fractal characteristics of passenger follow in the rail transit network. Finally, we validate the reasonability of our proposed method by using the actual data of Beijing subway network. It has been shown that our proposed method can effectively measure the scale-free range of the urban rail transit network, network development and the fractal characteristics of time-varying passenger flow, which further provides a reference for network planning and analysis of passenger flow.

Investigation of diamond wheel topography in Elliptical Ultrasonic Assisted Grinding (EUAG) of monocrystal sapphire using fractal analysis method.

PubMed

Wang, Qiuyan; Zhao, Wenxiang; Liang, Zhiqiang; Wang, Xibin; Zhou, Tianfeng; Wu, Yongbo; Jiao, Li

2018-03-01

The wear behaviors of grinding wheel have significant influence on the work-surface topography. However, a comprehensive and quantitative method is lacking for evaluating the wear conditions of grinding wheel. In this paper, a fractal analysis method is used to investigate the wear behavior of resin-bonded diamond wheel in Elliptical Ultrasonic Assisted Grinding (EUAG) of monocrystal sapphire, and a series of experiments on EUAG and conventional grinding (CG) are performed. The results show that the fractal dimension of grinding wheel topography is highly correlated to the wear behavior, i.e., grain fracture, grain pullout, and wheel loading. An increase in cutting edge density on the wheel surface results in an increase of the fractal dimension, but an increase in the grain pullout and wheel loading results in a decrease in the fractal dimension. The wheel topography in EUAG has a higher fractal dimension than that in CG before 60 passes due to better self-sharpening behavior, and then has a smaller fractal dimension because of more serious wheel loadings after 60 passes. By angle-dependent distribution analysis of profile fractal dimensions, the wheel surface topography is transformed from isotropic to anisotropic. These indicated that the fractal analysis method could be further used in monitoring of a grinding wheel performance in EUAG. Copyright © 2017 Elsevier B.V. All rights reserved.

Characterisation of human non-proliferative diabetic retinopathy using the fractal analysis

PubMed Central

Ţălu, Ştefan; Călugăru, Dan Mihai; Lupaşcu, Carmen Alina

2015-01-01

AIM To investigate and quantify changes in the branching patterns of the retina vascular network in diabetes using the fractal analysis method. METHODS This was a clinic-based prospective study of 172 participants managed at the Ophthalmological Clinic of Cluj-Napoca, Romania, between January 2012 and December 2013. A set of 172 segmented and skeletonized human retinal images, corresponding to both normal (24 images) and pathological (148 images) states of the retina were examined. An automatic unsupervised method for retinal vessel segmentation was applied before fractal analysis. The fractal analyses of the retinal digital images were performed using the fractal analysis software ImageJ. Statistical analyses were performed for these groups using Microsoft Office Excel 2003 and GraphPad InStat software. RESULTS It was found that subtle changes in the vascular network geometry of the human retina are influenced by diabetic retinopathy (DR) and can be estimated using the fractal geometry. The average of fractal dimensions D for the normal images (segmented and skeletonized versions) is slightly lower than the corresponding values of mild non-proliferative DR (NPDR) images (segmented and skeletonized versions). The average of fractal dimensions D for the normal images (segmented and skeletonized versions) is higher than the corresponding values of moderate NPDR images (segmented and skeletonized versions). The lowest values were found for the corresponding values of severe NPDR images (segmented and skeletonized versions). CONCLUSION The fractal analysis of fundus photographs may be used for a more complete undeTrstanding of the early and basic pathophysiological mechanisms of diabetes. The architecture of the retinal microvasculature in diabetes can be quantitative quantified by means of the fractal dimension. Microvascular abnormalities on retinal imaging may elucidate early mechanistic pathways for microvascular complications and distinguish patients with DR from healthy individuals. PMID:26309878

Characterisation of human non-proliferative diabetic retinopathy using the fractal analysis.

PubMed

Ţălu, Ştefan; Călugăru, Dan Mihai; Lupaşcu, Carmen Alina

2015-01-01

To investigate and quantify changes in the branching patterns of the retina vascular network in diabetes using the fractal analysis method. This was a clinic-based prospective study of 172 participants managed at the Ophthalmological Clinic of Cluj-Napoca, Romania, between January 2012 and December 2013. A set of 172 segmented and skeletonized human retinal images, corresponding to both normal (24 images) and pathological (148 images) states of the retina were examined. An automatic unsupervised method for retinal vessel segmentation was applied before fractal analysis. The fractal analyses of the retinal digital images were performed using the fractal analysis software ImageJ. Statistical analyses were performed for these groups using Microsoft Office Excel 2003 and GraphPad InStat software. It was found that subtle changes in the vascular network geometry of the human retina are influenced by diabetic retinopathy (DR) and can be estimated using the fractal geometry. The average of fractal dimensions D for the normal images (segmented and skeletonized versions) is slightly lower than the corresponding values of mild non-proliferative DR (NPDR) images (segmented and skeletonized versions). The average of fractal dimensions D for the normal images (segmented and skeletonized versions) is higher than the corresponding values of moderate NPDR images (segmented and skeletonized versions). The lowest values were found for the corresponding values of severe NPDR images (segmented and skeletonized versions). The fractal analysis of fundus photographs may be used for a more complete undeTrstanding of the early and basic pathophysiological mechanisms of diabetes. The architecture of the retinal microvasculature in diabetes can be quantitative quantified by means of the fractal dimension. Microvascular abnormalities on retinal imaging may elucidate early mechanistic pathways for microvascular complications and distinguish patients with DR from healthy individuals.

A Quantitative Approach to Scar Analysis

PubMed Central

Khorasani, Hooman; Zheng, Zhong; Nguyen, Calvin; Zara, Janette; Zhang, Xinli; Wang, Joyce; Ting, Kang; Soo, Chia

2011-01-01

Analysis of collagen architecture is essential to wound healing research. However, to date no consistent methodologies exist for quantitatively assessing dermal collagen architecture in scars. In this study, we developed a standardized approach for quantitative analysis of scar collagen morphology by confocal microscopy using fractal dimension and lacunarity analysis. Full-thickness wounds were created on adult mice, closed by primary intention, and harvested at 14 days after wounding for morphometrics and standard Fourier transform-based scar analysis as well as fractal dimension and lacunarity analysis. In addition, transmission electron microscopy was used to evaluate collagen ultrastructure. We demonstrated that fractal dimension and lacunarity analysis were superior to Fourier transform analysis in discriminating scar versus unwounded tissue in a wild-type mouse model. To fully test the robustness of this scar analysis approach, a fibromodulin-null mouse model that heals with increased scar was also used. Fractal dimension and lacunarity analysis effectively discriminated unwounded fibromodulin-null versus wild-type skin as well as healing fibromodulin-null versus wild-type wounds, whereas Fourier transform analysis failed to do so. Furthermore, fractal dimension and lacunarity data also correlated well with transmission electron microscopy collagen ultrastructure analysis, adding to their validity. These results demonstrate that fractal dimension and lacunarity are more sensitive than Fourier transform analysis for quantification of scar morphology. PMID:21281794

Fractality of eroded coastlines of correlated landscapes.

PubMed

Morais, P A; Oliveira, E A; Araújo, N A M; Herrmann, H J; Andrade, J S

2011-07-01

Using numerical simulations of a simple sea-coast mechanical erosion model, we investigate the effect of spatial long-range correlations in the lithology of coastal landscapes on the fractal behavior of the corresponding coastlines. In the model, the resistance of a coast section to erosion depends on the local lithology configuration as well as on the number of neighboring sea sides. For weak sea forces, the sea is trapped by the coastline and the eroding process stops after some time. For strong sea forces erosion is perpetual. The transition between these two regimes takes place at a critical sea force, characterized by a fractal coastline front. For uncorrelated landscapes, we obtain, at the critical value, a fractal dimension D=1.33, which is consistent with the dimension of the accessible external perimeter of the spanning cluster in two-dimensional percolation. For sea forces above the critical value, our results indicate that the coastline is self-affine and belongs to the Kardar-Parisi-Zhang universality class. In the case of landscapes generated with power-law spatial long-range correlations, the coastline fractal dimension changes continuously with the Hurst exponent H, decreasing from D=1.34 to 1.04, for H=0 and 1, respectively. This nonuniversal behavior is compatible with the multitude of fractal dimensions found for real coastlines.

On uses, misuses and potential abuses of fractal analysis in zooplankton behavioral studies: A review, a critique and a few recommendations

NASA Astrophysics Data System (ADS)

Seuront, Laurent

2015-08-01

Fractal analysis is increasingly used to describe, and provide further understanding to, zooplankton swimming behavior. This may be related to the fact that fractal analysis and the related fractal dimension D have the desirable properties to be independent of measurement scale and to be very sensitive to even subtle behavioral changes that may be undetectable to other behavioral variables. As early claimed by Coughlin et al. (1992), this creates "the need for fractal analysis" in behavioral studies, which has hence the potential to become a valuable tool in zooplankton behavioral ecology. However, this paper stresses that fractal analysis, as well as the more elaborated multifractal analysis, is also a risky business that may lead to irrelevant results, without paying extreme attention to a series of both conceptual and practical steps that are all likely to bias the results of any analysis. These biases are reviewed and exemplified on the basis of the published literature, and remedial procedures are provided not only for geometric and stochastic fractal analyses, but also for the more complicated multifractal analysis. The concept of multifractals is finally introduced as a direct, objective and quantitative tool to identify models of motion behavior, such as Brownian motion, fractional Brownian motion, ballistic motion, Lévy flight/walk and multifractal random walk. I finally briefly review the state of this emerging field in zooplankton behavioral research.

Monte Carlo Sampling in Fractal Landscapes

NASA Astrophysics Data System (ADS)

Leitão, Jorge C.; Lopes, J. M. Viana Parente; Altmann, Eduardo G.

2013-05-01

We design a random walk to explore fractal landscapes such as those describing chaotic transients in dynamical systems. We show that the random walk moves efficiently only when its step length depends on the height of the landscape via the largest Lyapunov exponent of the chaotic system. We propose a generalization of the Wang-Landau algorithm which constructs not only the density of states (transient time distribution) but also the correct step length. As a result, we obtain a flat-histogram Monte Carlo method which samples fractal landscapes in polynomial time, a dramatic improvement over the exponential scaling of traditional uniform-sampling methods. Our results are not limited by the dimensionality of the landscape and are confirmed numerically in chaotic systems with up to 30 dimensions.

Theory and discretization of ideal magnetohydrodynamic equilibria with fractal pressure profiles

DOE PAGES

Kraus, B. F.; Hudson, S. R.

2017-09-29

In three-dimensional ideal magnetohydrodynamics, closed flux surfaces cannot maintain both rational rotational-transform and pressure gradients, as these features together produce unphysical, infinite currents. A proposed set of equilibria nullifies these currents by flattening the pressure on sufficiently wide intervals around each rational surface. Such rational surfaces exist at every scale, which characterizes the pressure profile as self-similar and thus fractal. The pressure profile is approximated numerically by considering a finite number of rational regions and analyzed mathematically by classifying the irrational numbers that support gradients into subsets. As a result, applying these results to a given rotational-transform profile in cylindricalmore » geometry, we find magnetic field and current density profiles compatible with the fractal pressure.« less

Theory and discretization of ideal magnetohydrodynamic equilibria with fractal pressure profiles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kraus, B. F.; Hudson, S. R.

In three-dimensional ideal magnetohydrodynamics, closed flux surfaces cannot maintain both rational rotational-transform and pressure gradients, as these features together produce unphysical, infinite currents. A proposed set of equilibria nullifies these currents by flattening the pressure on sufficiently wide intervals around each rational surface. Such rational surfaces exist at every scale, which characterizes the pressure profile as self-similar and thus fractal. The pressure profile is approximated numerically by considering a finite number of rational regions and analyzed mathematically by classifying the irrational numbers that support gradients into subsets. As a result, applying these results to a given rotational-transform profile in cylindricalmore » geometry, we find magnetic field and current density profiles compatible with the fractal pressure.« less

Self-stabilized Fractality of Sea-coasts Through Damped Erosion

NASA Astrophysics Data System (ADS)

Sapoval, B.; Baldassari, A.; Gabrielli, A.

2004-05-01

Coastline morphology is of current interest in geophysical research and coastline erosion has important economic consequences. At the same time, although the geometry of seacoasts is often used as an introductory archetype of fractal morphology in nature there has been no explanation about which physical mechanism could justify that empirical observation. The present work propose a minimal, but robust, model of evolution of rocky coasts towards fractality. The model describes how a stationary fractal geometry arises spontaneously from the mutual self-stabilization of a rocky coast morphology and sea eroding power. If, on one hand, erosion generally increases the geometrical irregularity of the coast, on the other hand this increase creates a stronger damping of the sea and a consequent diminution of its eroding power. The increased damping argument relies on the studies of fractal acoustical cavities, which have shown that viscous damping is augmented on a longer, irregular, surface. A minimal two-dimensional model of erosion is introduced which leads to the through a complex dynamics of the earth-sea interface, to the appearance of a stationary fractal seacoast with dimension close to 4/3. Fractal geometry plays here the role of a morphological attractor directly related to percolation geometry. The model reproduces at least qualitatively some of the features of real coasts using only simple ingredients: the randomness of the lithology and the decrease of the erosion power of the sea. B. Sapoval, Fractals (Aditech, Paris, 1989). B. Sapoval, O. Haeberlé, and S.Russ, J. Acoust. Soc. Am., 2014 (1997). B. Hébert B., B. Sapoval, and S.Russ, J. Acoust. Soc. Am., 1567 (1999).

The Fractal Behavior of Crystal Distribution of la Gloria Pluton, Chile

NASA Astrophysics Data System (ADS)

Gutiérrez, F. J.; Payacán, I. J.; Pasten, D.; Aravena, A.; Gelman, S. E.; Bachmann, O.; Parada, M. A.

2013-12-01

We utilize fractal analysis to study the spatial distributions of crystals in a 10 Ma granitic intrusion (La Gloria pluton) located in the central Chilean Andes. Previous work determined the crystal size distribution (CSD) and anisotropy of magnetic susceptibility (AMS) tensors throughout this pluton. Using orthogonal thin sections oriented along the AMS tensor axes, we have applied fractal analysis in three magmatic crystal families: plagioclase, ferromagnesian minerals (biotite and amphibole), and Fe-Ti oxides (magnetite with minor ilmenite). We find that plagioclase and ferromagnesian minerals have a Semi-logarithmic CSD (S-CSD), given by: log(n/n0)= -L/C (1) where n [mm-4], n0 [mm-4], L [mm] and C [mm] are crystal density, intercept (nucleation density; L=0), size of crystals (three axes) and characteristic length, respectively. In contrast, Fe-Ti oxides have a Fractal CSD (F-CSD, power law size distribution), given by: log(n)= - Dn log(L) + n1 (2) where Dn and n1 [log(mm-4)] are a non-dimensional proportionality constant and the logarithm of the initial crystallization density (n1 = log(n(L=1 mm))), respectively. Finally, we calculate the fractal dimension (D0) by applying the box-counting method on each crystal thin section image, using: log(N) = -D0 log(ɛ) (3) where N and ɛ are the number of boxes occupied by minerals and the length of the square box, respectively. Results indicate that D0 values (eq. 3) are well defined for all minerals, and are higher for plagioclase than for ferromagnesian minerals and lowest for Fe-Ti oxides. D0 values are correlated with n0 and -1/C for S-CSD (eq. 1), and with n1 values for F-CSD (eq. 2). These correlations between fractal dimensions with CSD parameters suggest crystal growth follows a fractal behaviour in magmatic systems. Fractal behaviour of CSD means that the spatial distribution of crystals follows an all-scale pattern as part of a self-organized magmatic system. We interpret S-CSD of plagioclase and ferromagnesian minerals as consequence of early to intermediate crystal growth, whereas F-CSD of magnetite is also a consequence of late magmatic equilibration by increasing of fine magnetite crystals (e.g. reaction of hornblende to magnetite plus actinolite, biotite and titanite). Acknowledgments. This research has been developed by the FONDECYT N°11100241 and PBCT-PDA07 projects granted by CONICYT (Chilean National Commission for Science and Technology). I.P. is supported by CONICYT magister grant N°22130729. F.G. and I.P. thank to FONDAP N°15090013 for supporting during the conference. D.P. acknowledges FONDECYT grant N° 3120237.

Reconstruction of the dynamics of the climatic system from time-series data

PubMed Central

Nicolis, C.; Nicolis, G.

1986-01-01

The oxygen isotope record of the last million years, as provided by a deep sea core sediment, is analyzed by a method recently developed in the theory of dynamical systems. The analysis suggests that climatic variability is the manifestation of a chaotic dynamics described by an attractor of fractal dimensionality. A quantitative measure of the limited predictability of the climatic system is provided by the evaluation of the time-correlation function and the largest positive Lyapounov exponent of the system. PMID:16593650

Power dissipation in fractal AC circuits

NASA Astrophysics Data System (ADS)

Chen, Joe P.; Rogers, Luke G.; Anderson, Loren; Andrews, Ulysses; Brzoska, Antoni; Coffey, Aubrey; Davis, Hannah; Fisher, Lee; Hansalik, Madeline; Loew, Stephen; Teplyaev, Alexander

2017-08-01

We extend Feynman’s analysis of an infinite ladder circuit to fractal circuits, providing examples in which fractal circuits constructed with purely imaginary impedances can have characteristic impedances with positive real part. Using (weak) self-similarity of our fractal structures, we provide algorithms for studying the equilibrium distribution of energy on these circuits. This extends the analysis of self-similar resistance networks introduced by Fukushima, Kigami, Kusuoka, and more recently studied by Strichartz et al.

Detection and classification of Breast Cancer in Wavelet Sub-bands of Fractal Segmented Cancerous Zones.

PubMed

Shirazinodeh, Alireza; Noubari, Hossein Ahmadi; Rabbani, Hossein; Dehnavi, Alireza Mehri

2015-01-01

Recent studies on wavelet transform and fractal modeling applied on mammograms for the detection of cancerous tissues indicate that microcalcifications and masses can be utilized for the study of the morphology and diagnosis of cancerous cases. It is shown that the use of fractal modeling, as applied to a given image, can clearly discern cancerous zones from noncancerous areas. In this paper, for fractal modeling, the original image is first segmented into appropriate fractal boxes followed by identifying the fractal dimension of each windowed section using a computationally efficient two-dimensional box-counting algorithm. Furthermore, using appropriate wavelet sub-bands and image Reconstruction based on modified wavelet coefficients, it is shown that it is possible to arrive at enhanced features for detection of cancerous zones. In this paper, we have attempted to benefit from the advantages of both fractals and wavelets by introducing a new algorithm. By using a new algorithm named F1W2, the original image is first segmented into appropriate fractal boxes, and the fractal dimension of each windowed section is extracted. Following from that, by applying a maximum level threshold on fractal dimensions matrix, the best-segmented boxes are selected. In the next step, the segmented Cancerous zones which are candidates are then decomposed by utilizing standard orthogonal wavelet transform and db2 wavelet in three different resolution levels, and after nullifying wavelet coefficients of the image at the first scale and low frequency band of the third scale, the modified reconstructed image is successfully utilized for detection of breast cancer regions by applying an appropriate threshold. For detection of cancerous zones, our simulations indicate the accuracy of 90.9% for masses and 88.99% for microcalcifications detection results using the F1W2 method. For classification of detected mictocalcification into benign and malignant cases, eight features are identified and utilized in radial basis function neural network. Our simulation results indicate the accuracy of 92% classification using F1W2 method.

A spectrum fractal feature classification algorithm for agriculture crops with hyper spectrum image

NASA Astrophysics Data System (ADS)

Su, Junying

2011-11-01

A fractal dimension feature analysis method in spectrum domain for hyper spectrum image is proposed for agriculture crops classification. Firstly, a fractal dimension calculation algorithm in spectrum domain is presented together with the fast fractal dimension value calculation algorithm using the step measurement method. Secondly, the hyper spectrum image classification algorithm and flowchart is presented based on fractal dimension feature analysis in spectrum domain. Finally, the experiment result of the agricultural crops classification with FCL1 hyper spectrum image set with the proposed method and SAM (spectral angle mapper). The experiment results show it can obtain better classification result than the traditional SAM feature analysis which can fulfill use the spectrum information of hyper spectrum image to realize precision agricultural crops classification.

Spectral action models of gravity on packed swiss cheese cosmology

NASA Astrophysics Data System (ADS)

Ball, Adam; Marcolli, Matilde

2016-06-01

We present a model of (modified) gravity on spacetimes with fractal structure based on packing of spheres, which are (Euclidean) variants of the packed swiss cheese cosmology models. As the action functional for gravity we consider the spectral action of noncommutative geometry, and we compute its expansion on a space obtained as an Apollonian packing of three-dimensional spheres inside a four-dimensional ball. Using information from the zeta function of the Dirac operator of the spectral triple, we compute the leading terms in the asymptotic expansion of the spectral action. They consist of a zeta regularization of the divergent sum of the leading terms of the spectral actions of the individual spheres in the packing. This accounts for the contribution of points 1 and 3 in the dimension spectrum (as in the case of a 3-sphere). There is an additional term coming from the residue at the additional point in the real dimension spectrum that corresponds to the packing constant, as well as a series of fluctuations coming from log-periodic oscillations, created by the points of the dimension spectrum that are off the real line. These terms detect the fractality of the residue set of the sphere packing. We show that the presence of fractality influences the shape of the slow-roll potential for inflation, obtained from the spectral action. We also discuss the effect of truncating the fractal structure at a certain scale related to the energy scale in the spectral action.

Scaling relations for watersheds

NASA Astrophysics Data System (ADS)

Fehr, E.; Kadau, D.; Araújo, N. A. M.; Andrade, J. S., Jr.; Herrmann, H. J.

2011-09-01

We study the morphology of watersheds in two and three dimensional systems subjected to different degrees of spatial correlations. The response of these objects to small, local perturbations is also investigated with extensive numerical simulations. We find the fractal dimension of the watersheds to generally decrease with the Hurst exponent, which quantifies the degree of spatial correlations. Moreover, in two dimensions, our results match the range of fractal dimensions 1.10≤df≤1.15 observed for natural landscapes. We report that the watershed is strongly affected by local perturbations. For perturbed two and three dimensional systems, we observe a power-law scaling behavior for the distribution of areas (volumes) enclosed by the original and the displaced watershed and for the distribution of distances between outlets. Finite-size effects are analyzed and the resulting scaling exponents are shown to depend significantly on the Hurst exponent. The intrinsic relation between watershed and invasion percolation, as well as relations between exponents conjectured in previous studies with two dimensional systems, are now confirmed by our results in three dimensions.

Investigation into How 8th Grade Students Define Fractals

ERIC Educational Resources Information Center

Karakus, Fatih

2015-01-01

The analysis of 8th grade students' concept definitions and concept images can provide information about their mental schema of fractals. There is limited research on students' understanding and definitions of fractals. Therefore, this study aimed to investigate the elementary students' definitions of fractals based on concept image and concept…

Paradigms of Complexity: Fractals and Structures in the Sciences

NASA Astrophysics Data System (ADS)

Novak, Miroslav M.

The Table of Contents for the book is as follows: * Preface * The Origin of Complexity (invited talk) * On the Existence of Spatially Uniform Scaling Laws in the Climate System * Multispectral Backscattering: A Fractal-Structure Probe * Small-Angle Multiple Scattering on a Fractal System of Point Scatterers * Symmetric Fractals Generated by Cellular Automata * Bispectra and Phase Correlations for Chaotic Dynamical Systems * Self-Organized Criticality Models of Neural Development * Altered Fractal and Irregular Heart Rate Behavior in Sick Fetuses * Extract Multiple Scaling in Long-Term Heart Rate Variability * A Semi-Continous Box Counting Method for Fractal Dimension Measurement of Short Single Dimension Temporal Signals - Preliminary Study * A Fractional Brownian Motion Model of Cracking * Self-Affine Scaling Studies on Fractography * Coarsening of Fractal Interfaces * A Fractal Model of Ocean Surface Superdiffusion * Stochastic Subsurface Flow and Transport in Fractal Fractal Conductivity Fields * Rendering Through Iterated Function Systems * The σ-Hull - The Hull Where Fractals Live - Calculating a Hull Bounded by Log Spirals to Solve the Inverse IFS-Problem by the Detected Orbits * On the Multifractal Properties of Passively Convected Scalar Fields * New Statistical Textural Transforms for Non-Stationary Signals: Application to Generalized Mutlifractal Analysis * Laplacian Growth of Parallel Needles: Their Mullins-Sekerka Instability * Entropy Dynamics Associated with Self-Organization * Fractal Properties in Economics (invited talk) * Fractal Approach to the Regional Seismic Event Discrimination Problem * Fractal and Topological Complexity of Radioactive Contamination * Pattern Selection: Nonsingular Saffman-Taylor Finger and Its Dynamic Evolution with Zero Surface Tension * A Family of Complex Wavelets for the Characterization of Singularities * Stabilization of Chaotic Amplitude Fluctuations in Multimode, Intracavity-Doubled Solid-State Lasers * Chaotic Dynamics of Elastic-Plastic Beams * The Riemann Non-Differentiable Function and Identities for the Gaussian Sums * Revealing the Multifractal Nature of Failure Sequence * The Fractal Nature of wood Revealed by Drying * Squaring the Circle: Diffusion Volume and Acoustic Behaviour of a Fractal Structure * Relationship Between Acupuncture Holographic Units and Fetus Development; Fractal Features of Two Acupuncture Holographic Unit Systems * The Fractal Properties of the Large-Scale Magnetic Fields on the Sun * Fractal Analysis of Tide Gauge Data * Author Index

A fractal image analysis methodology for heat damage inspection in carbon fiber reinforced composites

NASA Astrophysics Data System (ADS)

Haridas, Aswin; Crivoi, Alexandru; Prabhathan, P.; Chan, Kelvin; Murukeshan, V. M.

2017-06-01

The use of carbon fiber-reinforced polymer (CFRP) composite materials in the aerospace industry have far improved the load carrying properties and the design flexibility of aircraft structures. A high strength to weight ratio, low thermal conductivity, and a low thermal expansion coefficient gives it an edge for applications demanding stringent loading conditions. Specifically, this paper focuses on the behavior of CFRP composites under stringent thermal loads. The properties of composites are largely affected by external thermal loads, especially when the loads are beyond the glass temperature, Tg, of the composite. Beyond this, the composites are subject to prominent changes in mechanical and thermal properties which may further lead to material decomposition. Furthermore, thermal damage formation being chaotic, a strict dimension cannot be associated with the formed damage. In this context, this paper focuses on comparing multiple speckle image analysis algorithms to effectively characterize the formed thermal damages on the CFRP specimen. This would provide us with a fast method for quantifying the extent of heat damage in carbon composites, thus reducing the required time for inspection. The image analysis methods used for the comparison include fractal dimensional analysis of the formed speckle pattern and analysis of number and size of various connecting elements in the binary image.

The fractal characteristic of facial anthropometric data for developing PCA fit test panels for youth born in central China.

PubMed

Yang, Lei; Wei, Ran; Shen, Henggen

2017-01-01

New principal component analysis (PCA) respirator fit test panels had been developed for current American and Chinese civilian workers based on anthropometric surveys. The PCA panels used the first two principal components (PCs) obtained from a set of 10 facial dimensions. Although the PCA panels for American and Chinese subjects adopted the bivairate framework with two PCs, the number of the PCs retained in the PCA analysis was different between Chinese subjects and Americans. For the Chinese youth group, the third PC should be retained in the PCA analysis for developing new fit test panels. In this article, an additional number label (ANL) is used to explain the third PC in PCA analysis when the first two PCs are used to construct the PCA half-facepiece respirator fit test panel for Chinese group. The three-dimensional box-counting method is proposed to estimate the ANLs by calculating fractal dimensions of the facial anthropometric data of the Chinese youth. The linear regression coefficients of scale-free range R 2 are all over 0.960, which demonstrates that the facial anthropometric data of the Chinese youth has fractal characteristic. The youth subjects born in Henan province has an ANL of 2.002, which is lower than the composite facial anthropometric data of Chinese subjects born in many provinces. Hence, Henan youth subjects have the self-similar facial anthropometric characteristic and should use the particular ANL (2.002) as the important tool along with using the PCA panel. The ANL method proposed in this article not only provides a new methodology in quantifying the characteristics of facial anthropometric dimensions for any ethnic/racial group, but also extends the scope of PCA panel studies to higher dimensions.

A fractal analysis of quaternary, Cenozoic-Mesozoic, and Late Pennsylvanian sea level changes

NASA Technical Reports Server (NTRS)

Hsui, Albert T.; Rust, Kelly A.; Klein, George D.

1993-01-01

Sea level changes are related to both climatic variations and tectonic movements. The fractal dimensions of several sea level curves were compared to a modern climatic fractal dimension of 1.26 established for annual precipitation records. A similar fractal dimension (1.22) based on delta(O-18/O-16) in deep-sea sediments has been suggested to characterize climatic change during the past 2 m.y. Our analysis indicates that sea level changes over the past 150,000 to 250,000 years also exhibit comparable fractal dimensions. Sea level changes for periods longer than about 30 m.y. are found to produce fractal dimensions closer to unity and Missourian (Late Pennsylvanian) sea level changes yield a fractal dimension of 1.41. The fact that these sea level curves all possess fractal dimensions less than 1.5 indicates that sea level changes exhibit nonperiodic, long-run persistence. The different fractal dimensions calculated for the various time periods could be the result of a characteristic overprinting of the sediment recored by prevailing processes during deposition. For example, during the Quaternary, glacio-eustatic sea level changes correlate well with the present climatic signature. During the Missourian, however, mechanisms such as plate reorganization may have dominated, resulting in a significantly different fractal dimension.

Zn-metalloprotease sequences in extremophiles

NASA Astrophysics Data System (ADS)

Holden, T.; Dehipawala, S.; Golebiewska, U.; Cheung, E.; Tremberger, G., Jr.; Williams, E.; Schneider, P.; Gadura, N.; Lieberman, D.; Cheung, T.

2010-09-01

The Zn-metalloprotease family contains conserved amino acid structures such that the nucleotide fluctuation at the DNA level would exhibit correlated randomness as described by fractal dimension. A nucleotide sequence fractal dimension can be calculated from a numerical series consisting of the atomic numbers of each nucleotide. The structure's vibration modes can also be studied using a Gaussian Network Model. The vibration measure and fractal dimension values form a two-dimensional plot with a standard vector metric that can be used for comparison of structures. The preference for amino acid usage in extremophiles may suppress nucleotide fluctuations that could be analyzed in terms of fractal dimension and Shannon entropy. A protein level cold adaptation study of the thermolysin Zn-metalloprotease family using molecular dynamics simulation was reported recently and our results show that the associated nucleotide fluctuation suppression is consistent with a regression pattern generated from the sequences's fractal dimension and entropy values (R-square { 0.98, N =5). It was observed that cold adaptation selected for high entropy and low fractal dimension values. Extension to the Archaemetzincin M54 family in extremophiles reveals a similar regression pattern (R-square = 0.98, N = 6). It was observed that the metalloprotease sequences of extremely halophilic organisms possess high fractal dimension and low entropy values as compared with non-halophiles. The zinc atom is usually bonded to the histidine residue, which shows limited levels of vibration in the Gaussian Network Model. The variability of the fractal dimension and entropy for a given protein structure suggests that extremophiles would have evolved after mesophiles, consistent with the bias usage of non-prebiotic amino acids by extremophiles. It may be argued that extremophiles have the capacity to offer extinction protection during drastic changes in astrobiological environments.

Verifying the Dependence of Fractal Coefficients on Different Spatial Distributions

NASA Astrophysics Data System (ADS)

Gospodinov, Dragomir; Marekova, Elisaveta; Marinov, Alexander

2010-01-01

A fractal distribution requires that the number of objects larger than a specific size r has a power-law dependence on the size N(r) = C/rD∝r-D where D is the fractal dimension. Usually the correlation integral is calculated to estimate the correlation fractal dimension of epicentres. A `box-counting' procedure could also be applied giving the `capacity' fractal dimension. The fractal dimension can be an integer and then it is equivalent to a Euclidean dimension (it is zero of a point, one of a segment, of a square is two and of a cube is three). In general the fractal dimension is not an integer but a fractional dimension and there comes the origin of the term `fractal'. The use of a power-law to statistically describe a set of events or phenomena reveals the lack of a characteristic length scale, that is fractal objects are scale invariant. Scaling invariance and chaotic behavior constitute the base of a lot of natural hazards phenomena. Many studies of earthquakes reveal that their occurrence exhibits scale-invariant properties, so the fractal dimension can characterize them. It has first been confirmed that both aftershock rate decay in time and earthquake size distribution follow a power law. Recently many other earthquake distributions have been found to be scale-invariant. The spatial distribution of both regional seismicity and aftershocks show some fractal features. Earthquake spatial distributions are considered fractal, but indirectly. There are two possible models, which result in fractal earthquake distributions. The first model considers that a fractal distribution of faults leads to a fractal distribution of earthquakes, because each earthquake is characteristic of the fault on which it occurs. The second assumes that each fault has a fractal distribution of earthquakes. Observations strongly favour the first hypothesis. The fractal coefficients analysis provides some important advantages in examining earthquake spatial distribution, which are:—Simple way to quantify scale-invariant distributions of complex objects or phenomena by a small number of parameters.—It is becoming evident that the applicability of fractal distributions to geological problems could have a more fundamental basis. Chaotic behaviour could underlay the geotectonic processes and the applicable statistics could often be fractal. The application of fractal distribution analysis has, however, some specific aspects. It is usually difficult to present an adequate interpretation of the obtained values of fractal coefficients for earthquake epicenter or hypocenter distributions. That is why in this paper we aimed at other goals—to verify how a fractal coefficient depends on different spatial distributions. We simulated earthquake spatial data by generating randomly points first in a 3D space - cube, then in a parallelepiped, diminishing one of its sides. We then continued this procedure in 2D and 1D space. For each simulated data set we calculated the points' fractal coefficient (correlation fractal dimension of epicentres) and then checked for correlation between the coefficients values and the type of spatial distribution. In that way one can obtain a set of standard fractal coefficients' values for varying spatial distributions. These then can be used when real earthquake data is analyzed by comparing the real data coefficients values to the standard fractal coefficients. Such an approach can help in interpreting the fractal analysis results through different types of spatial distributions.

Fractal Analyses of High-Resolution Cloud Droplet Measurements.

NASA Astrophysics Data System (ADS)

Malinowski, Szymon P.; Leclerc, Monique Y.; Baumgardner, Darrel G.

1994-02-01

Fractal analyses of individual cloud droplet distributions using aircraft measurements along one-dimensional horizontal cross sections through clouds are performed. Box counting and cluster analyses are used to determine spatial scales of inhomogeneity of cloud droplet spacing. These analyses reveal that droplet spatial distributions do not exhibit a fractal behavior. A high variability in local droplet concentration in cloud volumes undergoing mixing was found. In these regions, thin filaments of cloudy air with droplet concentration close to those observed in cloud cores were found. Results suggest that these filaments may be anisotropic. Additional box counting analyses performed for various classes of cloud droplet diameters indicate that large and small droplets are similarly distributed, except for the larger characteristic spacing of large droplets.A cloud-clear air interface defined by a certain threshold of total droplet count (TDC) was investigated. There are indications that this interface is a convoluted surface of a fractal nature, at least in actively developing cumuliform clouds. In contrast, TDC in the cloud interior does not have fractal or multifractal properties. Finally a random Cantor set (RCS) was introduced as a model of a fractal process with an ill-defined internal scale. A uniform measure associated with the RCS after several generations was introduced to simulate the TDC records. Comparison of the model with real TDC records indicates similar properties of both types of data series.

Fractal Electronic Circuits Assembled From Nanoclusters

NASA Astrophysics Data System (ADS)

Fairbanks, M. S.; McCarthy, D.; Taylor, R. P.; Brown, S. A.

2009-07-01

Many patterns in nature can be described using fractal geometry. The effect of this fractal character is an array of properties that can include high internal connectivity, high dispersivity, and enhanced surface area to volume ratios. These properties are often desirable in applications and, consequently, fractal geometry is increasingly employed in technologies ranging from antenna to storm barriers. In this paper, we explore the application of fractal geometry to electrical circuits, inspired by the pervasive fractal structure of neurons in the brain. We show that, under appropriate growth conditions, nanoclusters of Sb form into islands on atomically flat substrates via a process close to diffusion-limited aggregation (DLA), establishing fractal islands that will form the basis of our fractal circuits. We perform fractal analysis of the islands to determine the spatial scaling properties (characterized by the fractal dimension, D) of the proposed circuits and demonstrate how varying growth conditions can affect D. We discuss fabrication approaches for establishing electrical contact to the fractal islands. Finally, we present fractal circuit simulations, which show that the fractal character of the circuit translates into novel, non-linear conduction properties determined by the circuit's D value.

Detrending moving average algorithm for multifractals

NASA Astrophysics Data System (ADS)

Gu, Gao-Feng; Zhou, Wei-Xing

2010-07-01

The detrending moving average (DMA) algorithm is a widely used technique to quantify the long-term correlations of nonstationary time series and the long-range correlations of fractal surfaces, which contains a parameter θ determining the position of the detrending window. We develop multifractal detrending moving average (MFDMA) algorithms for the analysis of one-dimensional multifractal measures and higher-dimensional multifractals, which is a generalization of the DMA method. The performance of the one-dimensional and two-dimensional MFDMA methods is investigated using synthetic multifractal measures with analytical solutions for backward (θ=0) , centered (θ=0.5) , and forward (θ=1) detrending windows. We find that the estimated multifractal scaling exponent τ(q) and the singularity spectrum f(α) are in good agreement with the theoretical values. In addition, the backward MFDMA method has the best performance, which provides the most accurate estimates of the scaling exponents with lowest error bars, while the centered MFDMA method has the worse performance. It is found that the backward MFDMA algorithm also outperforms the multifractal detrended fluctuation analysis. The one-dimensional backward MFDMA method is applied to analyzing the time series of Shanghai Stock Exchange Composite Index and its multifractal nature is confirmed.

Modeling liver physiology: combining fractals, imaging and animation.

PubMed

Lin, Debbie W; Johnson, Scott; Hunt, C Anthony

2004-01-01

Physiological modeling of vascular and microvascular networks in several key human organ systems is critical for a deeper understanding of pharmacology and the effect of pharmacotherapies on disease. Like the lung and the kidney, the morphology of its vascular and microvascular system plays a major role in its functional capability. To understand liver function in absorption and metabolism of food and drugs, one must examine the morphology and physiology at both higher and lower level liver function. We have developed validated virtualized dynamic three dimensional (3D) models of liver secondary units and primary units by combining a number of different methods: three-dimensional rendering, fractals, and animation. We have simulated particle dynamics in the liver secondary unit. The resulting models are suitable for use in helping researchers easily visualize and gain intuition on results of in silico liver experiments.

Fifth dimension of life and the 4/5 allometric scaling law for human brain.

PubMed

He, Ji-Huan; Zhang, Juan

2004-01-01

Brain cells are not spherical. The basal metabolic rate (B) of a spherical cell scales as B approximately r2, where r is the radius of the cell; that of a brain cell scales as B approximately r(d), where r is the characteristic radius of the cell and d is the fractal dimensionality of its contour. The fractal geometry of the cell leads to a 4/5 allometric scaling law for human brain, uniquely endowing humans with a 5th dimension and successfully explains why the scaling exponent varies during rest and exercise. A striking analogy between Kleiber's 3/4 law and Newton's second law is heuristically illustrated. A physical explanation is given for the 4th dimension of life for three-dimensional organisms and the 5th dimension for human brain.

Rheological and fractal characteristics of unconditioned and conditioned water treatment residuals.

PubMed

Dong, Y J; Wang, Y L; Feng, J

2011-07-01

The rheological and fractal characteristics of raw (unconditioned) and conditioned water treatment residuals (WTRs) were investigated in this study. Variations in morphology, size, and image fractal dimensions of the flocs/aggregates in these WTR systems with increasing polymer doses were analyzed. The results showed that when the raw WTRs were conditioned with the polymer CZ8688, the optimum polymer dosage was observed at 24 kg/ton dry sludge. The average diameter of irregularly shaped flocs/aggregates in the WTR suspensions increased from 42.54 μm to several hundred micrometers with increasing polymer doses. Furthermore, the aggregates in the conditioned WTR system displayed boundary/surface and mass fractals. At the optimum polymer dosage, the aggregates formed had a volumetric average diameter of about 820.7 μm, with a one-dimensional fractal dimension of 1.01 and a mass fractal dimension of 2.74 on the basis of the image analysis. Rheological tests indicated that the conditioned WTRs at the optimum polymer dosage showed higher levels of shear-thinning behavior than the raw WTRs. Variations in the limiting viscosity (η(∞)) of conditioned WTRs with sludge content could be described by a linear equation, which were different from the often-observed empirical exponential relationship for most municipal sludge. With increasing temperature, the η(∞) of the raw WTRs decreased more rapidly than that of the raw WTRs. Good fitting results for the relationships between lgη(∞)∼T using the Arrhenius equation indicate that the WTRs had a much higher activation energy for viscosity of about 17.86-26.91 J/mol compared with that of anaerobic granular sludge (2.51 J/mol) (Mu and Yu, 2006). In addition, the Bingham plastic model adequately described the rheological behavior of the conditioned WTRs, whereas the rheology of the raw WTRs fit the Herschel-Bulkley model well at only certain sludge contents. Considering the good power-law relationships between the limiting viscosity and sludge content of the conditioned WTRs, their mass fractal dimensions were calculated through the models proposed by Shih et al. (1990), which were 2.48 for these conditioned WTR aggregates. The results demonstrate that conditioned WTRs behave like weak-link flocs/aggregates. Copyright © 2011 Elsevier Ltd. All rights reserved.

Experiences on Cryogenic Injection under Supercritical Condition

DTIC Science & Technology

2000-05-22

and Roshko [2] for incompressible but variable-density gaseous turbulent mixing layers. Fractal analysis of the jet boundary also shows a similarity to...spreading angle versus the chamber-to-injectant density ratio.(* refers to data taken at AFRL. - FRACTAL ANALYSIS OF THE JET RaLhtINRECDPSUE *This appeared to...be a suitable analysis method to investigate the morphology of the interfacial phenomena and in recent years a number of applications of fractal

Fractal cometary dust - a window into the early Solar system

NASA Astrophysics Data System (ADS)

Mannel, T.; Bentley, M. S.; Schmied, R.; Jeszenszky, H.; Levasseur-Regourd, A. C.; Romstedt, J.; Torkar, K.

2016-11-01

The properties of dust in the protoplanetary disc are key to understanding the formation of planets in our Solar system. Many models of dust growth predict the development of fractal structures which evolve into non-fractal, porous dust pebbles representing the main component for planetesimal accretion. In order to understand comets and their origins, the Rosetta orbiter followed comet 67P/Churyumov-Gerasimenko for over two years and carried a dedicated instrument suite for dust analysis. One of these instruments, the MIDAS (Micro-Imaging Dust Analysis System) atomic force microscope, recorded the 3D topography of micro- to nanometre-sized dust. All particles analysed to date have been found to be hierarchical agglomerates. Most show compact packing; however, one is extremely porous. This paper contains a structural description of a compact aggregate and the outstanding porous one. Both particles are tens of micrometres in size and show rather narrow subunit size distributions with noticeably similar mean values of 1.48^{+0.13}_{-0.59} μm for the porous particle and 1.36^{+0.15}_{-0.59} μm for the compact. The porous particle allows a fractal analysis, where a density-density correlation function yields a fractal dimension of Df = 1.70 ± 0.1. GIADA, another dust analysis instrument on board Rosetta, confirms the existence of a dust population with a similar fractal dimension. The fractal particles are interpreted as pristine agglomerates built in the protoplanetary disc and preserved in the comet. The similar subunits of both fractal and compact dust indicate a common origin which is, given the properties of the fractal, dominated by slow agglomeration of equally sized aggregates known as cluster-cluster agglomeration.

Fractal dynamics of heartbeat time series of young persons with metabolic syndrome

NASA Astrophysics Data System (ADS)

Muñoz-Diosdado, A.; Alonso-Martínez, A.; Ramírez-Hernández, L.; Martínez-Hernández, G.

2012-10-01

Many physiological systems have been in recent years quantitatively characterized using fractal analysis. We applied it to study heart variability of young subjects with metabolic syndrome (MS); we examined the RR time series (time between two R waves in ECG) with the detrended fluctuation analysis (DFA) method, the Higuchi's fractal dimension method and the multifractal analysis to detect the possible presence of heart problems. The results show that although the young persons have MS, the majority do not present alterations in the heart dynamics. However, there were cases where the fractal parameter values differed significantly from the healthy people values.

Impact of triacylglycerol composition on shear-induced textural changes in highly saturated fats.

PubMed

Gregersen, Sandra B; Andersen, Morten D; Hammershøj, Marianne; Wiking, Lars

2017-01-15

This study demonstrates a strong interaction between triacylglycerol (TAG) composition and effects of shear rate on the microstructure and texture of fats. Cocoa butter alternatives with similar saturated fat content, but different major TAGs (PPO-, PSO-, SSO-, POP- and SOS-rich blends) were evaluated. Results show how shear can create a harder texture in fat blends based on symmetric monounsaturated TAGs (up to ∼200%), primarily due to reduction in crystal size, whereas shear has little effect on hardness of asymmetric monounsaturated TAGs. Such differences could not be ascribed to differences in the degree of supercooling, but was found to be a consequence of differences in the crystallisation behaviour of different TAGs. The fractal dimension was evaluated by dimensional detrended fluctuation analysis and Fourier transformation of microscopy images. However, the concept of fractal patterns was found to be insufficient to describe microstructural changes of fat blends with high solid fat content. Copyright © 2016 Elsevier Ltd. All rights reserved.

Enhanced electronic excitation energy transfer between dye molecules incorporated in nano-scale media with apparent fractal dimensionality

NASA Astrophysics Data System (ADS)

Yefimova, Svetlana L.; Rekalo, Andrey M.; Gnap, Bogdan A.; Viagin, Oleg G.; Sorokin, Alexander V.; Malyukin, Yuri V.

2014-09-01

In the present study, we analyze the efficiency of Electronic Excitation Energy Transfer (EEET) between two dyes, an energy donor (D) and acceptor (A), concentrated in structurally heterogeneous media (surfactant micelles, liposomes, and porous SiO2 matrices). In all three cases, highly effective EEET in pairs of dyes has been found and cannot be explained by Standard Förster-type theory for homogeneous solutions. Two independent approaches based on the analysis of either the D relative quantum yield () or the D fluorescence decay have been used to study the deviation of experimental results from the theoretical description of EEET process. The observed deviation is quantified by the apparent fractal distribution of molecules parameter . We conclude that the highly effective EEET observed in the nano-scale media under study can be explained by both forced concentration of the hydrophobic dyes within nano-volumes and non-uniform cluster-like character of the distribution of D and A dye molecules within nano-volumes.

Fractal analysis of the spatial distribution of earthquakes along the Hellenic Subduction Zone

NASA Astrophysics Data System (ADS)

Papadakis, Giorgos; Vallianatos, Filippos; Sammonds, Peter

2014-05-01

The Hellenic Subduction Zone (HSZ) is the most seismically active region in Europe. Many destructive earthquakes have taken place along the HSZ in the past. The evolution of such active regions is expressed through seismicity and is characterized by complex phenomenology. The understanding of the tectonic evolution process and the physical state of subducting regimes is crucial in earthquake prediction. In recent years, there is a growing interest concerning an approach to seismicity based on the science of complex systems (Papadakis et al., 2013; Vallianatos et al., 2012). In this study we calculate the fractal dimension of the spatial distribution of earthquakes along the HSZ and we aim to understand the significance of the obtained values to the tectonic and geodynamic evolution of this area. We use the external seismic sources provided by Papaioannou and Papazachos (2000) to create a dataset regarding the subduction zone. According to the aforementioned authors, we define five seismic zones. Then, we structure an earthquake dataset which is based on the updated and extended earthquake catalogue for Greece and the adjacent areas by Makropoulos et al. (2012), covering the period 1976-2009. The fractal dimension of the spatial distribution of earthquakes is calculated for each seismic zone and for the HSZ as a unified system using the box-counting method (Turcotte, 1997; Robertson et al., 1995; Caneva and Smirnov, 2004). Moreover, the variation of the fractal dimension is demonstrated in different time windows. These spatiotemporal variations could be used as an additional index to inform us about the physical state of each seismic zone. As a precursor in earthquake forecasting, the use of the fractal dimension appears to be a very interesting future work. Acknowledgements Giorgos Papadakis wish to acknowledge the Greek State Scholarships Foundation (IKY). References Caneva, A., Smirnov, V., 2004. Using the fractal dimension of earthquake distributions and the slope of the recurrence curve to forecast earthquakes in Colombia. Earth Sci. Res. J., 8, 3-9. Makropoulos, K., Kaviris, G., Kouskouna, V., 2012. An updated and extended earthquake catalogue for Greece and adjacent areas since 1900. Nat. Hazards Earth Syst. Sci., 12, 1425-1430. Papadakis, G., Vallianatos, F., Sammonds, P., 2013. Evidence of non extensive statistical physics behavior of the Hellenic Subduction Zone seismicity. Tectonophysics, 608, 1037-1048. Papaioannou, C.A., Papazachos, B.C., 2000. Time-independent and time-dependent seismic hazard in Greece based on seismogenic sources. Bull. Seismol. Soc. Am., 90, 22-33. Robertson, M.C., Sammis, C.G., Sahimi, M., Martin, A.J., 1995. Fractal analysis of three-dimensional spatial distributions of earthquakes with a percolation interpretation. J. Geophys. Res., 100, 609-620. Turcotte, D.L., 1997. Fractals and chaos in geology and geophysics. Second Edition, Cambridge University Press. Vallianatos, F., Michas, G., Papadakis, G., Sammonds, P., 2012. A non-extensive statistical physics view to the spatiotemporal properties of the June 1995, Aigion earthquake (M6.2) aftershock sequence (West Corinth rift, Greece). Acta Geophys., 60, 758-768.

Dark matter and cosmological nucleosynthesis

NASA Technical Reports Server (NTRS)

Schramm, D. N.

1986-01-01

Existing dark matter problems, i.e., dynamics, galaxy formation and inflation, are considered, along with a model which proposes dark baryons as the bulk of missing matter in a fractal universe. It is shown that no combination of dark, nonbaryonic matter can either provide a cosmological density parameter value near unity or, as in the case of high energy neutrinos, allow formation of condensed matter at epochs when quasars already existed. The possibility that correlations among galactic clusters are scale-free is discussed. Such a distribution of matter would yield a fractal of 1.2, close to a one-dimensional universe. Biasing, cosmic superstrings, and percolated explosions and hot dark matter are theoretical approaches that would satisfy the D = 1.2 fractal model of the large-scale structure of the universe and which would also allow sufficient dark matter in halos to close the universe.

Multi-Scale Fractal Analysis of Image Texture and Pattern

NASA Technical Reports Server (NTRS)

Emerson, Charles W.; Lam, Nina Siu-Ngan; Quattrochi, Dale A.

1999-01-01

Analyses of the fractal dimension of Normalized Difference Vegetation Index (NDVI) images of homogeneous land covers near Huntsville, Alabama revealed that the fractal dimension of an image of an agricultural land cover indicates greater complexity as pixel size increases, a forested land cover gradually grows smoother, and an urban image remains roughly self-similar over the range of pixel sizes analyzed (10 to 80 meters). A similar analysis of Landsat Thematic Mapper images of the East Humboldt Range in Nevada taken four months apart show a more complex relation between pixel size and fractal dimension. The major visible difference between the spring and late summer NDVI images is the absence of high elevation snow cover in the summer image. This change significantly alters the relation between fractal dimension and pixel size. The slope of the fractal dimension-resolution relation provides indications of how image classification or feature identification will be affected by changes in sensor spatial resolution.

Fractal Dimension Analysis of Transient Visual Evoked Potentials: Optimisation and Applications.

PubMed

Boon, Mei Ying; Henry, Bruce Ian; Chu, Byoung Sun; Basahi, Nour; Suttle, Catherine May; Luu, Chi; Leung, Harry; Hing, Stephen

2016-01-01

The visual evoked potential (VEP) provides a time series signal response to an external visual stimulus at the location of the visual cortex. The major VEP signal components, peak latency and amplitude, may be affected by disease processes. Additionally, the VEP contains fine detailed and non-periodic structure, of presently unclear relevance to normal function, which may be quantified using the fractal dimension. The purpose of this study is to provide a systematic investigation of the key parameters in the measurement of the fractal dimension of VEPs, to develop an optimal analysis protocol for application. VEP time series were mathematically transformed using delay time, τ, and embedding dimension, m, parameters. The fractal dimension of the transformed data was obtained from a scaling analysis based on straight line fits to the numbers of pairs of points with separation less than r versus log(r) in the transformed space. Optimal τ, m, and scaling analysis were obtained by comparing the consistency of results using different sampling frequencies. The optimised method was then piloted on samples of normal and abnormal VEPs. Consistent fractal dimension estimates were obtained using τ = 4 ms, designating the fractal dimension = D2 of the time series based on embedding dimension m = 7 (for 3606 Hz and 5000 Hz), m = 6 (for 1803 Hz) and m = 5 (for 1000Hz), and estimating D2 for each embedding dimension as the steepest slope of the linear scaling region in the plot of log(C(r)) vs log(r) provided the scaling region occurred within the middle third of the plot. Piloting revealed that fractal dimensions were higher from the sampled abnormal than normal achromatic VEPs in adults (p = 0.02). Variances of fractal dimension were higher from the abnormal than normal chromatic VEPs in children (p = 0.01). A useful analysis protocol to assess the fractal dimension of transformed VEPs has been developed.

Origin of generalized entropies and generalized statistical mechanics for superstatistical multifractal systems

NASA Astrophysics Data System (ADS)

Gadjiev, Bahruz; Progulova, Tatiana

2015-01-01

We consider a multifractal structure as a mixture of fractal substructures and introduce a distribution function f (α), where α is a fractal dimension. Then we can introduce g(p)˜ ∫- ln p μe-yf(y)dy and show that the distribution functions f (α) in the form of f(α) = δ(α-1), f(α) = δ(α-θ) , f(α) = 1/α-1 , f(y)= y α-1 lead to the Boltzmann - Gibbs, Shafee, Tsallis and Anteneodo - Plastino entropies conformably. Here δ(x) is the Dirac delta function. Therefore the Shafee entropy corresponds to a fractal structure, the Tsallis entropy describes a multifractal structure with a homogeneous distribution of fractal substructures and the Anteneodo - Plastino entropy appears in case of a power law distribution f (y). We consider the Fokker - Planck equation for a fractal substructure and determine its stationary solution. To determine the distribution function of a multifractal structure we solve the two-dimensional Fokker - Planck equation and obtain its stationary solution. Then applying the Bayes theorem we obtain a distribution function for the entire system in the form of q-exponential function. We compare the results of the distribution functions obtained due to the superstatistical approach with the ones obtained according to the maximum entropy principle.

Consideration of the method of image diagnosis with respect to frontal lobe atrophy

NASA Astrophysics Data System (ADS)

Sato, K.; Sugawara, K.; Narita, Y.; Namura, I.

1996-12-01

Proposes a segmentation method for a quantitative image diagnosis as a means of realizing an objective diagnosis of the frontal lobe atrophy. From the data obtained on the grade of membership, the fractal dimensions of the cerebral tissue [cerebral spinal fluid (CSF), gray matter, and white matter] and the contours are estimated. The mutual relationship between the degree of atrophy and the fractal dimension has been analyzed based on the estimated fractal dimensions. Using a sample of 42 male and female cases, ranging In age from 50's to 70's, it has been concluded that the frontal lobe atrophy can be quantified by regarding it as an expansion of CSF region on the magnetic resonance imaging (MRI) of the brain. Furthermore, when the process of frontal lobe atrophy is separated into early and advanced stages, the volumetric change of CSF and white matter in frontal lobe displays meaningful differences between the two stages, demonstrating that the fractal dimension of CSF rises with the progress of atrophy. Moreover, an interpolation method for three-dimensional (3-D) shape reconstruction of the region of diagnostic interest is proposed and 3-D shape visualization, with respect to the degree and form of atrophy, is performed on the basis of the estimated fractal dimension of the segmented cerebral tissue.

Spatial analysis of cities using Renyi entropy and fractal parameters

NASA Astrophysics Data System (ADS)

Chen, Yanguang; Feng, Jian

2017-12-01

The spatial distributions of cities fall into two groups: one is the simple distribution with characteristic scale (e.g. exponential distribution), and the other is the complex distribution without characteristic scale (e.g. power-law distribution). The latter belongs to scale-free distributions, which can be modeled with fractal geometry. However, fractal dimension is not suitable for the former distribution. In contrast, spatial entropy can be used to measure any types of urban distributions. This paper is devoted to generalizing multifractal parameters by means of dual relation between Euclidean and fractal geometries. The main method is mathematical derivation and empirical analysis, and the theoretical foundation is the discovery that the normalized fractal dimension is equal to the normalized entropy. Based on this finding, a set of useful spatial indexes termed dummy multifractal parameters are defined for geographical analysis. These indexes can be employed to describe both the simple distributions and complex distributions. The dummy multifractal indexes are applied to the population density distribution of Hangzhou city, China. The calculation results reveal the feature of spatio-temporal evolution of Hangzhou's urban morphology. This study indicates that fractal dimension and spatial entropy can be combined to produce a new methodology for spatial analysis of city development.

Langevin Equation on Fractal Curves

NASA Astrophysics Data System (ADS)

Satin, Seema; Gangal, A. D.

2016-07-01

We analyze random motion of a particle on a fractal curve, using Langevin approach. This involves defining a new velocity in terms of mass of the fractal curve, as defined in recent work. The geometry of the fractal curve, plays an important role in this analysis. A Langevin equation with a particular model of noise is proposed and solved using techniques of the Fα-Calculus.

Direct determination approach for the multifractal detrending moving average analysis

NASA Astrophysics Data System (ADS)

Xu, Hai-Chuan; Gu, Gao-Feng; Zhou, Wei-Xing

2017-11-01

In the canonical framework, we propose an alternative approach for the multifractal analysis based on the detrending moving average method (MF-DMA). We define a canonical measure such that the multifractal mass exponent τ (q ) is related to the partition function and the multifractal spectrum f (α ) can be directly determined. The performances of the direct determination approach and the traditional approach of the MF-DMA are compared based on three synthetic multifractal and monofractal measures generated from the one-dimensional p -model, the two-dimensional p -model, and the fractional Brownian motions. We find that both approaches have comparable performances to unveil the fractal and multifractal nature. In other words, without loss of accuracy, the multifractal spectrum f (α ) can be directly determined using the new approach with less computation cost. We also apply the new MF-DMA approach to the volatility time series of stock prices and confirm the presence of multifractality.

Robust thermal quantum correlation and quantum phase transition of spin system on fractal lattices

NASA Astrophysics Data System (ADS)

Xu, Yu-Liang; Zhang, Xin; Liu, Zhong-Qiang; Kong, Xiang-Mu; Ren, Ting-Qi

2014-06-01

We investigate the quantum correlation measured by quantum discord (QD) for thermalized ferromagnetic Heisenberg spin systems in one-dimensional chains and on fractal lattices using the decimation renormalization group approach. It is found that the QD between two non-nearest-neighbor end spins exhibits some interesting behaviors which depend on the anisotropic parameter Δ, the temperature T, and the size of system L. With increasing Δ continuously, the QD possesses a cuspate change at Δ = 0 which is a critical point of quantum phase transition (QPT). There presents the "regrowth" tendency of QD with increasing T at Δ < 0, in contrast to the "growth" of QD at Δ > 0. As the size of the system L becomes large, there still exists considerable thermal QD between long-distance end sites in spin chains and on the fractal lattices even at unentangled states, and the long-distance QD can spotlight the presence of QPT. The robustness of QD on the diamond-type hierarchical lattices is stronger than that in spin chains and Koch curves, which indicates that the fractal can affect the behaviors of quantum correlation.

Performance assessment of methods for estimation of fractal dimension from scanning electron microscope images.

PubMed

Risović, Dubravko; Pavlović, Zivko

2013-01-01

Processing of gray scale images in order to determine the corresponding fractal dimension is very important due to widespread use of imaging technologies and application of fractal analysis in many areas of science, technology, and medicine. To this end, many methods for estimation of fractal dimension from gray scale images have been developed and routinely used. Unfortunately different methods (dimension estimators) often yield significantly different results in a manner that makes interpretation difficult. Here, we report results of comparative assessment of performance of several most frequently used algorithms/methods for estimation of fractal dimension. To that purpose, we have used scanning electron microscope images of aluminum oxide surfaces with different fractal dimensions. The performance of algorithms/methods was evaluated using the statistical Z-score approach. The differences between performances of six various methods are discussed and further compared with results obtained by electrochemical impedance spectroscopy on the same samples. The analysis of results shows that the performance of investigated algorithms varies considerably and that systematically erroneous fractal dimensions could be estimated using certain methods. The differential cube counting, triangulation, and box counting algorithms showed satisfactory performance in the whole investigated range of fractal dimensions. Difference statistic is proved to be less reliable generating 4% of unsatisfactory results. The performances of the Power spectrum, Partitioning and EIS were unsatisfactory in 29%, 38%, and 75% of estimations, respectively. The results of this study should be useful and provide guidelines to researchers using/attempting fractal analysis of images obtained by scanning microscopy or atomic force microscopy. © Wiley Periodicals, Inc.

MORPH-II, a software package for the analysis of scanning-electron-micrograph images for the assessment of the fractal dimension of exposed stone surfaces

USGS Publications Warehouse

Mossotti, Victor G.; Eldeeb, A. Raouf

2000-01-01

Turcotte, 1997, and Barton and La Pointe, 1995, have identified many potential uses for the fractal dimension in physicochemical models of surface properties. The image-analysis program described in this report is an extension of the program set MORPH-I (Mossotti and others, 1998), which provided the fractal analysis of electron-microscope images of pore profiles (Mossotti and Eldeeb, 1992). MORPH-II, an integration of the modified kernel of the program MORPH-I with image calibration and editing facilities, was designed to measure the fractal dimension of the exposed surfaces of stone specimens as imaged in cross section in an electron microscope.

Fuzzyics =CATEGORYICS =PRAGMATYICS (``Son of ``TRIZ''')/CATEGORY-SEMANTICS Cognition (fcp/csc) of Plato-Aristotle ``SQUARE-of-OPPOSITION''(SoO): Linguistics: Antonyms VS ``SYNONYMS'' VS Analogy/ Metaphor: Coarsest-Possible Topology: Shocks/High-Pressures Applications

NASA Astrophysics Data System (ADS)

Siegel, Edward Plato Aristotle Archimedes Carl-Ludwig; Young, Frederic; Lewis, Thomas

2013-06-01

Siegel[MRS Fall-Mtgs,:Symp.Fractals(89)-5-papers!!!;Symp.Scaling(90)] FCP/CSC {aka SPD}(Tic-Tac-Toe-Matrix/Tabular List-Format) ``COMMON-FUNCTIONING-PRINCIPLE'' DI/TRI-CHOTOMY GENERIC ``INEVITABILITY_-WEB'' PURPOSEFUL PARSIMONY-of-DI/TRI-CHOTOMY STRATEGY REdiscovery of SoO automatically/optimality is in NON-list-format/matrix: DIMENSIONALITY-DOMINATION -INEVIT-ABILITY ROOT-CAUSE(RC) ULTIMATE-ORIGIN(UO): (level-0.-logic) DIMENSIONALITY (level-0. logic): [dst = ODD-Z] <->{Dst=FRACTAL-UNcertainty FLUCTUATIONS} <->(dst = EVEN-Z): CAUSES: (level- I.-logic): EXTENT/SCALE/RADIUS: (relative)-[LOCALITY] <-> (relative)-(...GLOBALITY...) & (level-II.-logic): POWER-SPECTRUM{noise ≅generalized-susceptibility}: [``l''/ω0-White] <->(...-``l''/ω 1 . 000 . . . - HYPERBOLICITY...) & (level-III.-logic) CRITICAL-EXPONENT:n =0 <->n = 1.000... ; BUT ALL 3 ALSO CAUSED BY ANOTHER INdependent RCUO (level-IV.-logic):

Two-dimensional free-surface flow under gravity: A new benchmark case for SPH method

NASA Astrophysics Data System (ADS)

Wu, J. Z.; Fang, L.

2018-02-01

Currently there are few free-surface benchmark cases with analytical results for the Smoothed Particle Hydrodynamics (SPH) simulation. In the present contribution we introduce a two-dimensional free-surface flow under gravity, and obtain an analytical expression on the surface height difference and a theoretical estimation on the surface fractal dimension. They are preliminarily validated and supported by SPH calculations.

Chaos, ergodic convergence, and fractal instability for a thermostated canonical harmonic oscillator

NASA Astrophysics Data System (ADS)

Hoover, Wm. G.; Hoover, Carol G.; Isbister, Dennis J.

2001-02-01

The authors thermostat a qp harmonic oscillator using the two additional control variables ζ and ξ to simulate Gibbs' canonical distribution. In contrast to the motion of purely Hamiltonian systems, the thermostated oscillator motion is completely ergodic, covering the full four-dimensional \\{q,p,ζ,ξ\\} phase space. The local Lyapunov spectrum (instantaneous growth rates of a comoving corotating phase-space hypersphere) exhibits singularities like those found earlier for Hamiltonian chaos, reinforcing the notion that chaos requires kinetic-as opposed to statistical-study, both at and away from equilibrium. The exponent singularities appear to have a fractal character.

A fractal model of effective stress of porous media and the analysis of influence factors

NASA Astrophysics Data System (ADS)

Li, Wei; Zhao, Huan; Li, Siqi; Sun, Wenfeng; Wang, Lei; Li, Bing

2018-03-01

The basic concept of effective stress describes the characteristics of fluid and solid interaction in porous media. In this paper, based on the theory of fractal geometry, a fractal model was built to analyze the relationship between the microstructure and the effective stress of porous media. From the microscopic point of view, the influence of effective stress on pore structure of porous media was demonstrated. Theoretical analysis and experimental results show that: (i) the fractal model of effective stress can be used to describe the relationship between effective stress and the microstructure of porous media; (ii) a linear increase in the effective stress leads to exponential increases in fractal dimension, porosity and pore number of the porous media, and causes a decreasing trend in the average pore radius.

Influence of the artificial saliva storage on 3-D surface texture characteristics of contemporary dental nanocomposites.

PubMed

Ţălu, Ştefan; Bramowicz, Miroslaw; Kulesza, Slawomir; Lainović, Tijana; Vilotić, Marko; Blažić, Larisa

2016-11-01

The aim of this study was to analyse the influence of the artificial saliva on a three-dimensional (3-D) surface texture of contemporary dental composites. The representatives of four composites types were tested: nanofilled (Filtek Ultimate Body, FUB), nanohybrid (Filtek Z550, FZ550), microfilled (Gradia Direct, GD) and microhybrid (Filtek Z250, FZ250). The specimens were polymerised and polished by the multistep protocol (SuperSnap, Shofu). Their surface was examined, before and after 3 weeks' exposure to artificial saliva storage. The surface texture was analysed using the atomic force microscope (AFM). The obtained images were processed to calculate the areal autocorrelation function (AACF), anisotropy ratio S tr (texture aspect ratio), and structure function (SF). The log-log plots of SF were used to calculate fractal properties, such as fractal dimension D, and pseudo-topothesy K. The analysis showed changes in surface anisotropy ratio S tr values, which became higher, whereas the S q roughness (root-mean-square) reduced after the artificial saliva storage. All the samples exhibited bifractal structure before the saliva treatment, but only half of them remained bifractal afterwards (GD, FZ250), whereas the other half turned into a monofractal (FUB, FZ550). The cube-count fractal dimension D cc was found to be material- and treatment-insensitive. © 2016 The Authors Journal of Microscopy © 2016 Royal Microscopical Society.

COMPARISON OF CHAOTIC AND FRACTAL PROPERTIES OF POLAR FACULAE WITH SUNSPOT ACTIVITY

DOE Office of Scientific and Technical Information (OSTI.GOV)

Deng, L. H.; Xiang, Y. Y.; Dun, G. T.

The solar magnetic activity is governed by a complex dynamo mechanism and exhibits a nonlinear dissipation behavior in nature. The chaotic and fractal properties of solar time series are of great importance to understanding the solar dynamo actions, especially with regard to the nonlinear dynamo theories. In the present work, several nonlinear analysis approaches are proposed to investigate the nonlinear dynamical behavior of the polar faculae and sunspot activity for the time interval from 1951 August to 1998 December. The following prominent results are found: (1) both the high- and the low-latitude solar activity are governed by a three-dimensional chaoticmore » attractor, and the chaotic behavior of polar faculae is the most complex, followed by that of the sunspot areas, and then the sunspot numbers; (2) both the high- and low-latitude solar activity exhibit a high degree of persistent behavior, and their fractal nature is due to such long-range correlation; (3) the solar magnetic activity cycle is predictable in nature, but the high-accuracy prediction should only be done for short- to mid-term due to its intrinsically dynamical complexity. With the help of the Babcock–Leighton dynamo model, we suggest that the nonlinear coupling of the polar magnetic fields with strong active-region fields exhibits a complex manner, causing the statistical similarities and differences between the polar faculae and the sunspot-related indicators.« less

Fractal structures in centrifugal flywheel governor system

NASA Astrophysics Data System (ADS)

Rao, Xiao-Bo; Chu, Yan-Dong; Lu-Xu; Chang, Ying-Xiang; Zhang, Jian-Gang

2017-09-01

The global structure of nonlinear response of mechanical centrifugal governor, forming in two-dimensional parameter space, is studied in this paper. By using three kinds of phases, we describe how responses of periodicity, quasi-periodicity and chaos organize some self-similarity structures with parameters varying. For several parameter combinations, the regular vibration shows fractal characteristic, that is, the comb-shaped self-similarity structure is generated by alternating periodic response with intermittent chaos, and Arnold's tongues embedded in quasi-periodic response are organized according to Stern-Brocot tree. In particular, a new type of mixed-mode oscillations (MMOs) is found in the periodic response. These unique structures reveal the natural connection of various responses between part and part, part and the whole in parameter space based on self-similarity of fractal. Meanwhile, the remarkable and unexpected results are to contribute a valid dynamic reference for practical applications with respect to mechanical centrifugal governor.

Understanding soft glassy materials using an energy landscape approach

NASA Astrophysics Data System (ADS)

Hwang, Hyun Joo; Riggleman, Robert A.; Crocker, John C.

2016-09-01

Many seemingly different soft materials--such as soap foams, mayonnaise, toothpaste and living cells--display strikingly similar viscoelastic behaviour. A fundamental physical understanding of such soft glassy rheology and how it can manifest in such diverse materials, however, remains unknown. Here, by using a model soap foam consisting of compressible spherical bubbles, whose sizes slowly evolve and whose collective motion is simply dictated by energy minimization, we study the foam's dynamics as it corresponds to downhill motion on an energy landscape function spanning a high-dimensional configuration space. We find that these downhill paths, when viewed in this configuration space, are, surprisingly, fractal. The complex behaviour of our model, including power-law rheology and non-diffusive bubble motion and avalanches, stems directly from the fractal dimension and energy function of these paths. Our results suggest that ubiquitous soft glassy rheology may be a consequence of emergent fractal geometry in the energy landscapes of many complex fluids.

An improved stochastic fractal search algorithm for 3D protein structure prediction.

PubMed

Zhou, Changjun; Sun, Chuan; Wang, Bin; Wang, Xiaojun

2018-05-03

Protein structure prediction (PSP) is a significant area for biological information research, disease treatment, and drug development and so on. In this paper, three-dimensional structures of proteins are predicted based on the known amino acid sequences, and the structure prediction problem is transformed into a typical NP problem by an AB off-lattice model. This work applies a novel improved Stochastic Fractal Search algorithm (ISFS) to solve the problem. The Stochastic Fractal Search algorithm (SFS) is an effective evolutionary algorithm that performs well in exploring the search space but falls into local minimums sometimes. In order to avoid the weakness, Lvy flight and internal feedback information are introduced in ISFS. In the experimental process, simulations are conducted by ISFS algorithm on Fibonacci sequences and real peptide sequences. Experimental results prove that the ISFS performs more efficiently and robust in terms of finding the global minimum and avoiding getting stuck in local minimums.

A comparative analysis of spectral exponent estimation techniques for 1/fβ processes with applications to the analysis of stride interval time series

PubMed Central

Schaefer, Alexander; Brach, Jennifer S.; Perera, Subashan; Sejdić, Ervin

2013-01-01

Background The time evolution and complex interactions of many nonlinear systems, such as in the human body, result in fractal types of parameter outcomes that exhibit self similarity over long time scales by a power law in the frequency spectrum S(f) = 1/fβ. The scaling exponent β is thus often interpreted as a “biomarker” of relative health and decline. New Method This paper presents a thorough comparative numerical analysis of fractal characterization techniques with specific consideration given to experimentally measured gait stride interval time series. The ideal fractal signals generated in the numerical analysis are constrained under varying lengths and biases indicative of a range of physiologically conceivable fractal signals. This analysis is to complement previous investigations of fractal characteristics in healthy and pathological gait stride interval time series, with which this study is compared. Results The results of our analysis showed that the averaged wavelet coefficient method consistently yielded the most accurate results. Comparison with Existing Methods: Class dependent methods proved to be unsuitable for physiological time series. Detrended fluctuation analysis as most prevailing method in the literature exhibited large estimation variances. Conclusions The comparative numerical analysis and experimental applications provide a thorough basis for determining an appropriate and robust method for measuring and comparing a physiologically meaningful biomarker, the spectral index β. In consideration of the constraints of application, we note the significant drawbacks of detrended fluctuation analysis and conclude that the averaged wavelet coefficient method can provide reasonable consistency and accuracy for characterizing these fractal time series. PMID:24200509

A comparative analysis of spectral exponent estimation techniques for 1/f(β) processes with applications to the analysis of stride interval time series.

PubMed

Schaefer, Alexander; Brach, Jennifer S; Perera, Subashan; Sejdić, Ervin

2014-01-30

The time evolution and complex interactions of many nonlinear systems, such as in the human body, result in fractal types of parameter outcomes that exhibit self similarity over long time scales by a power law in the frequency spectrum S(f)=1/f(β). The scaling exponent β is thus often interpreted as a "biomarker" of relative health and decline. This paper presents a thorough comparative numerical analysis of fractal characterization techniques with specific consideration given to experimentally measured gait stride interval time series. The ideal fractal signals generated in the numerical analysis are constrained under varying lengths and biases indicative of a range of physiologically conceivable fractal signals. This analysis is to complement previous investigations of fractal characteristics in healthy and pathological gait stride interval time series, with which this study is compared. The results of our analysis showed that the averaged wavelet coefficient method consistently yielded the most accurate results. Class dependent methods proved to be unsuitable for physiological time series. Detrended fluctuation analysis as most prevailing method in the literature exhibited large estimation variances. The comparative numerical analysis and experimental applications provide a thorough basis for determining an appropriate and robust method for measuring and comparing a physiologically meaningful biomarker, the spectral index β. In consideration of the constraints of application, we note the significant drawbacks of detrended fluctuation analysis and conclude that the averaged wavelet coefficient method can provide reasonable consistency and accuracy for characterizing these fractal time series. Copyright © 2013 Elsevier B.V. All rights reserved.

Fractal analysis and its impact factors on pore structure of artificial cores based on the images obtained using magnetic resonance imaging

NASA Astrophysics Data System (ADS)

Wang, Heming; Liu, Yu; Song, Yongchen; Zhao, Yuechao; Zhao, Jiafei; Wang, Dayong

2012-11-01

Pore structure is one of important factors affecting the properties of porous media, but it is difficult to describe the complexity of pore structure exactly. Fractal theory is an effective and available method for quantifying the complex and irregular pore structure. In this paper, the fractal dimension calculated by box-counting method based on fractal theory was applied to characterize the pore structure of artificial cores. The microstructure or pore distribution in the porous material was obtained using the nuclear magnetic resonance imaging (MRI). Three classical fractals and one sand packed bed model were selected as the experimental material to investigate the influence of box sizes, threshold value, and the image resolution when performing fractal analysis. To avoid the influence of box sizes, a sequence of divisors of the image was proposed and compared with other two algorithms (geometric sequence and arithmetic sequence) with its performance of partitioning the image completely and bringing the least fitted error. Threshold value selected manually and automatically showed that it plays an important role during the image binary processing and the minimum-error method can be used to obtain an appropriate or reasonable one. Images obtained under different pixel matrices in MRI were used to analyze the influence of image resolution. Higher image resolution can detect more quantity of pore structure and increase its irregularity. With benefits of those influence factors, fractal analysis on four kinds of artificial cores showed the fractal dimension can be used to distinguish the different kinds of artificial cores and the relationship between fractal dimension and porosity or permeability can be expressed by the model of D = a - bln(x + c).

Fractal analysis of bone structure with applications to osteoporosis and microgravity effects

NASA Astrophysics Data System (ADS)

Acharya, Raj S.; LeBlanc, Adrian; Shackelford, Linda; Swarnakar, Vivek; Krishnamurthy, Ram; Hausman, E.; Lin, Chin-Shoou

1995-05-01

We characterize the trabecular structure with the aid of fractal dimension. We use alternating sequential filters (ASF) to generate a nonlinear pyramid for fractal dimension computations. We do not make any assumptions of the statistical distributions of the underlying fractal bone structure. The only assumption of our scheme is the rudimentary definition of self-similarity. This allows us the freedom of not being constrained by statistical estimation schemes. With mathematical simulations, we have shown that the ASF methods outperform other existing methods for fractal dimension estimation. We have shown that the fractal dimension remains the same when computed with both the x-ray images and the MRI images of the patella. We have shown that the fractal dimension of osteoporotic subjects is lower than that of the normal subjects. In animal models, we have shown that the fractal dimension of osteoporotic rats was lower than that of the normal rats. In a 17 week bedrest study, we have shown that the subject's prebedrest fractal dimension is higher than that of the postbedrest fractal dimension.

Fractal analysis of bone structure with applications to osteoporosis and microgravity effects

DOE Office of Scientific and Technical Information (OSTI.GOV)

Acharya, R.S.; Swarnarkar, V.; Krishnamurthy, R.

1995-12-31

The authors characterize the trabecular structure with the aid of fractal dimension. The authors use Alternating Sequential filters to generate a nonlinear pyramid for fractal dimension computations. The authors do not make any assumptions of the statistical distributions of the underlying fractal bone structure. The only assumption of the scheme is the rudimentary definition of self similarity. This allows them the freedom of not being constrained by statistical estimation schemes. With mathematical simulations, the authors have shown that the ASF methods outperform other existing methods for fractal dimension estimation. They have shown that the fractal dimension remains the same whenmore » computed with both the X-Ray images and the MRI images of the patella. They have shown that the fractal dimension of osteoporotic subjects is lower than that of the normal subjects. In animal models, the authors have shown that the fractal dimension of osteoporotic rats was lower than that of the normal rats. In a 17 week bedrest study, they have shown that the subject`s prebedrest fractal dimension is higher than that of the postbedrest fractal dimension.« less

Analysis of Fractional Flow for Transient Two-Phase Flow in Fractal Porous Medium

NASA Astrophysics Data System (ADS)

Lu, Ting; Duan, Yonggang; Fang, Quantang; Dai, Xiaolu; Wu, Jinsui

2016-03-01

Prediction of fractional flow in fractal porous medium is important for reservoir engineering and chemical engineering as well as hydrology. A physical conceptual fractional flow model of transient two-phase flow is developed in fractal porous medium based on the fractal characteristics of pore-size distribution and on the approximation that porous medium consist of a bundle of tortuous capillaries. The analytical expression for fractional flow for wetting phase is presented, and the proposed expression is the function of structural parameters (such as tortuosity fractal dimension, pore fractal dimension, maximum and minimum diameters of capillaries) and fluid properties (such as contact angle, viscosity and interfacial tension) in fractal porous medium. The sensitive parameters that influence fractional flow and its derivative are formulated, and their impacts on fractional flow are discussed.

Pitfalls in Fractal Time Series Analysis: fMRI BOLD as an Exemplary Case

PubMed Central

Eke, Andras; Herman, Peter; Sanganahalli, Basavaraju G.; Hyder, Fahmeed; Mukli, Peter; Nagy, Zoltan

2012-01-01

This article will be positioned on our previous work demonstrating the importance of adhering to a carefully selected set of criteria when choosing the suitable method from those available ensuring its adequate performance when applied to real temporal signals, such as fMRI BOLD, to evaluate one important facet of their behavior, fractality. Earlier, we have reviewed on a range of monofractal tools and evaluated their performance. Given the advance in the fractal field, in this article we will discuss the most widely used implementations of multifractal analyses, too. Our recommended flowchart for the fractal characterization of spontaneous, low frequency fluctuations in fMRI BOLD will be used as the framework for this article to make certain that it will provide a hands-on experience for the reader in handling the perplexed issues of fractal analysis. The reason why this particular signal modality and its fractal analysis has been chosen was due to its high impact on today’s neuroscience given it had powerfully emerged as a new way of interpreting the complex functioning of the brain (see “intrinsic activity”). The reader will first be presented with the basic concepts of mono and multifractal time series analyses, followed by some of the most relevant implementations, characterization by numerical approaches. The notion of the dichotomy of fractional Gaussian noise and fractional Brownian motion signal classes and their impact on fractal time series analyses will be thoroughly discussed as the central theme of our application strategy. Sources of pitfalls and way how to avoid them will be identified followed by a demonstration on fractal studies of fMRI BOLD taken from the literature and that of our own in an attempt to consolidate the best practice in fractal analysis of empirical fMRI BOLD signals mapped throughout the brain as an exemplary case of potentially wide interest. PMID:23227008

Self-Similarity of Plasmon Edge Modes on Koch Fractal Antennas.

PubMed

Bellido, Edson P; Bernasconi, Gabriel D; Rossouw, David; Butet, Jérémy; Martin, Olivier J F; Botton, Gianluigi A

2017-11-28

We investigate the plasmonic behavior of Koch snowflake fractal geometries and their possible application as broadband optical antennas. Lithographically defined planar silver Koch fractal antennas were fabricated and characterized with high spatial and spectral resolution using electron energy loss spectroscopy. The experimental data are supported by numerical calculations carried out with a surface integral equation method. Multiple surface plasmon edge modes supported by the fractal structures have been imaged and analyzed. Furthermore, by isolating and reproducing self-similar features in long silver strip antennas, the edge modes present in the Koch snowflake fractals are identified. We demonstrate that the fractal response can be obtained by the sum of basic self-similar segments called characteristic edge units. Interestingly, the plasmon edge modes follow a fractal-scaling rule that depends on these self-similar segments formed in the structure after a fractal iteration. As the size of a fractal structure is reduced, coupling of the modes in the characteristic edge units becomes relevant, and the symmetry of the fractal affects the formation of hybrid modes. This analysis can be utilized not only to understand the edge modes in other planar structures but also in the design and fabrication of fractal structures for nanophotonic applications.

Fractal-Based Analysis of the Influence of Music on Human Respiration

NASA Astrophysics Data System (ADS)

Reza Namazi, H.

An important challenge in respiration related studies is to investigate the influence of external stimuli on human respiration. Auditory stimulus is an important type of stimuli that influences human respiration. However, no one discovered any trend, which relates the characteristics of the auditory stimuli to the characteristics of the respiratory signal. In this paper, we investigate the correlation between auditory stimuli and respiratory signal from fractal point of view. We found out that the fractal structure of respiratory signal is correlated with the fractal structure of the applied music. Based on the obtained results, the music with greater fractal dimension will result in respiratory signal with smaller fractal dimension. In order to verify this result, we benefit from approximate entropy. The results show the respiratory signal will have smaller approximate entropy by choosing the music with smaller approximate entropy. The method of analysis could be further investigated to analyze the variations of different physiological time series due to the various types of stimuli when the complexity is the main concern.

Fractal scaling in bottlenose dolphin (Tursiops truncatus) echolocation: A case study

NASA Astrophysics Data System (ADS)

Perisho, Shaun T.; Kelty-Stephen, Damian G.; Hajnal, Alen; Houser, Dorian; Kuczaj, Stan A., II

2016-02-01

Fractal scaling patterns, which entail a power-law relationship between magnitude of fluctuations in a variable and the scale at which the variable is measured, have been found in many aspects of human behavior. These findings have led to advances in behavioral models (e.g. providing empirical support for cascade-driven theories of cognition) and have had practical medical applications (e.g. providing new methods for early diagnosis of medical conditions). In the present paper, fractal analysis is used to investigate whether similar fractal scaling patterns exist in inter-click interval and peak-peak amplitude measurements of bottlenose dolphin click trains. Several echolocation recordings taken from two male bottlenose dolphins were analyzed using Detrended Fluctuation Analysis and Higuchi's (1988) method for determination of fractal dimension. Both animals were found to exhibit fractal scaling patterns near what is consistent with persistent long range correlations. These findings suggest that recent advances in human cognition and medicine may have important parallel applications to echolocation as well.

[Features of fractal dynamics EEG of alpha-rhythm in patients with neurotic and neurosis-like disorders].

PubMed

Shul'ts, E V; Baburin, I N; Karavaeva, T A; Karvasarskiĭ, B D; Slezin, V B

2011-01-01

Fifty-five patients with neurotic and neurosis-like disorders and 20 healthy controls, aged 17-64 years, have been examined. The basic research method was electroencephalography (EEG) with the fractal analysis of alpha power fluctuations. In patients, the changes in the fractal structure were of the same direction: the decrease of fractal indexes of low-frequency fluctuations and the increase of fractal indexes of mid-frequency fluctuations. Patients with neurosis-like disorders, in comparison to those with neurotic disorders, were characterized by more expressed (quantitative) changes in fractal structures of more extended character. It suggests the presence of deeper pathological changes in patients with neurosis-like disorders.

The "Chaos Theory" and nonlinear dynamics in heart rate variability analysis: does it work in short-time series in patients with coronary heart disease?

PubMed

Krstacic, Goran; Krstacic, Antonija; Smalcelj, Anton; Milicic, Davor; Jembrek-Gostovic, Mirjana

2007-04-01

Dynamic analysis techniques may quantify abnormalities in heart rate variability (HRV) based on nonlinear and fractal analysis (chaos theory). The article emphasizes clinical and prognostic significance of dynamic changes in short-time series applied on patients with coronary heart disease (CHD) during the exercise electrocardiograph (ECG) test. The subjects were included in the series after complete cardiovascular diagnostic data. Series of R-R and ST-T intervals were obtained from exercise ECG data after sampling digitally. The range rescaled analysis method determined the fractal dimension of the intervals. To quantify fractal long-range correlation's properties of heart rate variability, the detrended fluctuation analysis technique was used. Approximate entropy (ApEn) was applied to quantify the regularity and complexity of time series, as well as unpredictability of fluctuations in time series. It was found that the short-term fractal scaling exponent (alpha(1)) is significantly lower in patients with CHD (0.93 +/- 0.07 vs 1.09 +/- 0.04; P < 0.001). The patients with CHD had higher fractal dimension in each exercise test program separately, as well as in exercise program at all. ApEn was significant lower in CHD group in both RR and ST-T ECG intervals (P < 0.001). The nonlinear dynamic methods could have clinical and prognostic applicability also in short-time ECG series. Dynamic analysis based on chaos theory during the exercise ECG test point out the multifractal time series in CHD patients who loss normal fractal characteristics and regularity in HRV. Nonlinear analysis technique may complement traditional ECG analysis.

Fractal pharmacokinetics of the drug mibefradil in the liver

NASA Astrophysics Data System (ADS)

Fuite, J.; Marsh, R.; Tuszyński, J.

2002-08-01

We explore the ramifications of the fractal geometry of the key organ for drug elimination, the liver, on pharmacokinetic data analysis. A formalism is developed for the use of a combination of well-stirred Euclidean and fractal compartments in the body. Perturbation analysis is carried out to obtain analytical solutions for the drug concentration time evolution. These results are then fitted to experimental data collected from clinically instrumented dogs [see, A. Skerjanec et al., J. Pharm. Sci. 85, 189 (1995)] using the drug mibefradil. The thus obtained spectral fractal dimension has a range of values that is consistent with the value found in independently performed ultrasound experiments on the liver.

Classification of daily solar irradiation by fractional analysis of 10-min-means of solar irradiance

NASA Astrophysics Data System (ADS)

Harrouni, S.; Guessoum, A.; Maafi, A.

2005-02-01

This paper deals with fractal analysis of daily solar irradiances measured with a time step of 10 minutes at Golden and Boulder located in Colorado. The aim is to estimate the fractal dimensions in order to perform classification of daily solar irradiances. The estimated fractal dimension hat{D} and the clearness index KT are used as classification criteria. The results show that these criteria lead to three classes: clear sky, partially covered sky and overcast sky. The results also show that the evaluation of the fractal dimension of the irradiance signal based on a data set with 10 minutes time step is possible.

A fractal analysis of pathogen detection by biosensors

NASA Astrophysics Data System (ADS)

Doke, Atul M.; Sadana, Ajit

2006-05-01

A fractal analysis is presented for the detection of pathogens such as Franscisela tularensis, and Yersinia pestis (the bacterium that causes plague) using a CANARY (cellular analysis and notification of antigens risks and yields) biosensor (Rider et al., 2003). In general, the binding and dissociation rate coefficients may be adequately described by either a single- or a dual-fractal analysis. An attempt is made to relate the binding rate coefficient to the degree of heterogeneity (fractal dimension value) present on the biosensor surface. Binding and dissociation rate coefficient values obtained are presented. The kinetics aspects along with the affinity values presented are of interest, and should along with the rate coefficients presented for the binding and the dissociation phase be of significant interest in help designing better biosensors for an application area that is bound to gain increasing importance in the future.

A Fractal Analysis of CT Liver Images for the Discrimination of Hepatic Lesions: A Comparative Study

DTIC Science & Technology

2001-10-25

liver images in order to estimate their fractal dimension and to differentiate normal liver parenchyma from hepatocellular carcinoma . Four fractal...methods; thus discriminating up to 93% of the normal parenchyma and up to 82% of the hepatocellular carcinoma , correctly.

Correlation of Fractal Dimension Values with Implant Insertion Torque and Resonance Frequency Values at Implant Recipient Sites.

PubMed

Suer, Berkay Tolga; Yaman, Zekai; Buyuksarac, Bora

2016-01-01

Fractal analysis is a mathematical method used to describe the internal architecture of complex structures such as trabecular bone. Fractal analysis of panoramic radiographs of implant recipient sites could help to predict the quality of the bone prior to implant placement. This study investigated the correlations between the fractal dimension values obtained from panoramic radiographs and the insertion torque and resonance frequency values of mandibular implants. Thirty patients who received a total of 55 implants of the same brand, diameter, and length in the mandibular premolar and molar regions were included in the study. The same surgical procedures were applied to each patient, and the insertion torque and resonance frequency values were recorded for each implant at the time of placement. The radiographic fractal dimensions of the alveolar bone in the implant recipient area were calculated from preoperative panoramic radiographs using a box-counting algorithm. The insertion torque and resonance frequency values were compared with the fractal dimension values using the Spearman test. All implants were successful, and none were lost during the follow-up period. Linear correlations were observed between the fractal dimension and resonance frequency, between the fractal dimension and insertion torque, and between resonance frequency and insertion torque. These results suggest that the noninvasive measurement of the fractal dimension from panoramic radiographs might help to predict the bone quality, and thus the primary stability of dental implants, before implant surgery.

Fractals in the neurosciences, Part II: clinical applications and future perspectives.

PubMed

Di Ieva, Antonio; Esteban, Francisco J; Grizzi, Fabio; Klonowski, Wlodzimierz; Martín-Landrove, Miguel

2015-02-01

It has been ascertained that the human brain is a complex system studied at multiple scales, from neurons and microcircuits to macronetworks. The brain is characterized by a hierarchical organization that gives rise to its highly topological and functional complexity. Over the last decades, fractal geometry has been shown as a universal tool for the analysis and quantification of the geometric complexity of natural objects, including the brain. The fractal dimension has been identified as a quantitative parameter for the evaluation of the roughness of neural structures, the estimation of time series, and the description of patterns, thus able to discriminate different states of the brain in its entire physiopathological spectrum. Fractal-based computational analyses have been applied to the neurosciences, particularly in the field of clinical neurosciences including neuroimaging and neuroradiology, neurology and neurosurgery, psychiatry and psychology, and neuro-oncology and neuropathology. After a review of the basic concepts of fractal analysis and its main applications to the basic neurosciences in part I of this series, here, we review the main applications of fractals to the clinical neurosciences for a holistic approach towards a fractal geometry model of the brain. © The Author(s) 2013.

Editorial

NASA Astrophysics Data System (ADS)

Liu, Shuai

Fractal represents a special feature of nature and functional objects. However, fractal based computing can be applied to many research domains because of its fixed property resisted deformation, variable parameters and many unpredictable changes. Theoretical research and practical application of fractal based computing have been hotspots for 30 years and will be continued. There are many pending issues awaiting solutions in this domain, thus this thematic issue containing 14 papers publishes the state-of-the-art developments in theorem and application of fractal based computing, including mathematical analysis and novel engineering applications. The topics contain fractal and multifractal features in application and solution of nonlinear odes and equation.

Fractal and Multifractal Models Applied to Porous Media - Editorial

USDA-ARS?s Scientific Manuscript database

Given the current high level of interest in the use of fractal geometry to characterize natural porous media, a special issue of the Vadose Zone Journal was organized in order to expose established fractal analysis techniques and cutting-edge new developments to a wider Earth science audience. The ...

Random-fractal Ansatz for the configurations of two-dimensional critical systems

NASA Astrophysics Data System (ADS)

Lee, Ching Hua; Ozaki, Dai; Matsueda, Hiroaki

2016-12-01

Critical systems have always intrigued physicists and precipitated the development of new techniques. Recently, there has been renewed interest in the information contained in the configurations of classical critical systems, whose computation do not require full knowledge of the wave function. Inspired by holographic duality, we investigated the entanglement properties of the classical configurations (snapshots) of the Potts model by introducing an Ansatz ensemble of random fractal images. By virtue of the central limit theorem, our Ansatz accurately reproduces the entanglement spectra of actual Potts snapshots without any fine tuning of parameters or artificial restrictions on ensemble choice. It provides a microscopic interpretation of the results of previous studies, which established a relation between the scaling behavior of snapshot entropy and the critical exponent. More importantly, it elucidates the role of ensemble disorder in restoring conformal invariance, an aspect previously ignored. Away from criticality, the breakdown of scale invariance leads to a renormalization of the parameter Σ in the random fractal Ansatz, whose variation can be used as an alternative determination of the critical exponent. We conclude by providing a recipe for the explicit construction of fractal unit cells consistent with a given scaling exponent.

Study of Fractal Features of Geomagnetic Activity Through an MHD Shell Model

NASA Astrophysics Data System (ADS)

Dominguez, M.; Nigro, G.; Munoz, V.; Carbone, V.

2013-12-01

Studies on complexity have been of great interest in plasma physics, because they provide new insights and reveal possible universalities on issues such as geomagnetic activity, turbulence in laboratory plasmas, physics of the solar wind, etc. [1, 2]. In particular, various studies have discussed the relationship between the fractal dimension, as a measure of complexity, and physical processes in magnetized plasmas such as the Sun's surface, the solar wind and the Earth's magnetosphere, including the possibility of forecasting geomagnetic activity [3, 4, 5]. Shell models are low dimensional dynamical models describing the main statistical properties of magnetohydrodynamic (MHD) turbulence [6]. These models allow us to describe extreme parameter conditions hence reaching very high Reynolds (Re) numbers. In this work a MHD shell model is used to describe the dissipative events which are taking place in the Earth's magnetosphere and causing geomagnetic storms. The box-counting fractal dimension (D) [7] is calculated for the time series of the magnetic energy dissipation rate obtained in this MHD shell model. We analyze the correlation between D and the energy dissipation rate in order to make a comparison with the same analysis made on the geomagnetic data. We show that, depending on the values of the viscosity and the diffusivity, the fractal dimension and the occurrence of bursts exhibit correlations similar as those observed in geomagnetic and solar data, [8] suggesting that the latter parameters could play a fundamental role in these processes. References [1] R. O. Dendy, S. C. Chapman, and M. Paczuski, Plasma Phys. Controlled Fusion 49, A95 (2007). [2] T. Chang and C. C. Wu, Phys. Rev. E 77, 045401 (2008). [3] R. T. J. McAteer, P. T. Gallagher, and J. Ireland, Astrophys. J. 631, 628 (2005). [4] V. M. Uritsky, A. J. Klimas, and D. Vassiliadis, Adv. Space Res. 37, 539 (2006). [5] S. C. Chapman, B. Hnat, and K. Kiyani, Nonlinear Proc. Geophys. 15, 445 (2008). [6] G. Boffetta, V. Carbone, P. Giuliani, P. Veltri, and A. Vulpiani, Phys. Rev. Lett. 83, 4662 (1999). [7] P. S. Addison, Fractals and Chaos, an Illustrated Course, vol. 1 (Institute of Physics Publishing, Bristol and Philadelphia, 1997), second ed. [8] M. Domínguez, V. Muñoz, and J. A. Valdivia, Temporal evolution of fractality in the Earth's magnetosphere and the solar photosphere, in preparation.

Fractal Interrelationships in Field and Seismic Data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wilson, T.H.; Dominic, Jovita; Halverson, Joel

1997-10-01

Size scaling interrelationships are evaluated in this study using a fractal model. Fractal models of several geologic variables are examined and include fracture patterns, reflection travel times, structural relief, drainage, topographic relief and active fault patterns. The fractal properties of structural relief inferred from seismic data and structural cross sections provide a quantitative means to characterize and compare complex structural patterns. Studies were conducted using seismic data from the Granny Creek oil field in the Appalachian Plateau. Previous studies of the field reveal that subtle detached structures present on the limb of a larger structure are associated with enhanced productionmore » from the field. Vertical increases of fractal dimension across the zone of detachment provide a measure of the extent to which detachment has occurred. The increases of fractal dimension are greatest in the more productive areas of the field. A result with equally important ramifications is that fracture systems do not appear to be intrinsically fractal as is often suggested in the literature. While examples of nearly identical patterns can be found at different scales supporting the idea of self-similarity, these examples are often taken from different areas and from different lithologies. Examination of fracture systems at different scales in the Valley and Ridge Province suggest that their distribution become increasingly sparse with scale reduction, and therefore are dissimilar or non-fractal. Box counting data in all cases failed to yield a fractal regime. The results obtained from this analysis bring into question the general applicability of reservoir simulations employing fractal models of fracture distribution. The same conclusions were obtained from the analysis of 1D fracture patterns such as those that might appear in a horizontal well.« less

Small-angle scattering from the Cantor surface fractal on the plane and the Koch snowflake

NASA Astrophysics Data System (ADS)

Cherny, Alexander Yu.; Anitas, Eugen M.; Osipov, Vladimir A.; Kuklin, Alexander I.

The small-angle scattering (SAS) from the Cantor surface fractal on the plane and Koch snowflake is considered. We develop the construction algorithm for the Koch snowflake, which makes possible the recurrence relation for the scattering amplitude. The surface fractals can be decomposed into a sum of surface mass fractals for arbitrary fractal iteration, which enables various approximations for the scattering intensity. It is shown that for the Cantor fractal, one can neglect with a good accuracy the correlations between the mass fractal amplitudes, while for the Koch snowflake, these correlations are important. It is shown that nevertheless, the correlations can be build in the mass fractal amplitudes, which explains the decay of the scattering intensity $I(q)\\sim q^{D_{\\mathrm{s}}-4}$ with $1 < D_{\\mathrm{s}} < 2$ being the fractal dimension of the perimeter. The curve $I(q)q^{4-D_{\\mathrm{s}}}$ is found to be log-periodic in the fractal region with the period equal to the scaling factor of the fractal. The log-periodicity arises from the self-similarity of sizes of basic structural units rather than from correlations between their distances. A recurrence relation is obtained for the radius of gyration of Koch snowflake, which is solved in the limit of infinite iterations. The present analysis allows us to obtain additional information from SAS data, such as the edges of the fractal regions, the fractal iteration number and the scaling factor.

Using the 1989 Calendar as a Resource.

ERIC Educational Resources Information Center

Chick, Helen

1989-01-01

Presents 10 space-related ideas, thoughts, and questions represented on the Australian Association of Mathematics Teachers (AAMT) calendar. The ideas are on impossible shapes, fractals, space itself, galaxy, tesselated pigs, spirals, helices, black holes and three-dimensional surfaces, tesseracts, and mobius bands. (YP)

Singular spectrum decomposition of Bouligand-Minkowski fractal descriptors: an application to the classification of texture Images

NASA Astrophysics Data System (ADS)

Florindo, João. Batista

2018-04-01

This work proposes the use of Singular Spectrum Analysis (SSA) for the classification of texture images, more specifically, to enhance the performance of the Bouligand-Minkowski fractal descriptors in this task. Fractal descriptors are known to be a powerful approach to model and particularly identify complex patterns in natural images. Nevertheless, the multiscale analysis involved in those descriptors makes them highly correlated. Although other attempts to address this point was proposed in the literature, none of them investigated the relation between the fractal correlation and the well-established analysis employed in time series. And SSA is one of the most powerful techniques for this purpose. The proposed method was employed for the classification of benchmark texture images and the results were compared with other state-of-the-art classifiers, confirming the potential of this analysis in image classification.

Generalized Weierstrass-Mandelbrot Function Model for Actual Stocks Markets Indexes with Nonlinear Characteristics

NASA Astrophysics Data System (ADS)

Zhang, L.; Yu, C.; Sun, J. Q.

2015-03-01

It is difficult to simulate the dynamical behavior of actual financial markets indexes effectively, especially when they have nonlinear characteristics. So it is significant to propose a mathematical model with these characteristics. In this paper, we investigate a generalized Weierstrass-Mandelbrot function (WMF) model with two nonlinear characteristics: fractal dimension D where 2 > D > 1.5 and Hurst exponent (H) where 1 > H > 0.5 firstly. And then we study the dynamical behavior of H for WMF as D and the spectrum of the time series γ change in three-dimensional space, respectively. Because WMF and the actual stock market indexes have two common features: fractal behavior using fractal dimension and long memory effect by Hurst exponent, we study the relationship between WMF and the actual stock market indexes. We choose a random value of γ and fixed value of D for WMF to simulate the S&P 500 indexes at different time ranges. As shown in the simulation results of three-dimensional space, we find that γ is important in WMF model and different γ may have the same effect for the nonlinearity of WMF. Then we calculate the skewness and kurtosis of actual Daily S&P 500 index in different time ranges which can be used to choose the value of γ. Based on these results, we choose appropriate γ, D and initial value into WMF to simulate Daily S&P 500 indexes. Using the fit line method in two-dimensional space for the simulated values, we find that the generalized WMF model is effective for simulating different actual stock market indexes in different time ranges. It may be useful for understanding the dynamical behavior of many different financial markets.

Fractal dimension analysis of weight-bearing bones of rats during skeletal unloading

NASA Technical Reports Server (NTRS)

Pornprasertsuk, S.; Ludlow, J. B.; Webber, R. L.; Tyndall, D. A.; Sanhueza, A. I.; Yamauchi, M.

2001-01-01

Fractal analysis was used to quantify changes in trabecular bone induced through the use of a rat tail-suspension model to simulate microgravity-induced osteopenia. Fractal dimensions were estimated from digitized radiographs obtained from tail-suspended and ambulatory rats. Fifty 4-month-old male Sprague-Dawley rats were divided into groups of 24 ambulatory (control) and 26 suspended (test) animals. Rats of both groups were killed after periods of 1, 4, and 8 weeks. Femurs and tibiae were removed and radiographed with standard intraoral films and digitized using a flatbed scanner. Square regions of interest were cropped at proximal, middle, and distal areas of each bone. Fractal dimensions were estimated from slopes of regression lines fitted to circularly averaged plots of log power vs. log spatial frequency. The results showed that the computed fractal dimensions were significantly greater for images of trabecular bones from tail-suspended groups than for ambulatory groups (p < 0.01) at 1 week. Periods between 1 and 4 weeks likewise yielded significantly different estimates (p < 0.05), consistent with an increase in bone loss. In the tibiae, the proximal regions of the suspended group produced significantly greater fractal dimensions than other regions (p < 0.05), which suggests they were more susceptible to unloading. The data are consistent with other studies demonstrating osteopenia in microgravity environments and the regional response to skeletal unloading. Thus, fractal analysis could be a useful technique to evaluate the structural changes of bone.

New methodology for evaluating osteoclastic activity induced by orthodontic load

PubMed Central

ARAÚJO, Adriele Silveira; FERNANDES, Alline Birra Nolasco; MACIEL, José Vinicius Bolognesi; NETTO, Juliana de Noronha Santos; BOLOGNESE, Ana Maria

2015-01-01

Orthodontic tooth movement (OTM) is a dynamic process of bone modeling involving osteoclast-driven resorption on the compression side. Consequently, to estimate the influence of various situations on tooth movement, experimental studies need to analyze this cell. Objectives The aim of this study was to test and validate a new method for evaluating osteoclastic activity stimulated by mechanical loading based on the fractal analysis of the periodontal ligament (PDL)-bone interface. Material and Methods The mandibular right first molars of 14 rabbits were tipped mesially by a coil spring exerting a constant force of 85 cN. To evaluate the actual influence of osteoclasts on fractal dimension of bone surface, alendronate (3 mg/Kg) was injected weekly in seven of those rabbits. After 21 days, the animals were killed and their jaws were processed for histological evaluation. Osteoclast counts and fractal analysis (by the box counting method) of the PDL-bone interface were performed in histological sections of the right and left sides of the mandible. Results An increase in the number of osteoclasts and in fractal dimension after OTM only happened when alendronate was not administered. Strong correlation was found between the number of osteoclasts and fractal dimension. Conclusions Our results suggest that osteoclastic activity leads to an increase in bone surface irregularity, which can be quantified by its fractal dimension. This makes fractal analysis by the box counting method a potential tool for the assessment of osteoclastic activity on bone surfaces in microscopic examination. PMID:25760264

Proliferative diabetic retinopathy characterization based on fractal features: Evaluation on a publicly available dataset.

PubMed

Orlando, José Ignacio; van Keer, Karel; Barbosa Breda, João; Manterola, Hugo Luis; Blaschko, Matthew B; Clausse, Alejandro

2017-12-01

Diabetic retinopathy (DR) is one of the most widespread causes of preventable blindness in the world. The most dangerous stage of this condition is proliferative DR (PDR), in which the risk of vision loss is high and treatments are less effective. Fractal features of the retinal vasculature have been previously explored as potential biomarkers of DR, yet the current literature is inconclusive with respect to their correlation with PDR. In this study, we experimentally assess their discrimination ability to recognize PDR cases. A statistical analysis of the viability of using three reference fractal characterization schemes - namely box, information, and correlation dimensions - to identify patients with PDR is presented. These descriptors are also evaluated as input features for training ℓ1 and ℓ2 regularized logistic regression classifiers, to estimate their performance. Our results on MESSIDOR, a public dataset of 1200 fundus photographs, indicate that patients with PDR are more likely to exhibit a higher fractal dimension than healthy subjects or patients with mild levels of DR (P≤1.3×10-2). Moreover, a supervised classifier trained with both fractal measurements and red lesion-based features reports an area under the ROC curve of 0.93 for PDR screening and 0.96 for detecting patients with optic disc neovascularizations. The fractal dimension of the vasculature increases with the level of DR. Furthermore, PDR screening using multiscale fractal measurements is more feasible than using their derived fractal dimensions. Code and further resources are provided at https://github.com/ignaciorlando/fundus-fractal-analysis. © 2017 American Association of Physicists in Medicine.

On the fractal morphology of combustion-generated soot aggregates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Koylu, U.O.

1995-12-31

The fractal properties of soot aggregates were investigated using ex-situ and in-situ experimental methods as well as computer simulations. Ex-situ experiments involved thermophoretic sampling and analysis by transmission electron microscopy (TEM), while in-situ measurements employed angular static light scattering and data inversion based on Rayleigh-Debye-Gans (RDG) approximation. Computer simulations used a sequential algorithm which mimics mass fractal-like structures. So from a variety of hydrocarbon-fueled laminar and turbulent nonpremixed flame environments were considered in the present study. The TEM analysis of projected soot images sampled from fuel-rich conditions of buoyant and weakly-buoyant laminar flames indicated that the fractal dimension of sootmore » was relatively independent of position in flames, fuel type and flame condition. These measurements yielded an average fractal dimension of 1.8, although other structure parameters such as the primary particle diameters and number of primary particles in aggregates had wide range of values. Fractal prefactor (lacunarity) was also measured for soot sampled from the fuel-lean conditions of turbulent flames, considering the actual morphology by tilting the samples during TEM analysis. These measurements yielded a fractal dimension of 1.65 and a lacunarity of 8.5, with experimental uncertainties (95% confidence) of 0.08 and 0.5, respectively. Relationships between the actual and projected structure properties of soot were also developed by combining TEM observations with numerical simulations. Practical approximate formulae were suggested to find radius of gyration of an aggregate from its maximum dimension, and number of primary particles in an aggregate from projected area. Finally, the fractal dimension and lacunarity of soot were obtained using light scattering for the same conditions of the above TEM measurements.« less

Thermodynamics of photons on fractals.

PubMed

Akkermans, Eric; Dunne, Gerald V; Teplyaev, Alexander

2010-12-03

A thermodynamical treatment of a massless scalar field (a photon) confined to a fractal spatial manifold leads to an equation of state relating pressure to internal energy, PV(s) = U/d(s), where d(s) is the spectral dimension and V(s) defines the "spectral volume." For regular manifolds, V(s) coincides with the usual geometric spatial volume, but on a fractal this is not necessarily the case. This is further evidence that on a fractal, momentum space can have a different dimension than position space. Our analysis also provides a natural definition of the vacuum (Casimir) energy of a fractal. We suggest ways that these unusual properties might be probed experimentally.

Fractals in biology and medicine

NASA Technical Reports Server (NTRS)

Havlin, S.; Buldyrev, S. V.; Goldberger, A. L.; Mantegna, R. N.; Ossadnik, S. M.; Peng, C. K.; Simons, M.; Stanley, H. E.

1995-01-01

Our purpose is to describe some recent progress in applying fractal concepts to systems of relevance to biology and medicine. We review several biological systems characterized by fractal geometry, with a particular focus on the long-range power-law correlations found recently in DNA sequences containing noncoding material. Furthermore, we discuss the finding that the exponent alpha quantifying these long-range correlations ("fractal complexity") is smaller for coding than for noncoding sequences. We also discuss the application of fractal scaling analysis to the dynamics of heartbeat regulation, and report the recent finding that the normal heart is characterized by long-range "anticorrelations" which are absent in the diseased heart.

Singularity analysis: theory and further developments

NASA Astrophysics Data System (ADS)

Cheng, Qiuming

2015-04-01

Since the concept of singularity and local singularity analysis method (LSA) were originally proposed by the author for characterizing the nonlinear property of hydrothermal mineralization processes, the local singularity analysis technique has been successfully applied for identification of geochemical and geophysical anomalies related to various types of mineral deposits. It has also been shown that the singularity is the generic property of singular geo-processes which result in anomalous amounts of energy release or material accumulation within a narrow spatial-temporal interval. In the current paper we introduce several new developments about singularity analysis. First is a new concept of 'fractal density' which describes the singularity of complex phenomena of fractal nature. While the ordinary density possesses a unit of ratio of mass and volume (e.g. g/cm3, kg/m3) or ratio of energy over volume or time (e.g. J/cm3, w/L3, w/s), the fractal density has a unit of ratio of mass over fractal set or energy over fractal set (e.g. g/cmα, kg/mα, J/ mα, w/Lα, where α can be a non-integer). For the matter with fractal density (a non-integer α), the ordinary density of the phenomena (mass or energy) no longer exists and depicts singularity. We demonstrate that most of extreme geo-processes occurred in the earth crust originated from cascade earth dynamics (mental convection, plate tectonics, orogeny and weathering etc) may cause fractal density of mass accumulation or energy release. The examples to be used to demonstrate the concepts of fractal density and singularity are earthquakes, floods, volcanos, hurricanes, heat flow over oceanic ridge, hydrothermal mineralization in orogenic belt, and anomalies in regolith over mine caused by ore and toxic elements vertical migration. Other developments of singularity theory and methodologies including singular Kriging and singularity weights of evidence model for information integration will also be introduced.

Noninvasive, label-free, three-dimensional imaging of melanoma with confocal photothermal microscopy: Differentiate malignant melanoma from benign tumor tissue

NASA Astrophysics Data System (ADS)

He, Jinping; Wang, Nan; Tsurui, Hiromichi; Kato, Masashi; Iida, Machiko; Kobayashi, Takayoshi

2016-07-01

Skin cancer is one of the most common cancers. Melanoma accounts for less than 2% of skin cancer cases but causes a large majority of skin cancer deaths. Early detection of malignant melanoma remains the key factor in saving lives. However, the melanoma diagnosis is still clinically challenging. Here, we developed a confocal photothermal microscope for noninvasive, label-free, three-dimensional imaging of melanoma. The axial resolution of confocal photothermal microscope is ~3 times higher than that of commonly used photothermal microscope. Three-dimensional microscopic distribution of melanin in pigmented lesions of mouse skin is obtained directly with this setup. Classic morphometric and fractal analysis of sixteen 3D images (eight for benign melanoma and eight for malignant) showed a capability of pathology of melanoma: melanin density and size become larger during the melanoma growth, and the melanin distribution also becomes more chaotic and unregulated. The results suggested new options for monitoring the melanoma growth and also for the melanoma diagnosis.

Physics in space-time with scale-dependent metrics

NASA Astrophysics Data System (ADS)

Balankin, Alexander S.

2013-10-01

We construct three-dimensional space Rγ3 with the scale-dependent metric and the corresponding Minkowski space-time Mγ,β4 with the scale-dependent fractal (DH) and spectral (DS) dimensions. The local derivatives based on scale-dependent metrics are defined and differential vector calculus in Rγ3 is developed. We state that Mγ,β4 provides a unified phenomenological framework for dimensional flow observed in quite different models of quantum gravity. Nevertheless, the main attention is focused on the special case of flat space-time M1/3,14 with the scale-dependent Cantor-dust-like distribution of admissible states, such that DH increases from DH=2 on the scale ≪ℓ0 to DH=4 in the infrared limit ≫ℓ0, where ℓ0 is the characteristic length (e.g. the Planck length, or characteristic size of multi-fractal features in heterogeneous medium), whereas DS≡4 in all scales. Possible applications of approach based on the scale-dependent metric to systems of different nature are briefly discussed.

Correlating brain blood oxygenation level dependent (BOLD) fractal dimension mapping with magnetic resonance spectroscopy (MRS) in Alzheimer's disease.

PubMed

Warsi, Mohammed A; Molloy, William; Noseworthy, Michael D

2012-10-01

To correlate temporal fractal structure of resting state blood oxygen level dependent (rsBOLD) functional magnetic resonance imaging (fMRI) with in vivo proton magnetic resonance spectroscopy ((1)H-MRS), in Alzheimer's disease (AD) and healthy age-matched normal controls (NC). High temporal resolution (4 Hz) rsBOLD signal and single voxel (left putamen) magnetic resonance spectroscopy data was acquired in 33 AD patients and 13 NC. The rsBOLD data was analyzed using two types of fractal dimension (FD) analysis based on relative dispersion and frequency power spectrum. Comparisons in FD were performed between AD and NC, and FD measures were correlated with (1)H-MRS findings. Temporal fractal analysis of rsBOLD, was able to differentiate AD from NC subjects (P = 0.03). Low FD correlated with markers of AD severity including decreased concentrations of N-acetyl aspartate (R = 0.44, P = 0.015) and increased myoinositol (mI) (R = -0.45, P = 0.012). Based on these results we suggest fractal analysis of rsBOLD could provide an early marker of AD.

Fractal binding and dissociation kinetics of lecithin cholesterol acyl transferase (LCAT), a heart-related compound, on biosensor surfaces

NASA Astrophysics Data System (ADS)

Doke, Atul M.; Sadana, Ajit

2006-05-01

A fractal analysis is presented for the binding and dissociation of different heart-related compounds in solution to receptors immobilized on biosensor surfaces. The data analyzed include LCAT (lecithin cholesterol acyl transferase) concentrations in solution to egg-white apoA-I rHDL immobilized on a biosensor chip surface.1 Single- and dual- fractal models were employed to fit the data. Values of the binding and the dissociation rate coefficient(s), affinity values, and the fractal dimensions were obtained from the regression analysis provided by Corel Quattro Pro 8.0 (Corel Corporation Limited).2 The binding rate coefficients are quite sensitive to the degree of heterogeneity on the sensor chip surface. Predictive equations are developed for the binding rate coefficient as a function of the degree of heterogeneity present on the sensor chip surface and on the LCAT concentration in solution, and for the affinity as a function of the ratio of fractal dimensions present in the binding and the dissociation phases. The analysis presented provided physical insights into these analyte-receptor reactions occurring on different biosensor surfaces.

Pseudochaos and anomalous transport: A study on saw-tooth map

NASA Astrophysics Data System (ADS)

Fan, Rong

The observation of chaotic dynamics in digital filter in late 1980s propelled the interest in piecewise linear map beyond the border of theoretical electrical engineering. Also, during last two decades, various physical models and phenomena, such as stochastic web and sticky orbits, not only broadened our knowledge of chaos but also urged us to further our understanding of meaning of chaos and randomness. In this dissertation, a piecewise linear kicked oscillator model: saw-tooth map, is studied as an example of pseudochaos. Physically, kicked oscillator model describes one-dimensional harmonic oscillator effected by delta-like kicks from external force source at certain fixed frequency. Starting from a special case of global periodicity, numerical investigations were carefully carried out in two cases that deviate from global periodicity. We observe the appearance of stochastic web structure and accompanying erratic dynamical behavior in the system that can't be fully explained by the classical Kolmogorov-Arnold-Moser theorem. Also anomalous transport occurs in both cases. We perform accurate analysis of Poincare recurrences and reconstruct the probability density function of Poincare recurrence times, which suggests a relation between the transport and the Poincare recurrence exponents. Saw-tooth map has non-uniform phase space, in which domains of regular dynamics and domains of chaotic dynamics are intertwined. The large-scale dynamics of the system is hugely impacted by the heterogeneity of the phase space, especially by the existence of hierarchy of periodic islands. We carefully study the characteristics of phase space and numerically compute fractal dimensions of the so-called exceptional set Delta in both cases. Our results suggest that the fractal dimension is strictly less than 2 and that the fractal structures are unifractal rather than multifractal. We present a phenomenological theoretical framework of Fractional Kinetic Equation (FKE) and Renormalization Group of Kinetics (RGK). FKE, which is fractional generalization of the Fokker-Planck-Kolmogorov equation, adopts the fractality of time and space and serves probabilistic description of chaos in Hamiltonian systems. RGK bridges the self-similar structure in phase space and large-scale behavior of the dynamics, and establishes relationships among fractality, transport and Poincare recurrences.

Trabecular Bone Mechanical Properties and Fractal Dimension

NASA Technical Reports Server (NTRS)

Hogan, Harry A.

1996-01-01

Countermeasures for reducing bone loss and muscle atrophy due to extended exposure to the microgravity environment of space are continuing to be developed and improved. An important component of this effort is finite element modeling of the lower extremity and spinal column. These models will permit analysis and evaluation specific to each individual and thereby provide more efficient and effective exercise protocols. Inflight countermeasures and post-flight rehabilitation can then be customized and targeted on a case-by-case basis. Recent Summer Faculty Fellowship participants have focused upon finite element mesh generation, muscle force estimation, and fractal calculations of trabecular bone microstructure. Methods have been developed for generating the three-dimensional geometry of the femur from serial section magnetic resonance images (MRI). The use of MRI as an imaging modality avoids excessive exposure to radiation associated with X-ray based methods. These images can also detect trabecular bone microstructure and architecture. The goal of the current research is to determine the degree to which the fractal dimension of trabecular architecture can be used to predict the mechanical properties of trabecular bone tissue. The elastic modulus and the ultimate strength (or strain) can then be estimated from non-invasive, non-radiating imaging and incorporated into the finite element models to more accurately represent the bone tissue of each individual of interest. Trabecular bone specimens from the proximal tibia are being studied in this first phase of the work. Detailed protocols and procedures have been developed for carrying test specimens through all of the steps of a multi-faceted test program. The test program begins with MRI and X-ray imaging of the whole bones before excising a smaller workpiece from the proximal tibia region. High resolution MRI scans are then made and the piece further cut into slabs (roughly 1 cm thick). The slabs are X-rayed again and also scanned using dual-energy X-ray absorptiometry (DEXA). Cube specimens are then cut from the slabs and tested mechanically in compression. Correlations between mechanical properties and fractal dimension will then be examined to assess and quantify the predictive capability of the fractal calculations.

Fractal and Gray Level Cooccurrence Matrix Computational Analysis of Primary Osteosarcoma Magnetic Resonance Images Predicts the Chemotherapy Response.

PubMed

Djuričić, Goran J; Radulovic, Marko; Sopta, Jelena P; Nikitović, Marina; Milošević, Nebojša T

2017-01-01

The prediction of induction chemotherapy response at the time of diagnosis may improve outcomes in osteosarcoma by allowing for personalized tailoring of therapy. The aim of this study was thus to investigate the predictive potential of the so far unexploited computational analysis of osteosarcoma magnetic resonance (MR) images. Fractal and gray level cooccurrence matrix (GLCM) algorithms were employed in retrospective analysis of MR images of primary osteosarcoma localized in distal femur prior to the OsteoSa induction chemotherapy. The predicted and actual chemotherapy response outcomes were then compared by means of receiver operating characteristic (ROC) analysis and accuracy calculation. Dbin, Λ, and SCN were the standard fractal and GLCM features which significantly associated with the chemotherapy outcome, but only in one of the analyzed planes. Our newly developed normalized fractal dimension, called the space-filling ratio (SFR) exerted an independent and much better predictive value with the prediction significance accomplished in two of the three imaging planes, with accuracy of 82% and area under the ROC curve of 0.20 (95% confidence interval 0-0.41). In conclusion, SFR as the newly designed fractal coefficient provided superior predictive performance in comparison to standard image analysis features, presumably by compensating for the tumor size variation in MR images.

Fractal analysis as a potential tool for surface morphology of thin films

NASA Astrophysics Data System (ADS)

Soumya, S.; Swapna, M. S.; Raj, Vimal; Mahadevan Pillai, V. P.; Sankararaman, S.

2017-12-01

Fractal geometry developed by Mandelbrot has emerged as a potential tool for analyzing complex systems in the diversified fields of science, social science, and technology. Self-similar objects having the same details in different scales are referred to as fractals and are analyzed using the mathematics of non-Euclidean geometry. The present work is an attempt to correlate fractal dimension for surface characterization by Atomic Force Microscopy (AFM). Taking the AFM images of zinc sulphide (ZnS) thin films prepared by pulsed laser deposition (PLD) technique, under different annealing temperatures, the effect of annealing temperature and surface roughness on fractal dimension is studied. The annealing temperature and surface roughness show a strong correlation with fractal dimension. From the regression equation set, the surface roughness at a given annealing temperature can be calculated from the fractal dimension. The AFM images are processed using Photoshop and fractal dimension is calculated by box-counting method. The fractal dimension decreases from 1.986 to 1.633 while the surface roughness increases from 1.110 to 3.427, for a change of annealing temperature 30 ° C to 600 ° C. The images are also analyzed by power spectrum method to find the fractal dimension. The study reveals that the box-counting method gives better results compared to the power spectrum method.

Taxonomy of Individual Variations in Aesthetic Responses to Fractal Patterns

PubMed Central

Spehar, Branka; Walker, Nicholas; Taylor, Richard P.

2016-01-01

In two experiments, we investigate group and individual preferences in a range of different types of patterns with varying fractal-like scaling characteristics. In Experiment 1, we used 1/f filtered grayscale images as well as their thresholded (black and white) and edges only counterparts. Separate groups of observers viewed different types of images varying in slope of their amplitude spectra. Although with each image type, the groups exhibited the “universal” pattern of preference for intermediate amplitude spectrum slopes, we identified 4 distinct sub-groups in each case. Sub-group 1 exhibited a typical peak preference for intermediate amplitude spectrum slopes (“intermediate”; approx. 50%); sub-group 2 exhibited a linear increase in preference with increasing amplitude spectrum slope (“smooth”; approx. 20%), while sub-group 3 exhibited a linear decrease in preference as a function of the amplitude spectrum slope (“sharp”; approx. 20%). Sub-group 4 revealed no significant preference (“other”; approx. 10%). In Experiment 2, we extended the range of different image types and investigated preferences within the same observers. We replicate the results of our first experiment and show that individual participants exhibit stable patterns of preference across a wide range of image types. In both experiments, Q-mode factor analysis identified two principal factors that were able to explain more than 80% of interindividual variations in preference across all types of images, suggesting a highly similar dimensional structure of interindividual variations in preference for fractal-like scaling characteristics. PMID:27458365

a Predictive Model of Permeability for Fractal-Based Rough Rock Fractures during Shear

NASA Astrophysics Data System (ADS)

Huang, Na; Jiang, Yujing; Liu, Richeng; Li, Bo; Zhang, Zhenyu

This study investigates the roles of fracture roughness, normal stress and shear displacement on the fluid flow characteristics through three-dimensional (3D) self-affine fractal rock fractures, whose surfaces are generated using the modified successive random additions (SRA) algorithm. A series of numerical shear-flow tests under different normal stresses were conducted on rough rock fractures to calculate the evolutions of fracture aperture and permeability. The results show that the rough surfaces of fractal-based fractures can be described using the scaling parameter Hurst exponent (H), in which H = 3 - Df, where Df is the fractal dimension of 3D single fractures. The joint roughness coefficient (JRC) distribution of fracture profiles follows a Gauss function with a negative linear relationship between H and average JRC. The frequency curves of aperture distributions change from sharp to flat with increasing shear displacement, indicating a more anisotropic and heterogeneous flow pattern. Both the mean aperture and permeability of fracture increase with the increment of surface roughness and decrement of normal stress. At the beginning of shear, the permeability increases remarkably and then gradually becomes steady. A predictive model of permeability using the mean mechanical aperture is proposed and the validity is verified by comparisons with the experimental results reported in literature. The proposed model provides a simple method to approximate permeability of fractal-based rough rock fractures during shear using fracture aperture distribution that can be easily obtained from digitized fracture surface information.

Fractal analysis of plaque border, a novel method for the quantification of atherosclerotic plaque contour irregularity, is associated with pro-atherogenic plasma lipid profile in subjects with non-obstructive carotid stenoses.

PubMed

Moroni, Francesco; Magnoni, Marco; Vergani, Vittoria; Ammirati, Enrico; Camici, Paolo G

2018-01-01

Plaque border irregularity is a known imaging characteristic of vulnerable plaques, but its evaluation heavily relies on subjective evaluation and operator expertise. Aim of the present work is to propose a novel fractal-analysis based method for the quantification of atherosclerotic plaque border irregularity and assess its relation with cardiovascular risk factors. Forty-two asymptomatic subjects with carotid stenosis underwent ultrasound evaluation and assessment of cardiovascular risk factors. Total, low-density lipoprotein (LDL), high-density lipoprotein (HDL) plasma cholesterol and triglycerides concentrations were measured for each subject. Fractal analysis was performed in all the carotid segments affected by atherosclerosis, i.e. 147 segments. The resulting fractal dimension (FD) is a measure of irregularity of plaque profile on long axis view of the plaque. FD in the severest stenosis (main plaque FD,mFD) was 1.136±0.039. Average FD per patient (global FD,gFD) was 1.145±0.039. FD was independent of other plaque characteristics. mFD significantly correlated with plasma HDL (r = -0.367,p = 0.02) and triglycerides-to-HDL ratio (r = 0.480,p = 0.002). Fractal analysis is a novel, readily available, reproducible and inexpensive technique for the quantitative measurement of plaque irregularity. The correlation between low HDL levels and plaque FD suggests a role for HDL in the acquisition of morphologic features of plaque instability. Further studies are needed to validate the prognostic value of fractal analysis in carotid plaques evaluation.

Fractal profit landscape of the stock market.

PubMed

Grönlund, Andreas; Yi, Il Gu; Kim, Beom Jun

2012-01-01

We investigate the structure of the profit landscape obtained from the most basic, fluctuation based, trading strategy applied for the daily stock price data. The strategy is parameterized by only two variables, p and q Stocks are sold and bought if the log return is bigger than p and less than -q, respectively. Repetition of this simple strategy for a long time gives the profit defined in the underlying two-dimensional parameter space of p and q. It is revealed that the local maxima in the profit landscape are spread in the form of a fractal structure. The fractal structure implies that successful strategies are not localized to any region of the profit landscape and are neither spaced evenly throughout the profit landscape, which makes the optimization notoriously hard and hypersensitive for partial or limited information. The concrete implication of this property is demonstrated by showing that optimization of one stock for future values or other stocks renders worse profit than a strategy that ignores fluctuations, i.e., a long-term buy-and-hold strategy.

Fractal Clustering and Knowledge-driven Validation Assessment for Gene Expression Profiling.

PubMed

Wang, Lu-Yong; Balasubramanian, Ammaiappan; Chakraborty, Amit; Comaniciu, Dorin

2005-01-01

DNA microarray experiments generate a substantial amount of information about the global gene expression. Gene expression profiles can be represented as points in multi-dimensional space. It is essential to identify relevant groups of genes in biomedical research. Clustering is helpful in pattern recognition in gene expression profiles. A number of clustering techniques have been introduced. However, these traditional methods mainly utilize shape-based assumption or some distance metric to cluster the points in multi-dimension linear Euclidean space. Their results shows poor consistence with the functional annotation of genes in previous validation study. From a novel different perspective, we propose fractal clustering method to cluster genes using intrinsic (fractal) dimension from modern geometry. This method clusters points in such a way that points in the same clusters are more self-affine among themselves than to the points in other clusters. We assess this method using annotation-based validation assessment for gene clusters. It shows that this method is superior in identifying functional related gene groups than other traditional methods.

a Fractal Analysis for Net Present Value of Multi-Stage Hydraulic Fractured Horizontal Well

NASA Astrophysics Data System (ADS)

Lu, Hong-Lin; Zhang, Ji-Jun; Tan, Xiao-Hua; Li, Xiao-Ping; Zhao, Jia-Hui

Because of the low permeability, multi-stage hydraulic fractured horizontal wells (MHFHWs) occupy a dominant position among production wells in tight gas reservoir. However, net present value (NPV) estimation method for MHFHW in tight gas reservoirs often ignores the effect of heterogeneity in microscopic pore structure. Apart from that, a new fractal model is presented for NPV of MHFHW, based on the fractal expressions of formation parameters. First, with the aid of apparent permeability model, a pseudo pressure expression considering both reservoir fractal features and slippage effect is derived, contributing to establish the productivity model. Secondly, economic assessment method is built based on the fractal productivity model, in order to obtain the NPV of MHFHW. Thirdly, the type curves are illustrated and the influences of different fractal parameters are discussed. The pore fractal dimensions Df and the capillary tortuosity fractal dimensions DT have significant effects on the NPV of an MHFHW. Finally, the proposed model in this paper provides a new methodology for analyzing and predicting the NPV of an MHFHW and may be conducive to a better understanding of the optimal design of MHFHW.

Fractal and Multifractal Analysis of Human Gait

NASA Astrophysics Data System (ADS)

Muñoz-Diosdado, A.; del Río Correa, J. L.; Angulo-Brown, F.

2003-09-01

We carried out a fractal and multifractal analysis of human gait time series of young and old individuals, and adults with three illnesses that affect the march: The Parkinson's and Huntington's diseases and the amyotrophic lateral sclerosis (ALS). We obtained cumulative plots of events, the correlation function, the Hurst exponent and the Higuchi's fractal dimension of these time series and found that these fractal markers could be a factor to characterize the march, since we obtained different values of these quantities for youths and adults and they are different also for healthy and ill persons and the most anomalous values belong to ill persons. In other physiological signals there is complexity lost related with the age and the illness, in the case of the march the opposite occurs. The multifractal analysis could be also a useful tool to understand the dynamics of these and other complex systems.

Multi-Scale Fractal Analysis of Image Texture and Pattern

NASA Technical Reports Server (NTRS)

Emerson, Charles W.

1998-01-01

Fractals embody important ideas of self-similarity, in which the spatial behavior or appearance of a system is largely independent of scale. Self-similarity is defined as a property of curves or surfaces where each part is indistinguishable from the whole, or where the form of the curve or surface is invariant with respect to scale. An ideal fractal (or monofractal) curve or surface has a constant dimension over all scales, although it may not be an integer value. This is in contrast to Euclidean or topological dimensions, where discrete one, two, and three dimensions describe curves, planes, and volumes. Theoretically, if the digital numbers of a remotely sensed image resemble an ideal fractal surface, then due to the self-similarity property, the fractal dimension of the image will not vary with scale and resolution. However, most geographical phenomena are not strictly self-similar at all scales, but they can often be modeled by a stochastic fractal in which the scaling and self-similarity properties of the fractal have inexact patterns that can be described by statistics. Stochastic fractal sets relax the monofractal self-similarity assumption and measure many scales and resolutions in order to represent the varying form of a phenomenon as a function of local variables across space. In image interpretation, pattern is defined as the overall spatial form of related features, and the repetition of certain forms is a characteristic pattern found in many cultural objects and some natural features. Texture is the visual impression of coarseness or smoothness caused by the variability or uniformity of image tone or color. A potential use of fractals concerns the analysis of image texture. In these situations it is commonly observed that the degree of roughness or inexactness in an image or surface is a function of scale and not of experimental technique. The fractal dimension of remote sensing data could yield quantitative insight on the spatial complexity and information content contained within these data. A software package known as the Image Characterization and Modeling System (ICAMS) was used to explore how fractal dimension is related to surface texture and pattern. The ICAMS software was verified using simulated images of ideal fractal surfaces with specified dimensions. The fractal dimension for areas of homogeneous land cover in the vicinity of Huntsville, Alabama was measured to investigate the relationship between texture and resolution for different land covers.

The analysis of the influence of fractal structure of stimuli on fractal dynamics in fixational eye movements and EEG signal

NASA Astrophysics Data System (ADS)

Namazi, Hamidreza; Kulish, Vladimir V.; Akrami, Amin

2016-05-01

One of the major challenges in vision research is to analyze the effect of visual stimuli on human vision. However, no relationship has been yet discovered between the structure of the visual stimulus, and the structure of fixational eye movements. This study reveals the plasticity of human fixational eye movements in relation to the ‘complex’ visual stimulus. We demonstrated that the fractal temporal structure of visual dynamics shifts towards the fractal dynamics of the visual stimulus (image). The results showed that images with higher complexity (higher fractality) cause fixational eye movements with lower fractality. Considering the brain, as the main part of nervous system that is engaged in eye movements, we analyzed the governed Electroencephalogram (EEG) signal during fixation. We have found out that there is a coupling between fractality of image, EEG and fixational eye movements. The capability observed in this research can be further investigated and applied for treatment of different vision disorders.

A new numerical approximation of the fractal ordinary differential equation

NASA Astrophysics Data System (ADS)

Atangana, Abdon; Jain, Sonal

2018-02-01

The concept of fractal medium is present in several real-world problems, for instance, in the geological formation that constitutes the well-known subsurface water called aquifers. However, attention has not been quite devoted to modeling for instance, the flow of a fluid within these media. We deem it important to remind the reader that the concept of fractal derivative is not to represent the fractal sharps but to describe the movement of the fluid within these media. Since this class of ordinary differential equations is highly complex to solve analytically, we present a novel numerical scheme that allows to solve fractal ordinary differential equations. Error analysis of the method is also presented. Application of the method and numerical approximation are presented for fractal order differential equation. The stability and the convergence of the numerical schemes are investigated in detail. Also some exact solutions of fractal order differential equations are presented and finally some numerical simulations are presented.

Temporal fractals in seabird foraging behaviour: diving through the scales of time

PubMed Central

MacIntosh, Andrew J. J.; Pelletier, Laure; Chiaradia, Andre; Kato, Akiko; Ropert-Coudert, Yan

2013-01-01

Animal behaviour exhibits fractal structure in space and time. Fractal properties in animal space-use have been explored extensively under the Lévy flight foraging hypothesis, but studies of behaviour change itself through time are rarer, have typically used shorter sequences generated in the laboratory, and generally lack critical assessment of their results. We thus performed an in-depth analysis of fractal time in binary dive sequences collected via bio-logging from free-ranging little penguins (Eudyptula minor) across full-day foraging trips (216 data points; 4 orders of temporal magnitude). Results from 4 fractal methods show that dive sequences are long-range dependent and persistent across ca. 2 orders of magnitude. This fractal structure correlated with trip length and time spent underwater, but individual traits had little effect. Fractal time is a fundamental characteristic of penguin foraging behaviour, and its investigation is thus a promising avenue for research on interactions between animals and their environments. PMID:23703258

Abnormal growth kinetics of h-BN epitaxial monolayer on Ru(0001) enhanced by subsurface Ar species

NASA Astrophysics Data System (ADS)

Wei, Wei; Meng, Jie; Meng, Caixia; Ning, Yanxiao; Li, Qunxiang; Fu, Qiang; Bao, Xinhe

2018-04-01

Growth kinetics of epitaxial films often follows the diffusion-limited aggregation mechanism, which shows a "fractal-to-compact" morphological transition with increasing growth temperature or decreasing deposition flux. Here, we observe an abnormal "compact-to-fractal" morphological transition with increasing growth temperature for hexagonal boron nitride growth on the Ru(0001) surface. The unusual growth process can be explained by a reaction-limited aggregation (RLA) mechanism. Moreover, introduction of the subsurface Ar atoms has enhanced this RLA growth behavior by decreasing both reaction and diffusion barriers. Our work may shed light on the epitaxial growth of two-dimensional atomic crystals and help to control their morphology.

Most suitable mother wavelet for the analysis of fractal properties of stride interval time series via the average wavelet coefficient

PubMed Central

Zhang, Zhenwei; VanSwearingen, Jessie; Brach, Jennifer S.; Perera, Subashan

2016-01-01

Human gait is a complex interaction of many nonlinear systems and stride intervals exhibit self-similarity over long time scales that can be modeled as a fractal process. The scaling exponent represents the fractal degree and can be interpreted as a biomarker of relative diseases. The previous study showed that the average wavelet method provides the most accurate results to estimate this scaling exponent when applied to stride interval time series. The purpose of this paper is to determine the most suitable mother wavelet for the average wavelet method. This paper presents a comparative numerical analysis of sixteen mother wavelets using simulated and real fractal signals. Simulated fractal signals were generated under varying signal lengths and scaling exponents that indicate a range of physiologically conceivable fractal signals. The five candidates were chosen due to their good performance on the mean square error test for both short and long signals. Next, we comparatively analyzed these five mother wavelets for physiologically relevant stride time series lengths. Our analysis showed that the symlet 2 mother wavelet provides a low mean square error and low variance for long time intervals and relatively low errors for short signal lengths. It can be considered as the most suitable mother function without the burden of considering the signal length. PMID:27960102

Heterogeneity of Glucose Metabolism in Esophageal Cancer Measured by Fractal Analysis of Fluorodeoxyglucose Positron Emission Tomography Image: Correlation between Metabolic Heterogeneity and Survival.

PubMed

Tochigi, Toru; Shuto, Kiyohiko; Kono, Tsuguaki; Ohira, Gaku; Tohma, Takayuki; Gunji, Hisashi; Hayano, Koichi; Narushima, Kazuo; Fujishiro, Takeshi; Hanaoka, Toshiharu; Akutsu, Yasunori; Okazumi, Shinichi; Matsubara, Hisahiro

2017-01-01

Intratumoral heterogeneity is a well-recognized characteristic feature of cancer. The purpose of this study is to assess the heterogeneity of the intratumoral glucose metabolism using fractal analysis, and evaluate its prognostic value in patients with esophageal squamous cell carcinoma (ESCC). 18F-fluorodeoxyglucose positron emission tomography (FDG-PET) studies of 79 patients who received curative surgery were evaluated. FDG-PET images were analyzed using fractal analysis software, where differential box-counting method was employed to calculate the fractal dimension (FD) of the tumor lesion. Maximum standardized uptake value (SUVmax) and FD were compared with overall survival (OS). The median SUVmax and FD of ESCCs in this cohort were 13.8 and 1.95, respectively. In univariate analysis performed using Cox's proportional hazard model, T stage and FD showed significant associations with OS (p = 0.04, p < 0.0001, respectively), while SUVmax did not (p = 0.1). In Kaplan-Meier analysis, the low FD tumor (<1.95) showed a significant association with favorable OS (p < 0.0001). In wthe multivariate analysis among TNM staging, serum tumor markers, FD, and SUVmax, the FD was identified as the only independent prognostic factor for OS (p = 0.0006; hazards ratio 0.251, 95% CI 0.104-0.562). Metabolic heterogeneity measured by fractal analysis can be a novel imaging biomarker for survival in patients with ESCC. © 2016 S. Karger AG, Basel.

Colliding with the Speed of Light, Using Low-Energy Photon-Photon Collision Study the Nature of Matter and the universe

NASA Astrophysics Data System (ADS)

Zhang, Meggie

2013-03-01

Our research discovered logical inconsistence in physics and mathematics. Through reviewing the entire history of physics and mathematics we gained new understanding about our earlier assumptions, which led to a new interpretation of the wave function and quantum physics. We found the existing experimental data supported a 4-dimensional fractal structure of matter and the universe, we found the formation of wave, matter and the universe through the same process started from a single particle, and the process itself is a fractal that contributed to the diversity of matter. We also found physical evidence supporting a not-continuous fractal space structure. The new understanding also led to a reinterpretation of nuclear collision theories, based on this we succeeded a room-temperature low-energy photon-photon collision (RT-LE-PPC), this method allowed us to observe a topological disconnected fractal structure and succeeded a simulation of the formation of matter and the universe which provided evidences for the nature of light and matter and led to a quantum structure interpretation, and we found the formation of the universe started from two particles. However this work cannot be understood with current physics theories due to the logical problems in the current physics theories.

Lévy processes on a generalized fractal comb

NASA Astrophysics Data System (ADS)

Sandev, Trifce; Iomin, Alexander; Méndez, Vicenç

2016-09-01

Comb geometry, constituted of a backbone and fingers, is one of the most simple paradigm of a two-dimensional structure, where anomalous diffusion can be realized in the framework of Markov processes. However, the intrinsic properties of the structure can destroy this Markovian transport. These effects can be described by the memory and spatial kernels. In particular, the fractal structure of the fingers, which is controlled by the spatial kernel in both the real and the Fourier spaces, leads to the Lévy processes (Lévy flights) and superdiffusion. This generalization of the fractional diffusion is described by the Riesz space fractional derivative. In the framework of this generalized fractal comb model, Lévy processes are considered, and exact solutions for the probability distribution functions are obtained in terms of the Fox H-function for a variety of the memory kernels, and the rate of the superdiffusive spreading is studied by calculating the fractional moments. For a special form of the memory kernels, we also observed a competition between long rests and long jumps. Finally, we considered the fractal structure of the fingers controlled by a Weierstrass function, which leads to the power-law kernel in the Fourier space. This is a special case, when the second moment exists for superdiffusion in this competition between long rests and long jumps.

Surface layer protein characterization by small angle x-ray scattering and a fractal mean force concept: from protein structure to nanodisk assemblies.

PubMed

Horejs, Christine; Pum, Dietmar; Sleytr, Uwe B; Peterlik, Herwig; Jungbauer, Alois; Tscheliessnig, Rupert

2010-11-07

Surface layers (S-layers) are the most commonly observed cell surface structure of prokaryotic organisms. They are made up of proteins that spontaneously self-assemble into functional crystalline lattices in solution, on various solid surfaces, and interfaces. While classical experimental techniques failed to recover a complete structural model of an unmodified S-layer protein, small angle x-ray scattering (SAXS) provides an opportunity to study the structure of S-layer monomers in solution and of self-assembled two-dimensional sheets. For the protein under investigation we recently suggested an atomistic structural model by the use of molecular dynamics simulations. This structural model is now refined on the basis of SAXS data together with a fractal assembly approach. Here we show that a nondiluted critical system of proteins, which crystallize into monomolecular structures, might be analyzed by SAXS if protein-protein interactions are taken into account by relating a fractal local density distribution to a fractal local mean potential, which has to fulfill the Poisson equation. The present work demonstrates an important step into the elucidation of the structure of S-layers and offers a tool to analyze the structure of self-assembling systems in solution by means of SAXS and computer simulations.

Surface layer protein characterization by small angle x-ray scattering and a fractal mean force concept: From protein structure to nanodisk assemblies

NASA Astrophysics Data System (ADS)

Horejs, Christine; Pum, Dietmar; Sleytr, Uwe B.; Peterlik, Herwig; Jungbauer, Alois; Tscheliessnig, Rupert

2010-11-01

Surface layers (S-layers) are the most commonly observed cell surface structure of prokaryotic organisms. They are made up of proteins that spontaneously self-assemble into functional crystalline lattices in solution, on various solid surfaces, and interfaces. While classical experimental techniques failed to recover a complete structural model of an unmodified S-layer protein, small angle x-ray scattering (SAXS) provides an opportunity to study the structure of S-layer monomers in solution and of self-assembled two-dimensional sheets. For the protein under investigation we recently suggested an atomistic structural model by the use of molecular dynamics simulations. This structural model is now refined on the basis of SAXS data together with a fractal assembly approach. Here we show that a nondiluted critical system of proteins, which crystallize into monomolecular structures, might be analyzed by SAXS if protein-protein interactions are taken into account by relating a fractal local density distribution to a fractal local mean potential, which has to fulfill the Poisson equation. The present work demonstrates an important step into the elucidation of the structure of S-layers and offers a tool to analyze the structure of self-assembling systems in solution by means of SAXS and computer simulations.

Surface layer protein characterization by small angle x-ray scattering and a fractal mean force concept: From protein structure to nanodisk assemblies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Horejs, Christine; Pum, Dietmar; Sleytr, Uwe B.

2010-11-07

Surface layers (S-layers) are the most commonly observed cell surface structure of prokaryotic organisms. They are made up of proteins that spontaneously self-assemble into functional crystalline lattices in solution, on various solid surfaces, and interfaces. While classical experimental techniques failed to recover a complete structural model of an unmodified S-layer protein, small angle x-ray scattering (SAXS) provides an opportunity to study the structure of S-layer monomers in solution and of self-assembled two-dimensional sheets. For the protein under investigation we recently suggested an atomistic structural model by the use of molecular dynamics simulations. This structural model is now refined on themore » basis of SAXS data together with a fractal assembly approach. Here we show that a nondiluted critical system of proteins, which crystallize into monomolecular structures, might be analyzed by SAXS if protein-protein interactions are taken into account by relating a fractal local density distribution to a fractal local mean potential, which has to fulfill the Poisson equation. The present work demonstrates an important step into the elucidation of the structure of S-layers and offers a tool to analyze the structure of self-assembling systems in solution by means of SAXS and computer simulations.« less

Nonlinear dynamic mechanism of vocal tremor from voice analysis and model simulations

NASA Astrophysics Data System (ADS)

Zhang, Yu; Jiang, Jack J.

2008-09-01

Nonlinear dynamic analysis and model simulations are used to study the nonlinear dynamic characteristics of vocal folds with vocal tremor, which can typically be characterized by low-frequency modulation and aperiodicity. Tremor voices from patients with disorders such as paresis, Parkinson's disease, hyperfunction, and adductor spasmodic dysphonia show low-dimensional characteristics, differing from random noise. Correlation dimension analysis statistically distinguishes tremor voices from normal voices. Furthermore, a nonlinear tremor model is proposed to study the vibrations of the vocal folds with vocal tremor. Fractal dimensions and positive Lyapunov exponents demonstrate the evidence of chaos in the tremor model, where amplitude and frequency play important roles in governing vocal fold dynamics. Nonlinear dynamic voice analysis and vocal fold modeling may provide a useful set of tools for understanding the dynamic mechanism of vocal tremor in patients with laryngeal diseases.

Tree growth visualization

Treesearch

L. Linsen; B.J. Karis; E.G. McPherson; B. Hamann

2005-01-01

In computer graphics, models describing the fractal branching structure of trees typically exploit the modularity of tree structures. The models are based on local production rules, which are applied iteratively and simultaneously to create a complex branching system. The objective is to generate three-dimensional scenes of often many realistic- looking and non-...

Down syndrome's brain dynamics: analysis of fractality in resting state.

PubMed

Hemmati, Sahel; Ahmadlou, Mehran; Gharib, Masoud; Vameghi, Roshanak; Sajedi, Firoozeh

2013-08-01

To the best knowledge of the authors there is no study on nonlinear brain dynamics of down syndrome (DS) patients, whereas brain is a highly complex and nonlinear system. In this study, fractal dimension of EEG, as a key characteristic of brain dynamics, showing irregularity and complexity of brain dynamics, was used for evaluation of the dynamical changes in the DS brain. The results showed higher fractality of the DS brain in almost all regions compared to the normal brain, which indicates less centrality and higher irregular or random functioning of the DS brain regions. Also, laterality analysis of the frontal lobe showed that the normal brain had a right frontal laterality of complexity whereas the DS brain had an inverse pattern (left frontal laterality). Furthermore, the high accuracy of 95.8 % obtained by enhanced probabilistic neural network classifier showed the potential of nonlinear dynamic analysis of the brain for diagnosis of DS patients. Moreover, the results showed that the higher EEG fractality in DS is associated with the higher fractality in the low frequencies (delta and theta), in broad regions of the brain, and the high frequencies (beta and gamma), majorly in the frontal regions.

On fractality and chaos in Moroccan family business stock returns and volatility

NASA Astrophysics Data System (ADS)

Lahmiri, Salim

2017-05-01

The purpose of this study is to examine existence of fractality and chaos in returns and volatilities of family business companies listed on the Casablanca Stock Exchange (CSE) in Morocco, and also in returns and volatility of the CSE market index. Detrended fluctuation analysis based Hurst exponent and fractionally integrated generalized autoregressive conditional heteroskedasticity (FIGARCH) model are used to quantify fractality in returns and volatility time series respectively. Besides, the largest Lyapunov exponent is employed to quantify chaos in both time series. The empirical results from sixteen family business companies follow. For return series, fractality analysis show that most of family business returns listed on CSE exhibit anti-persistent dynamics, whilst market returns have persistent dynamics. Besides, chaos tests show that business family stock returns are not chaotic while market returns exhibit evidence of chaotic behaviour. For volatility series, fractality analysis shows that most of family business stocks and market index exhibit long memory in volatility. Furthermore, results from chaos tests show that volatility of family business returns is not chaotic, whilst volatility of market index is chaotic. These results may help understanding irregularities patterns in Moroccan family business stock returns and volatility, and how they are different from market dynamics.

Fractal Analysis of Rock Joint Profiles

NASA Astrophysics Data System (ADS)

Audy, Ondřej; Ficker, Tomáš

2017-10-01

Surface reliefs of rock joints are analyzed in geotechnics when shear strength of rocky slopes is estimated. The rock joint profiles actually are self-affine fractal curves and computations of their fractal dimensions require special methods. Many papers devoted to the fractal properties of these profiles were published in the past but only a few of those papers employed a convenient computational method that would have guaranteed a sound value of that dimension. As a consequence, anomalously low dimensions were presented. This contribution deals with two computational modifications that lead to sound fractal dimensions of the self-affine rock joint profiles. These are the modified box-counting method and the modified yard-stick method sometimes called the compass method. Both these methods are frequently applied to self-similar fractal curves but the self-affine profile curves due to their self-affine nature require modified computational procedures implemented in computer programs.

The fractal heart — embracing mathematics in the cardiology clinic

PubMed Central

Captur, Gabriella; Karperien, Audrey L.; Hughes, Alun D.; Francis, Darrel P.; Moon, James C.

2017-01-01

For clinicians grappling with quantifying the complex spatial and temporal patterns of cardiac structure and function (such as myocardial trabeculae, coronary microvascular anatomy, tissue perfusion, myocyte histology, electrical conduction, heart rate, and blood-pressure variability), fractal analysis is a powerful, but still underused, mathematical tool. In this Perspectives article, we explain some fundamental principles of fractal geometry and place it in a familiar medical setting. We summarize studies in the cardiovascular sciences in which fractal methods have successfully been used to investigate disease mechanisms, and suggest potential future clinical roles in cardiac imaging and time series measurements. We believe that clinical researchers can deploy innovative fractal solutions to common cardiac problems that might ultimately translate into advancements for patient care. PMID:27708281

Detection of crossover time scales in multifractal detrended fluctuation analysis

NASA Astrophysics Data System (ADS)

Ge, Erjia; Leung, Yee

2013-04-01

Fractal is employed in this paper as a scale-based method for the identification of the scaling behavior of time series. Many spatial and temporal processes exhibiting complex multi(mono)-scaling behaviors are fractals. One of the important concepts in fractals is crossover time scale(s) that separates distinct regimes having different fractal scaling behaviors. A common method is multifractal detrended fluctuation analysis (MF-DFA). The detection of crossover time scale(s) is, however, relatively subjective since it has been made without rigorous statistical procedures and has generally been determined by eye balling or subjective observation. Crossover time scales such determined may be spurious and problematic. It may not reflect the genuine underlying scaling behavior of a time series. The purpose of this paper is to propose a statistical procedure to model complex fractal scaling behaviors and reliably identify the crossover time scales under MF-DFA. The scaling-identification regression model, grounded on a solid statistical foundation, is first proposed to describe multi-scaling behaviors of fractals. Through the regression analysis and statistical inference, we can (1) identify the crossover time scales that cannot be detected by eye-balling observation, (2) determine the number and locations of the genuine crossover time scales, (3) give confidence intervals for the crossover time scales, and (4) establish the statistically significant regression model depicting the underlying scaling behavior of a time series. To substantive our argument, the regression model is applied to analyze the multi-scaling behaviors of avian-influenza outbreaks, water consumption, daily mean temperature, and rainfall of Hong Kong. Through the proposed model, we can have a deeper understanding of fractals in general and a statistical approach to identify multi-scaling behavior under MF-DFA in particular.

Design and analysis microstrip dipole using fractal Koch for 433 MHz applications

NASA Astrophysics Data System (ADS)

Zulfin, M.; Rambe, A. H.; Budi, B.

2018-02-01

This paper discussed the dipole microstrip antenna design using fractal Koch for working on frequency of 433 MHz. The fractal Koch was used to reduce the size of the microstrip antenna. The smaller the antenna size, the lighter the equipment. AWR simulator was employed to evaluate antenna parameters such as return loss, gain and radiation pattern. The antenna was designed on a FR4 substrate with relative permittivity of 4.4 and thickness 1.6 mm. The result shows that the fractal Koch reduce antenna size about 41.2% and decrease return loss about 30%.

The influence of the growth conditions of the plague microbe vaccine strain colonies on the fractal dimension of biospeckles

NASA Astrophysics Data System (ADS)

Ul'yanov, A. S.; Lyapina, A. M.; Ulianova, O. V.; Fedorova, V. A.; Uianov, S. S.

2011-04-01

Specific statistical characteristics of biospeckles, emerging under the diffraction of coherent beams on the bacterial colonies, are studied. The dependence of the fractal dimensions of biospeckles on the conditions of both illumination and growth of the colonies is studied theoretically and experimentally. Particular attention is paid to the fractal properties of biospeckles, emerging under the scattering of light by the colonies of the vaccinal strain of the plague microbe. The possibility in principle to classify the colonies of Yersinia pestis EV NIIEG using the fractal dimension analysis is demonstrated.

Fat fractal scaling of drainage networks from a random spatial network model

USGS Publications Warehouse

Karlinger, Michael R.; Troutman, Brent M.

1992-01-01

An alternative quantification of the scaling properties of river channel networks is explored using a spatial network model. Whereas scaling descriptions of drainage networks previously have been presented using a fractal analysis primarily of the channel lengths, we illustrate the scaling of the surface area of the channels defining the network pattern with an exponent which is independent of the fractal dimension but not of the fractal nature of the network. The methodology presented is a fat fractal analysis in which the drainage basin minus the channel area is considered the fat fractal. Random channel networks within a fixed basin area are generated on grids of different scales. The sample channel networks generated by the model have a common outlet of fixed width and a rule of upstream channel narrowing specified by a diameter branching exponent using hydraulic and geomorphologic principles. Scaling exponents are computed for each sample network on a given grid size and are regressed against network magnitude. Results indicate that the size of the exponents are related to magnitude of the networks and generally decrease as network magnitude increases. Cases showing differences in scaling exponents with like magnitudes suggest a direction of future work regarding other topologic basin characteristics as potential explanatory variables.

Threshold of coexistence and critical behavior of a predator-prey stochastic model in a fractal landscape

NASA Astrophysics Data System (ADS)

Argolo, C.; Barros, P.; Tomé, T.; Arashiro, E.; Gleria, Iram; Lyra, M. L.

2016-08-01

We investigate a stochastic lattice model describing a predator-prey system in a fractal scale-free landscape, mimicked by the fractal Sierpinski carpet. We determine the threshold of species coexistence, that is, the critical phase boundary related to the transition between an active state, where both species coexist and an absorbing state where one of the species is extinct. We show that the predators must live longer in order to persist in a fractal habitat. We further performed a finite-size scaling analysis in the vicinity of the absorbing-state phase transition to compute a set of stationary and dynamical critical exponents. Our results indicate that the transition belongs to the directed percolation universality class exhibited by the usual contact process model on the same fractal landscape.

The fractal architecture of cytoplasmic organization: scaling, kinetics and emergence in metabolic networks.

PubMed

Aon, Miguel Antonio; O'Rourke, Brian; Cortassa, Sonia

2004-01-01

In this work, we highlight the links between fractals and scaling in cells and explore the kinetic consequences for biochemical reactions operating in fractal media. Based on the proposal that the cytoskeletal architecture is organized as a percolation lattice, with clusters emerging as fractal forms, the analysis of kinetics in percolation clusters is especially emphasized. A key consequence of this spatiotemporal cytoplasmic organization is that enzyme reactions following Michaelis-Menten or allosteric type kinetics exhibit higher rates in fractal media (for short times and at lower substrate concentrations) at the percolation threshold than in Euclidean media. As a result, considerably faster and higher amplification of enzymatic activity is obtained. Finally, we describe some of the properties bestowed by cytoskeletal organization and dynamics on metabolic networks.

Exsanguinated blood volume estimation using fractal analysis of digital images.

PubMed

Sant, Sonia P; Fairgrieve, Scott I

2012-05-01

The estimation of bloodstain volume using fractal analysis of digital images of passive blood stains is presented. Binary digital photos of bloodstains of known volumes (ranging from 1 to 7 mL), dispersed in a defined area, were subjected to image analysis using FracLac V. 2.0 for ImageJ. The box-counting method was used to generate a fractal dimension for each trial. A positive correlation between the generated fractal number and the volume of blood was found (R(2) = 0.99). Regression equations were produced to estimate the volume of blood in blind trials. An error rate ranging from 78% for 1 mL to 7% for 6 mL demonstrated that as the volume increases so does the accuracy of the volume estimation. This method used in the preliminary study proved that bloodstain patterns may be deconstructed into mathematical parameters, thus removing the subjective element inherent in other methods of volume estimation. © 2012 American Academy of Forensic Sciences.

Fractal scaling of apparent soil moisture estimated from vertical planes of Vertisol pit images

NASA Astrophysics Data System (ADS)

Cumbrera, Ramiro; Tarquis, Ana M.; Gascó, Gabriel; Millán, Humberto

2012-07-01

SummaryImage analysis could be a useful tool for investigating the spatial patterns of apparent soil moisture at multiple resolutions. The objectives of the present work were (i) to define apparent soil moisture patterns from vertical planes of Vertisol pit images and (ii) to describe the scaling of apparent soil moisture distribution using fractal parameters. Twelve soil pits (0.70 m long × 0.60 m width × 0.30 m depth) were excavated on a bare Mazic Pellic Vertisol. Six of them were excavated in April/2011 and six pits were established in May/2011 after 3 days of a moderate rainfall event. Digital photographs were taken from each Vertisol pit using a Kodak™ digital camera. The mean image size was 1600 × 945 pixels with one physical pixel ≈373 μm of the photographed soil pit. Each soil image was analyzed using two fractal scaling exponents, box counting (capacity) dimension (DBC) and interface fractal dimension (Di), and three prefractal scaling coefficients, the total number of boxes intercepting the foreground pattern at a unit scale (A), fractal lacunarity at the unit scale (Λ1) and Shannon entropy at the unit scale (S1). All the scaling parameters identified significant differences between both sets of spatial patterns. Fractal lacunarity was the best discriminator between apparent soil moisture patterns. Soil image interpretation with fractal exponents and prefractal coefficients can be incorporated within a site-specific agriculture toolbox. While fractal exponents convey information on space filling characteristics of the pattern, prefractal coefficients represent the investigated soil property as seen through a higher resolution microscope. In spite of some computational and practical limitations, image analysis of apparent soil moisture patterns could be used in connection with traditional soil moisture sampling, which always renders punctual estimates.

Analysis of fractal dimensions of rat bones from film and digital images

NASA Technical Reports Server (NTRS)

Pornprasertsuk, S.; Ludlow, J. B.; Webber, R. L.; Tyndall, D. A.; Yamauchi, M.

2001-01-01

OBJECTIVES: (1) To compare the effect of two different intra-oral image receptors on estimates of fractal dimension; and (2) to determine the variations in fractal dimensions between the femur, tibia and humerus of the rat and between their proximal, middle and distal regions. METHODS: The left femur, tibia and humerus from 24 4-6-month-old Sprague-Dawley rats were radiographed using intra-oral film and a charge-coupled device (CCD). Films were digitized at a pixel density comparable to the CCD using a flat-bed scanner. Square regions of interest were selected from proximal, middle, and distal regions of each bone. Fractal dimensions were estimated from the slope of regression lines fitted to plots of log power against log spatial frequency. RESULTS: The fractal dimensions estimates from digitized films were significantly greater than those produced from the CCD (P=0.0008). Estimated fractal dimensions of three types of bone were not significantly different (P=0.0544); however, the three regions of bones were significantly different (P=0.0239). The fractal dimensions estimated from radiographs of the proximal and distal regions of the bones were lower than comparable estimates obtained from the middle region. CONCLUSIONS: Different types of image receptors significantly affect estimates of fractal dimension. There was no difference in the fractal dimensions of the different bones but the three regions differed significantly.

Fractals for Geoengineering

NASA Astrophysics Data System (ADS)

Oleshko, Klaudia; de Jesús Correa López, María; Romero, Alejandro; Ramírez, Victor; Pérez, Olga

2016-04-01

The effectiveness of fractal toolbox to capture the scaling or fractal probability distribution, and simply fractal statistics of main hydrocarbon reservoir attributes, was highlighted by Mandelbrot (1995) and confirmed by several researchers (Zhao et al., 2015). Notwithstanding, after more than twenty years, it's still common the opinion that fractals are not useful for the petroleum engineers and especially for Geoengineering (Corbett, 2012). In spite of this negative background, we have successfully applied the fractal and multifractal techniques to our project entitled "Petroleum Reservoir as a Fractal Reactor" (2013 up to now). The distinguishable feature of Fractal Reservoir is the irregular shapes and rough pore/solid distributions (Siler, 2007), observed across a broad range of scales (from SEM to seismic). At the beginning, we have accomplished the detailed analysis of Nelson and Kibler (2003) Catalog of Porosity and Permeability, created for the core plugs of siliciclastic rocks (around ten thousand data were compared). We enriched this Catalog by more than two thousand data extracted from the last ten years publications on PoroPerm (Corbett, 2012) in carbonates deposits, as well as by our own data from one of the PEMEX, Mexico, oil fields. The strong power law scaling behavior was documented for the major part of these data from the geological deposits of contrasting genesis. Based on these results and taking into account the basic principles and models of the Physics of Fractals, introduced by Per Back and Kan Chen (1989), we have developed new software (Muukíl Kaab), useful to process the multiscale geological and geophysical information and to integrate the static geological and petrophysical reservoir models to dynamic ones. The new type of fractal numerical model with dynamical power law relations among the shapes and sizes of mesh' cells was designed and calibrated in the studied area. The statistically sound power law relations were established for the reservoir' hydraulic units distribution in space and time, as well as for the corresponding well testing data. References: 1. Mandelbrot, B., 1995. Foreword to Fractals in Petroleum Geology and Earth Processes, Edited by: Christopher C. Barton and Paul R. La Pointe, Plenum Press, New York: vii-xii. 2. Jin-Zhou Zhao, Cui-Cui Sheng, Yong_Ming Li, and Shun-Chu Li, 2015. A Mathematical Model for the Analysis of the Pressure Transient Response of Fluid Flow in Fractal Reservoir. J. of Chemistry, ID 596597, 8p. 3. Siler, T. , 2007. Fractal Reactor. International Conference Series on Emerging Nuclear Energy Systems 4. Corbett, P. W. M., 2012. The Role of Geoengineering in field development. INTECH, Chapter 8: 181- 198. 5. Nelson, P.H. and J. Kibler, 2003. A Catalog of Porosity and Permeability from core plugs in siliciclastic rocks. U.S. Geological Survey. 6. Per Bak and Kan Chen, 1989. The Physics of Fractals. Physica D 38: 5-12.

Spatiotemporal Characterization of a Fibrin Clot Using Quantitative Phase Imaging

PubMed Central

Gannavarpu, Rajshekhar; Bhaduri, Basanta; Tangella, Krishnarao; Popescu, Gabriel

2014-01-01

Studying the dynamics of fibrin clot formation and its morphology is an important problem in biology and has significant impact for several scientific and clinical applications. We present a label-free technique based on quantitative phase imaging to address this problem. Using quantitative phase information, we characterized fibrin polymerization in real-time and present a mathematical model describing the transition from liquid to gel state. By exploiting the inherent optical sectioning capability of our instrument, we measured the three-dimensional structure of the fibrin clot. From this data, we evaluated the fractal nature of the fibrin network and extracted the fractal dimension. Our non-invasive and speckle-free approach analyzes the clotting process without the need for external contrast agents. PMID:25386701

Predicting age from cortical structure across the lifespan.

PubMed

Madan, Christopher R; Kensinger, Elizabeth A

2018-03-01

Despite interindividual differences in cortical structure, cross-sectional and longitudinal studies have demonstrated a large degree of population-level consistency in age-related differences in brain morphology. This study assessed how accurately an individual's age could be predicted by estimates of cortical morphology, comparing a variety of structural measures, including thickness, gyrification and fractal dimensionality. Structural measures were calculated across up to seven different parcellation approaches, ranging from one region to 1000 regions. The age prediction framework was trained using morphological measures obtained from T1-weighted MRI volumes collected from multiple sites, yielding a training dataset of 1056 healthy adults, aged 18-97. Age predictions were calculated using a machine-learning approach that incorporated nonlinear differences over the lifespan. In two independent, held-out test samples, age predictions had a median error of 6-7 years. Age predictions were best when using a combination of cortical metrics, both thickness and fractal dimensionality. Overall, the results reveal that age-related differences in brain structure are systematic enough to enable reliable age prediction based on metrics of cortical morphology. © 2018 Federation of European Neuroscience Societies and John Wiley & Sons Ltd.

Chaotic interactions of self-replicating RNA.

PubMed

Forst, C V

1996-03-01

A general system of high-order differential equations describing complex dynamics of replicating biomolecules is given. Symmetry relations and coordinate transformations of general replication systems leading to topologically equivalent systems are derived. Three chaotic attractors observed in Lotka-Volterra equations of dimension n = 3 are shown to represent three cross-sections of one and the same chaotic regime. Also a fractal torus in a generalized three-dimensional Lotka-Volterra Model has been linked to one of the chaotic attractors. The strange attractors are studied in the equivalent four-dimensional catalytic replicator network. The fractal torus has been examined in adapted Lotka-Volterra equations. Analytic expressions are derived for the Lyapunov exponents of the flow in the replicator system. Lyapunov spectra for different pathways into chaos has been calculated. In the generalized Lotka-Volterra system a second inner rest point--coexisting with (quasi)-periodic orbits--can be observed; with an abundance of different bifurcations. Pathways from chaotic tori, via quasi-periodic tori, via limit cycles, via multi-periodic orbits--emerging out of periodic doubling bifurcations--to "simple" chaotic attractors can be found.

Domain-wall excitations in the two-dimensional Ising spin glass

NASA Astrophysics Data System (ADS)

Khoshbakht, Hamid; Weigel, Martin

2018-02-01

The Ising spin glass in two dimensions exhibits rich behavior with subtle differences in the scaling for different coupling distributions. We use recently developed mappings to graph-theoretic problems together with highly efficient implementations of combinatorial optimization algorithms to determine exact ground states for systems on square lattices with up to 10 000 ×10 000 spins. While these mappings only work for planar graphs, for example for systems with periodic boundary conditions in at most one direction, we suggest here an iterative windowing technique that allows one to determine ground states for fully periodic samples up to sizes similar to those for the open-periodic case. Based on these techniques, a large number of disorder samples are used together with a careful finite-size scaling analysis to determine the stiffness exponents and domain-wall fractal dimensions with unprecedented accuracy, our best estimates being θ =-0.2793 (3 ) and df=1.273 19 (9 ) for Gaussian couplings. For bimodal disorder, a new uniform sampling algorithm allows us to study the domain-wall fractal dimension, finding df=1.279 (2 ) . Additionally, we also investigate the distributions of ground-state energies, of domain-wall energies, and domain-wall lengths.

Entrainment to a real time fractal visual stimulus modulates fractal gait dynamics.

PubMed

Rhea, Christopher K; Kiefer, Adam W; D'Andrea, Susan E; Warren, William H; Aaron, Roy K

2014-08-01

Fractal patterns characterize healthy biological systems and are considered to reflect the ability of the system to adapt to varying environmental conditions. Previous research has shown that fractal patterns in gait are altered following natural aging or disease, and this has potential negative consequences for gait adaptability that can lead to increased risk of injury. However, the flexibility of a healthy neurological system to exhibit different fractal patterns in gait has yet to be explored, and this is a necessary step toward understanding human locomotor control. Fifteen participants walked for 15min on a treadmill, either in the absence of a visual stimulus or while they attempted to couple the timing of their gait with a visual metronome that exhibited a persistent fractal pattern (contained long-range correlations) or a random pattern (contained no long-range correlations). The stride-to-stride intervals of the participants were recorded via analog foot pressure switches and submitted to detrended fluctuation analysis (DFA) to determine if the fractal patterns during the visual metronome conditions differed from the baseline (no metronome) condition. DFA α in the baseline condition was 0.77±0.09. The fractal patterns in the stride-to-stride intervals were significantly altered when walking to the fractal metronome (DFA α=0.87±0.06) and to the random metronome (DFA α=0.61±0.10) (both p<.05 when compared to the baseline condition), indicating that a global change in gait dynamics was observed. A variety of strategies were identified at the local level with a cross-correlation analysis, indicating that local behavior did not account for the consistent global changes. Collectively, the results show that a gait dynamics can be shifted in a prescribed manner using a visual stimulus and the shift appears to be a global phenomenon. Copyright © 2014 Elsevier B.V. All rights reserved.

Monitoring the soil degradation by Metastatistical Analysis

NASA Astrophysics Data System (ADS)

Oleschko, K.; Gaona, C.; Tarquis, A.

2009-04-01

The effectiveness of fractal toolbox to capture the critical behavior of soil structural patterns during the chemical and physical degradation was documented by our numerous experiments (Oleschko et al., 2008 a; 2008 b). The spatio-temporal dynamics of these patterns was measured and mapped with high precision in terms of fractal descriptors. All tested fractal techniques were able to detect the statistically significant differences in structure between the perfect spongy and massive patterns of uncultivated and sodium-saline agricultural soils, respectively. For instance, the Hurst exponent, extracted from the Chernozeḿ micromorphological images and from the time series of its physical and mechanical properties measured in situ, detected the roughness decrease (and therefore the increase in H - from 0.17 to 0.30 for images) derived from the loss of original structure complexity. The combined use of different fractal descriptors brings statistical precision into the quantification of natural system degradation and provides a means for objective soil structure comparison (Oleschko et al., 2000). The ability of fractal parameters to capture critical behavior and phase transition was documented for different contrasting situations, including from Andosols deforestation and erosion, to Vertisols high fructuring and consolidation. The Hurst exponent is used to measure the type of persistence and degree of complexity of structure dynamics. We conclude that there is an urgent need to select and adopt a standardized toolbox for fractal analysis and complexity measures in Earth Sciences. We propose to use the second-order (meta-) statistics as subtle measures of complexity (Atmanspacher et al., 1997). The high degree of correlation was documented between the fractal and high-order statistical descriptors (four central moments of stochastic variable distribution) used to the system heterogeneity and variability analysis. We proposed to call this combined fractal/statistical toolbox Metastatistical Analysis and recommend it to the projects directed to soil degradation monitoring. References: 1. Oleschko, K., B.S. Figueroa, M.E. Miranda, M.A. Vuelvas and E.R. Solleiro, Soil & Till. Res. 55, 43 (2000). 2. Oleschko, K., Korvin, G., Figueroa S. B., Vuelvas, M.A., Balankin, A., Flores L., Carreño, D. Fractal radar scattering from soil. Physical Review E.67, 041403, 2003. 3. Zamora-Castro S., Oleschko, K. Flores, L., Ventura, E. Jr., Parrot, J.-F., 2008. Fractal mapping of pore and solids attributes. Vadose Zone Journal, v. 7, Issue2: 473-492. 4. Oleschko, K., Korvin, G., Muñoz, A., Velásquez, J., Miranda, M.E., Carreon, D., Flores, L., Martínez, M., Velásquez-Valle, M., Brambilla, F., Parrot, J.-F. Ronquillo, G., 2008. Fractal mapping of soil moisture content from remote sensed multi-scale data. Nonlinear Proceses in Geophysics Journal, 15: 711-725. 5. Atmanspacher, H., Räth, Ch., Wiedenmann, G., 1997. Statistics and meta-statistics in the concept of complexity. Physica A, 234: 819-829.

Exhaled Aerosol Pattern Discloses Lung Structural Abnormality: A Sensitivity Study Using Computational Modeling and Fractal Analysis

PubMed Central

Xi, Jinxiang; Si, Xiuhua A.; Kim, JongWon; Mckee, Edward; Lin, En-Bing

2014-01-01

Background Exhaled aerosol patterns, also called aerosol fingerprints, provide clues to the health of the lung and can be used to detect disease-modified airway structures. The key is how to decode the exhaled aerosol fingerprints and retrieve the lung structural information for a non-invasive identification of respiratory diseases. Objective and Methods In this study, a CFD-fractal analysis method was developed to quantify exhaled aerosol fingerprints and applied it to one benign and three malign conditions: a tracheal carina tumor, a bronchial tumor, and asthma. Respirations of tracer aerosols of 1 µm at a flow rate of 30 L/min were simulated, with exhaled distributions recorded at the mouth. Large eddy simulations and a Lagrangian tracking approach were used to simulate respiratory airflows and aerosol dynamics. Aerosol morphometric measures such as concentration disparity, spatial distributions, and fractal analysis were applied to distinguish various exhaled aerosol patterns. Findings Utilizing physiology-based modeling, we demonstrated substantial differences in exhaled aerosol distributions among normal and pathological airways, which were suggestive of the disease location and extent. With fractal analysis, we also demonstrated that exhaled aerosol patterns exhibited fractal behavior in both the entire image and selected regions of interest. Each exhaled aerosol fingerprint exhibited distinct pattern parameters such as spatial probability, fractal dimension, lacunarity, and multifractal spectrum. Furthermore, a correlation of the diseased location and exhaled aerosol spatial distribution was established for asthma. Conclusion Aerosol-fingerprint-based breath tests disclose clues about the site and severity of lung diseases and appear to be sensitive enough to be a practical tool for diagnosis and prognosis of respiratory diseases with structural abnormalities. PMID:25105680

Detailed Analysis of the Interoccurrence Time Statistics in Seismic Activity

NASA Astrophysics Data System (ADS)

Tanaka, Hiroki; Aizawa, Yoji

2017-02-01

The interoccurrence time statistics of seismiciry is studied theoretically as well as numerically by taking into account the conditional probability and the correlations among many earthquakes in different magnitude levels. It is known so far that the interoccurrence time statistics is well approximated by the Weibull distribution, but the more detailed information about the interoccurrence times can be obtained from the analysis of the conditional probability. Firstly, we propose the Embedding Equation Theory (EET), where the conditional probability is described by two kinds of correlation coefficients; one is the magnitude correlation and the other is the inter-event time correlation. Furthermore, the scaling law of each correlation coefficient is clearly determined from the numerical data-analysis carrying out with the Preliminary Determination of Epicenter (PDE) Catalog and the Japan Meteorological Agency (JMA) Catalog. Secondly, the EET is examined to derive the magnitude dependence of the interoccurrence time statistics and the multi-fractal relation is successfully formulated. Theoretically we cannot prove the universality of the multi-fractal relation in seismic activity; nevertheless, the theoretical results well reproduce all numerical data in our analysis, where several common features or the invariant aspects are clearly observed. Especially in the case of stationary ensembles the multi-fractal relation seems to obey an invariant curve, furthermore in the case of non-stationary (moving time) ensembles for the aftershock regime the multi-fractal relation seems to satisfy a certain invariant curve at any moving times. It is emphasized that the multi-fractal relation plays an important role to unify the statistical laws of seismicity: actually the Gutenberg-Richter law and the Weibull distribution are unified in the multi-fractal relation, and some universality conjectures regarding the seismicity are briefly discussed.

Connotations of pixel-based scale effect in remote sensing and the modified fractal-based analysis method

NASA Astrophysics Data System (ADS)

Feng, Guixiang; Ming, Dongping; Wang, Min; Yang, Jianyu

2017-06-01

Scale problems are a major source of concern in the field of remote sensing. Since the remote sensing is a complex technology system, there is a lack of enough cognition on the connotation of scale and scale effect in remote sensing. Thus, this paper first introduces the connotations of pixel-based scale and summarizes the general understanding of pixel-based scale effect. Pixel-based scale effect analysis is essentially important for choosing the appropriate remote sensing data and the proper processing parameters. Fractal dimension is a useful measurement to analysis pixel-based scale. However in traditional fractal dimension calculation, the impact of spatial resolution is not considered, which leads that the scale effect change with spatial resolution can't be clearly reflected. Therefore, this paper proposes to use spatial resolution as the modified scale parameter of two fractal methods to further analyze the pixel-based scale effect. To verify the results of two modified methods (MFBM (Modified Windowed Fractal Brownian Motion Based on the Surface Area) and MDBM (Modified Windowed Double Blanket Method)); the existing scale effect analysis method (information entropy method) is used to evaluate. And six sub-regions of building areas and farmland areas were cut out from QuickBird images to be used as the experimental data. The results of the experiment show that both the fractal dimension and information entropy present the same trend with the decrease of spatial resolution, and some inflection points appear at the same feature scales. Further analysis shows that these feature scales (corresponding to the inflection points) are related to the actual sizes of the geo-object, which results in fewer mixed pixels in the image, and these inflection points are significantly indicative of the observed features. Therefore, the experiment results indicate that the modified fractal methods are effective to reflect the pixel-based scale effect existing in remote sensing data and it is helpful to analyze the observation scale from different aspects. This research will ultimately benefit for remote sensing data selection and application.

Fractal Analysis of Visual Search Activity for Mass Detection During Mammographic Screening

DOE PAGES

Alamudun, Folami T.; Yoon, Hong-Jun; Hudson, Kathy; ...

2017-02-21

Purpose: The objective of this study was to assess the complexity of human visual search activity during mammographic screening using fractal analysis and to investigate its relationship with case and reader characteristics. Methods: The study was performed for the task of mammographic screening with simultaneous viewing of four coordinated breast views as typically done in clinical practice. Eye-tracking data and diagnostic decisions collected for 100 mammographic cases (25 normal, 25 benign, 50 malignant) and 10 readers (three board certified radiologists and seven radiology residents), formed the corpus data for this study. The fractal dimension of the readers’ visual scanning patternsmore » was computed with the Minkowski–Bouligand box-counting method and used as a measure of gaze complexity. Individual factor and group-based interaction ANOVA analysis was performed to study the association between fractal dimension, case pathology, breast density, and reader experience level. The consistency of the observed trends depending on gaze data representation was also examined. Results: Case pathology, breast density, reader experience level, and individual reader differences are all independent predictors of the visual scanning pattern complexity when screening for breast cancer. No higher order effects were found to be significant. Conclusions: Fractal characterization of visual search behavior during mammographic screening is dependent on case properties and image reader characteristics.« less

Digenetic Changes in Macro- to Nano-Scale Porosity in the St. Peter Sandstone:L An (Ultra) Small Angle Neutron Scattering and Backscattered Electron Imagining Analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Anovitz, Lawrence; Cole, David; Rother, Gernot

2013-01-01

Small- and Ultra-Small Angle Neutron Scattering (SANS and USANS) provide powerful tools for quantitative analysis of porous rocks, yielding bulk statistical information over a wide range of length scales. This study utilized (U)SANS to characterize shallowly buried quartz arenites from the St. Peter Sandstone. Backscattered electron imaging was also used to extend the data to larger scales. These samples contain significant volumes of large-scale porosity, modified by quartz overgrowths, and neutron scattering results show significant sub-micron porosity. While previous scattering data from sandstones suggest scattering is dominated by surface fractal behavior over many orders of magnitude, careful analysis of ourmore » data shows both fractal and pseudo-fractal behavior. The scattering curves are composed of subtle steps, modeled as polydispersed assemblages of pores with log-normal distributions. However, in some samples an additional surface-fractal overprint is present, while in others there is no such structure, and scattering can be explained by summation of non-fractal structures. Combined with our work on other rock-types, these data suggest that microporosity is more prevalent, and may play a much more important role than previously thought in fluid/rock interactions.« less

Fractal Profit Landscape of the Stock Market

PubMed Central

Grönlund, Andreas; Yi, Il Gu; Kim, Beom Jun

2012-01-01

We investigate the structure of the profit landscape obtained from the most basic, fluctuation based, trading strategy applied for the daily stock price data. The strategy is parameterized by only two variables, p and q Stocks are sold and bought if the log return is bigger than p and less than –q, respectively. Repetition of this simple strategy for a long time gives the profit defined in the underlying two-dimensional parameter space of p and q. It is revealed that the local maxima in the profit landscape are spread in the form of a fractal structure. The fractal structure implies that successful strategies are not localized to any region of the profit landscape and are neither spaced evenly throughout the profit landscape, which makes the optimization notoriously hard and hypersensitive for partial or limited information. The concrete implication of this property is demonstrated by showing that optimization of one stock for future values or other stocks renders worse profit than a strategy that ignores fluctuations, i.e., a long-term buy-and-hold strategy. PMID:22558079

Twitching motility of bacteria with type-IV pili: Fractal walks, first passage time, and their consequences on microcolonies

NASA Astrophysics Data System (ADS)

Bisht, Konark; Klumpp, Stefan; Banerjee, Varsha; Marathe, Rahul

2017-11-01

A human pathogen, Neisseria gonorrhoeae (NG), moves on surfaces by attaching and retracting polymeric structures called Type IV pili. The tug-of-war between the pili results in a two-dimensional stochastic motion called twitching motility. In this paper, with the help of real-time NG trajectories, we develop coarse-grained models for their description. The fractal properties of these trajectories are determined and their influence on first passage time and formation of bacterial microcolonies is studied. Our main observations are as follows: (i) NG performs a fast ballistic walk on small time scales and a slow diffusive walk over long time scales with a long crossover region; (ii) there exists a characteristic persistent length lp*, which yields the fastest growth of bacterial aggregates or biofilms. Our simulations reveal that lp*˜L0.6 , where L ×L is the surface on which the bacteria move; (iii) the morphologies have distinct fractal characteristics as a consequence of the ballistic and diffusive motion of the constituting bacteria.

Fractal propagation method enables realistic optical microscopy simulations in biological tissues

PubMed Central

Glaser, Adam K.; Chen, Ye; Liu, Jonathan T.C.

2017-01-01

Current simulation methods for light transport in biological media have limited efficiency and realism when applied to three-dimensional microscopic light transport in biological tissues with refractive heterogeneities. We describe here a technique which combines a beam propagation method valid for modeling light transport in media with weak variations in refractive index, with a fractal model of refractive index turbulence. In contrast to standard simulation methods, this fractal propagation method (FPM) is able to accurately and efficiently simulate the diffraction effects of focused beams, as well as the microscopic heterogeneities present in tissue that result in scattering, refractive beam steering, and the aberration of beam foci. We validate the technique and the relationship between the FPM model parameters and conventional optical parameters used to describe tissues, and also demonstrate the method’s flexibility and robustness by examining the steering and distortion of Gaussian and Bessel beams in tissue with comparison to experimental data. We show that the FPM has utility for the accurate investigation and optimization of optical microscopy methods such as light-sheet, confocal, and nonlinear microscopy. PMID:28983499

The influence of the growth conditions of the plague microbe vaccine strain colonies on the fractal dimension of biospeckles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ul'yanov, A S; Lyapina, A M; Ulianova, O V

2011-04-30

Specific statistical characteristics of biospeckles, emerging under the diffraction of coherent beams on the bacterial colonies, are studied. The dependence of the fractal dimensions of biospeckles on the conditions of both illumination and growth of the colonies is studied theoretically and experimentally. Particular attention is paid to the fractal properties of biospeckles, emerging under the scattering of light by the colonies of the vaccinal strain of the plague microbe. The possibility in principle to classify the colonies of Yersinia pestis EV NIIEG using the fractal dimension analysis is demonstrated. (optical technologies in biophysics and medicine)

[Lithology feature extraction of CASI hyperspectral data based on fractal signal algorithm].

PubMed

Tang, Chao; Chen, Jian-Ping; Cui, Jing; Wen, Bo-Tao

2014-05-01

Hyperspectral data is characterized by combination of image and spectrum and large data volume dimension reduction is the main research direction. Band selection and feature extraction is the primary method used for this objective. In the present article, the authors tested methods applied for the lithology feature extraction from hyperspectral data. Based on the self-similarity of hyperspectral data, the authors explored the application of fractal algorithm to lithology feature extraction from CASI hyperspectral data. The "carpet method" was corrected and then applied to calculate the fractal value of every pixel in the hyperspectral data. The results show that fractal information highlights the exposed bedrock lithology better than the original hyperspectral data The fractal signal and characterized scale are influenced by the spectral curve shape, the initial scale selection and iteration step. At present, research on the fractal signal of spectral curve is rare, implying the necessity of further quantitative analysis and investigation of its physical implications.

Complex Patterns in Financial Time Series Through HIGUCHI’S Fractal Dimension

NASA Astrophysics Data System (ADS)

Grace Elizabeth Rani, T. G.; Jayalalitha, G.

2016-11-01

This paper analyzes the complexity of stock exchanges through fractal theory. Closing price indices of four stock exchanges with different industry sectors are selected. Degree of complexity is assessed through Higuchi’s fractal dimension. Various window sizes are considered in evaluating the fractal dimension. It is inferred that the data considered as a whole represents random walk for all the four indices. Analysis of financial data through windowing procedure exhibits multi-fractality. Attempts to apply moving averages to reduce noise in the data revealed lower estimates of fractal dimension, which was verified using fractional Brownian motion. A change in the normalization factor in Higuchi’s algorithm did improve the results. It is quintessential to focus on rural development to realize a standard and steady growth of economy. Tools must be devised to settle the issues in this regard. Micro level institutions are necessary for the economic growth of a country like India, which would induce a sporadic development in the present global economical scenario.

Super Water-Repellent Fractal Surfaces of a Photochromic Diarylethene Induced by UV Light

NASA Astrophysics Data System (ADS)

Izumi, Norikazu; Minami, Takayuki; Mayama, Hiroyuki; Takata, Atsushi; Nakamura, Shinichiro; Yokojima, Satoshi; Tsujii, Kaoru; Uchida, Kingo

2008-09-01

Photochromic diarylethene forms super water-repellent surfaces upon irradiation with UV light. Microfibril-like crystals grow on the solid diarylethene surface after UV irradiation, and the contact angle of water on the surface becomes larger with increasing surface roughness with time. The fractal analysis was made by the box-counting method for the rough surfaces. There are three regions in the roughness size having the fractal dimension of ca. 2.4 (size of roughness smaller than 5 µm), of ca. 2.2 (size of roughness between 5-40 µm), and of ca. 2.0 (size of roughness larger than 40 µm). The fractal dimension of ca. 2.4 was due to the fibril-like structures generated gradually by UV irradiation on diarylethene surfaces accompanied with an increase in the contact angle. The surface structure with larger fractal dimension mainly contributes to realizing the super water-repellency of the diarylethene surfaces. This mechanism of spontaneous formation of fractal surfaces is similar to that for triglyceride and alkylketene dimer waxes.

Mapping of the Bak, Tang, and Wiesenfeld sandpile model on a two-dimensional Ising-correlated percolation lattice to the two-dimensional self-avoiding random walk

NASA Astrophysics Data System (ADS)

Cheraghalizadeh, J.; Najafi, M. N.; Dashti-Naserabadi, H.; Mohammadzadeh, H.

2017-11-01

The self-organized criticality on the random fractal networks has many motivations, like the movement pattern of fluid in the porous media. In addition to the randomness, introducing correlation between the neighboring portions of the porous media has some nontrivial effects. In this paper, we consider the Ising-like interactions between the active sites as the simplest method to bring correlations in the porous media, and we investigate the statistics of the BTW model in it. These correlations are controlled by the artificial "temperature" T and the sign of the Ising coupling. Based on our numerical results, we propose that at the Ising critical temperature Tc the model is compatible with the universality class of two-dimensional (2D) self-avoiding walk (SAW). Especially the fractal dimension of the loops, which are defined as the external frontier of the avalanches, is very close to DfSAW=4/3 . Also, the corresponding open curves has conformal invariance with the root-mean-square distance Rrms˜t3 /4 (t being the parametrization of the curve) in accordance with the 2D SAW. In the finite-size study, we observe that at T =Tc the model has some aspects compatible with the 2D BTW model (e.g., the 1 /log(L ) -dependence of the exponents of the distribution functions) and some in accordance with the Ising model (e.g., the 1 /L -dependence of the fractal dimensions). The finite-size scaling theory is tested and shown to be fulfilled for all statistical observables in T =Tc . In the off-critical temperatures in the close vicinity of Tc the exponents show some additional power-law behaviors in terms of T -Tc with some exponents that are reported in the text. The spanning cluster probability at the critical temperature also scales with L1/2, which is different from the regular 2D BTW model.

Frequency-Specific Fractal Analysis of Postural Control Accounts for Control Strategies

PubMed Central

Gilfriche, Pierre; Deschodt-Arsac, Véronique; Blons, Estelle; Arsac, Laurent M.

2018-01-01

Diverse indicators of postural control in Humans have been explored for decades, mostly based on the trajectory of the center-of-pressure. Classical approaches focus on variability, based on the notion that if a posture is too variable, the subject is not stable. Going deeper, an improved understanding of underlying physiology has been gained from studying variability in different frequency ranges, pointing to specific short-loops (proprioception), and long-loops (visuo-vestibular) in neural control. More recently, fractal analyses have proliferated and become useful additional metrics of postural control. They allowed identifying two scaling phenomena, respectively in short and long timescales. Here, we show that one of the most widely used methods for fractal analysis, Detrended Fluctuation Analysis, could be enhanced to account for scalings on specific frequency ranges. By computing and filtering a bank of synthetic fractal signals, we established how scaling analysis can be focused on specific frequency components. We called the obtained method Frequency-specific Fractal Analysis (FsFA) and used it to associate the two scaling phenomena of postural control to proprioceptive-based control loop and visuo-vestibular based control loop. After that, convincing arguments of method validity came from an application on the study of unaltered vs. altered postural control in athletes. Overall, the analysis suggests that at least two timescales contribute to postural control: a velocity-based control in short timescales relying on proprioceptive sensors, and a position-based control in longer timescales with visuo-vestibular sensors, which is a brand-new vision of postural control. Frequency-specific scaling exponents are promising markers of control strategies in Humans. PMID:29643816

Association between stride time fractality and gait adaptability during unperturbed and asymmetric walking.

PubMed

Ducharme, Scott W; Liddy, Joshua J; Haddad, Jeffrey M; Busa, Michael A; Claxton, Laura J; van Emmerik, Richard E A

2018-04-01

Human locomotion is an inherently complex activity that requires the coordination and control of neurophysiological and biomechanical degrees of freedom across various spatiotemporal scales. Locomotor patterns must constantly be altered in the face of changing environmental or task demands, such as heterogeneous terrains or obstacles. Variability in stride times occurring at short time scales (e.g., 5-10 strides) is statistically correlated to larger fluctuations occurring over longer time scales (e.g., 50-100 strides). This relationship, known as fractal dynamics, is thought to represent the adaptive capacity of the locomotor system. However, this has not been tested empirically. Thus, the purpose of this study was to determine if stride time fractality during steady state walking associated with the ability of individuals to adapt their gait patterns when locomotor speed and symmetry are altered. Fifteen healthy adults walked on a split-belt treadmill at preferred speed, half of preferred speed, and with one leg at preferred speed and the other at half speed (2:1 ratio asymmetric walking). The asymmetric belt speed condition induced gait asymmetries that required adaptation of locomotor patterns. The slow speed manipulation was chosen in order to determine the impact of gait speed on stride time fractal dynamics. Detrended fluctuation analysis was used to quantify the correlation structure, i.e., fractality, of stride times. Cross-correlation analysis was used to measure the deviation from intended anti-phasing between legs as a measure of gait adaptation. Results revealed no association between unperturbed walking fractal dynamics and gait adaptability performance. However, there was a quadratic relationship between perturbed, asymmetric walking fractal dynamics and adaptive performance during split-belt walking, whereby individuals who exhibited fractal scaling exponents that deviated from 1/f performed the poorest. Compared to steady state preferred walking speed, fractal dynamics increased closer to 1/f when participants were exposed to asymmetric walking. These findings suggest there may not be a relationship between unperturbed preferred or slow speed walking fractal dynamics and gait adaptability. However, the emergent relationship between asymmetric walking fractal dynamics and limb phase adaptation may represent a functional reorganization of the locomotor system (i.e., improved interactivity between degrees of freedom within the system) to be better suited to attenuate externally generated perturbations at various spatiotemporal scales. Copyright © 2018 Elsevier B.V. All rights reserved.

The Conundrum of Functional Brain Networks: Small-World Efficiency or Fractal Modularity

PubMed Central

Gallos, Lazaros K.; Sigman, Mariano; Makse, Hernán A.

2012-01-01

The human brain has been studied at multiple scales, from neurons, circuits, areas with well-defined anatomical and functional boundaries, to large-scale functional networks which mediate coherent cognition. In a recent work, we addressed the problem of the hierarchical organization in the brain through network analysis. Our analysis identified functional brain modules of fractal structure that were inter-connected in a small-world topology. Here, we provide more details on the use of network science tools to elaborate on this behavior. We indicate the importance of using percolation theory to highlight the modular character of the functional brain network. These modules present a fractal, self-similar topology, identified through fractal network methods. When we lower the threshold of correlations to include weaker ties, the network as a whole assumes a small-world character. These weak ties are organized precisely as predicted by theory maximizing information transfer with minimal wiring costs. PMID:22586406

Factors Affecting the Changes of Ice Crystal Form in Ice Cream

NASA Astrophysics Data System (ADS)

Wang, Xin; Watanabe, Manabu; Suzuki, Toru

In this study, the shape of ice crystals in ice cream was quantitatively evaluated by introducing fractal analysis. A small droplet of commercial ice cream mix was quickly cooled to about -30°C on the cold stage of microscope. Subsequently, it was heated to -5°C or -10°C and then held for various holding time. Based on the captured images at each holding time, the cross-sectional area and the length of circumference for each ice crystal were measured to calculate fractal dimension using image analysis software. The results showed that the ice crystals were categorized into two groups, e.g. simple-shape and complicated-shape, according to their fractal dimensions. The fractal dimension of ice crystals became lower with increasing holding time and holding temperature. It was also indicated that the growing rate of complicated-shape ice crystals was relatively higher because of aggregation.

Site effect classification based on microtremor data analysis using a concentration-area fractal model

NASA Astrophysics Data System (ADS)

Adib, A.; Afzal, P.; Heydarzadeh, K.

2015-01-01

The aim of this study is to classify the site effect using concentration-area (C-A) fractal model in Meybod city, central Iran, based on microtremor data analysis. Log-log plots of the frequency, amplification and vulnerability index (k-g) indicate a multifractal nature for the parameters in the area. The results obtained from the C-A fractal modelling reveal that proper soil types are located around the central city. The results derived via the fractal modelling were utilized to improve the Nogoshi and Igarashi (1970, 1971) classification results in the Meybod city. The resulting categories are: (1) hard soil and weak rock with frequency of 6.2 to 8 Hz, (2) stiff soil with frequency of about 4.9 to 6.2 Hz, (3) moderately soft soil with the frequency of 2.4 to 4.9 Hz, and (4) soft soil with the frequency lower than 2.4 Hz.

Site effect classification based on microtremor data analysis using concentration-area fractal model

NASA Astrophysics Data System (ADS)

Adib, A.; Afzal, P.; Heydarzadeh, K.

2014-07-01

The aim of this study is to classify the site effect using concentration-area (C-A) fractal model in Meybod city, Central Iran, based on microtremor data analysis. Log-log plots of the frequency, amplification and vulnerability index (k-g) indicate a multifractal nature for the parameters in the area. The results obtained from the C-A fractal modeling reveal that proper soil types are located around the central city. The results derived via the fractal modeling were utilized to improve the Nogoshi's classification results in the Meybod city. The resulted categories are: (1) hard soil and weak rock with frequency of 6.2 to 8 Hz, (2) stiff soil with frequency of about 4.9 to 6.2 Hz, (3) moderately soft soil with the frequency of 2.4 to 4.9 Hz, and (4) soft soil with the frequency lower than 2.4 Hz.

Fractal analysis on human dynamics of library loans

NASA Astrophysics Data System (ADS)

Fan, Chao; Guo, Jin-Li; Zha, Yi-Long

2012-12-01

In this paper, the fractal characteristic of human behaviors is investigated from the perspective of time series constructed with the amount of library loans. The values of the Hurst exponent and length of non-periodic cycle calculated through rescaled range analysis indicate that the time series of human behaviors and their sub-series are fractal with self-similarity and long-range dependence. Then the time series are converted into complex networks by the visibility algorithm. The topological properties of the networks such as scale-free property and small-world effect imply that there is a close relationship among the numbers of repetitious behaviors performed by people during certain periods of time. Our work implies that there is intrinsic regularity in the human collective repetitious behaviors. The conclusions may be helpful to develop some new approaches to investigate the fractal feature and mechanism of human dynamics, and provide some references for the management and forecast of human collective behaviors.

Modeling fractal cities using the correlated percolation model.

NASA Astrophysics Data System (ADS)

Makse, Hernán A.; Havlin, Shlomo; Stanley, H. Eugene

1996-03-01

Cities grow in a way that might be expected to resemble the growth of two-dimensional aggregates of particles, and this has led to recent attempts to model urban growth using ideas from the statistical physics of clusters. In particular, the model of diffusion limited aggregation (DLA) has been invoked to rationalize the apparently fractal nature of urban morphologies(M. Batty and P. Longley, Fractal Cities) (Academic, San Diego, 1994). The DLA model predicts that there should exist only one large fractal cluster, which is almost perfectly screened from incoming 'development units' (representing, for example, people, capital or resources), so that almost all of the cluster growth takes place at the tips of the cluster's branches. We show that an alternative model(H. A. Makse, S. Havlin, H. E. Stanley, Nature 377), 608 (1995), in which development units are correlated rather than being added to the cluster at random, is better able to reproduce the observed morphology of cities and the area distribution of sub-clusters ('towns') in an urban system, and can also describe urban growth dynamics. Our physical model, which corresponds to the correlated percolation model in the presence of a density gradient, is motivated by the fact that in urban areas development attracts further development. The model offers the possibility of predicting the global properties (such as scaling behavior) of urban morphologies.

a New Method for Calculating the Fractal Dimension of Surface Topography

NASA Astrophysics Data System (ADS)

Zuo, Xue; Zhu, Hua; Zhou, Yuankai; Li, Yan

2015-06-01

A new method termed as three-dimensional root-mean-square (3D-RMS) method, is proposed to calculate the fractal dimension (FD) of machined surfaces. The measure of this method is the root-mean-square value of surface data, and the scale is the side length of square in the projection plane. In order to evaluate the calculation accuracy of the proposed method, the isotropic surfaces with deterministic FD are generated based on the fractional Brownian function and Weierstrass-Mandelbrot (WM) fractal function, and two kinds of anisotropic surfaces are generated by stretching or rotating a WM fractal curve. Their FDs are estimated by the proposed method, as well as differential boxing-counting (DBC) method, triangular prism surface area (TPSA) method and variation method (VM). The results show that the 3D-RMS method performs better than the other methods with a lower relative error for both isotropic and anisotropic surfaces, especially for the surfaces with dimensions higher than 2.5, since the relative error between the estimated value and its theoretical value decreases with theoretical FD. Finally, the electrodeposited surface, end-turning surface and grinding surface are chosen as examples to illustrate the application of 3D-RMS method on the real machined surfaces. This method gives a new way to accurately calculate the FD from the surface topographic data.

Edible oil structures at low and intermediate concentrations. II. Ultra-small angle X-ray scattering of in situ tristearin solids in triolein

NASA Astrophysics Data System (ADS)

Peyronel, Fernanda; Ilavsky, Jan; Mazzanti, Gianfranco; Marangoni, Alejandro G.; Pink, David A.

2013-12-01

Ultra-small angle X-ray scattering has been used for the first time to elucidate, in situ, the aggregation structure of a model edible oil system. The three-dimensional nano- to micro-structure of tristearin solid particles in triolein solvent was investigated using 5, 10, 15, and 20% solids. Three different sample preparation procedures were investigated: two slow cooling rates of 0.5°/min, case 1 (22 days of storage at room temperature) and case 2 (no storage), and one fast cooling of 30°/min, case 3 (no storage). The length scale investigated, by using the Bonse-Hart camera at beamline ID-15D at the Advanced Photon Source, Argonne National Laboratory, covered the range from 300 Å to 10 μm. The unified fit and the Guinier-Porod models in the Irena software were used to fit the data. The former was used to fit 3 structural levels. Level 1 structures showed that the primary scatterers were essentially 2-dimensional objects for the three cases. The scatterers possessed lateral dimensions between 1000 and 4300 Å. This is consistent with the sizes of crystalline nanoplatelets present which were observed using cryo-TEM. Level 2 structures were aggregates possessing radii of gyration, Rg2 between 1800 Å and 12000 Å and fractal dimensions of either D2=1 for case 3 or 1.8≤D2≤2.1 for case 1 and case 2. D2 = 1 is consistent with unaggregated 1-dimensional objects. 1.8 ≤ D2 ≤ 2.1 is consistent with these 1-dimensional objects (below) forming structures characteristic of diffusion or reaction limited cluster-cluster aggregation. Level 3 structures showed that the spatial distribution of the level 2 structures was uniform, on the average, for case 1, with fractal dimension D3≈3 while for case 2 and case 3 the fractal dimension was D3≈2.2, which suggested that the large-scale distribution had not come to equilibrium. The Guinier-Porod model showed that the structures giving rise to the aggregates with a fractal dimension given by D2 in the unified fit level 2 model were cylinders described by the parameter s ≈1 in the Guinier-Porod model. The size of the base of these cylinders was in agreement with the cryo-TEM observations as well as with the results of the level 1 unified fit model. By estimating the size of the nanoplatelets and understanding the structures formed via their aggregation, it will be possible to engineer novel lipids systems that embody desired functional characteristics.

Fractal Signals & Space-Time Cartoons

NASA Astrophysics Data System (ADS)

Oetama, H. C. Jakob; Maksoed, W. H.

2016-03-01

In ``Theory of Scale Relativity'', 1991- L. Nottale states whereas ``scale relativity is a geometrical & fractal space-time theory''. It took in comparisons to ``a unified, wavelet based framework for efficiently synthetizing, analyzing ∖7 processing several broad classes of fractal signals''-Gregory W. Wornell:``Signal Processing with Fractals'', 1995. Furthers, in Fig 1.1. a simple waveform from statistically scale-invariant random process [ibid.,h 3 ]. Accompanying RLE Technical Report 566 ``Synthesis, Analysis & Processing of Fractal Signals'' as well as from Wornell, Oct 1991 herewith intended to deducts =a Δt + (1 - β Δ t) ...in Petersen, et.al: ``Scale invariant properties of public debt growth'',2010 h. 38006p2 to [1/{1- (2 α (λ) /3 π) ln (λ/r)}depicts in Laurent Nottale,1991, h 24. Acknowledgment devotes to theLates HE. Mr. BrigadierGeneral-TNI[rtd].Prof. Ir. HANDOJO.

MORPH-I (Ver 1.0) a software package for the analysis of scanning electron micrograph (binary formatted) images for the assessment of the fractal dimension of enclosed pore surfaces

USGS Publications Warehouse

Mossotti, Victor G.; Eldeeb, A. Raouf; Oscarson, Robert

1998-01-01

MORPH-I is a set of C-language computer programs for the IBM PC and compatible minicomputers. The programs in MORPH-I are used for the fractal analysis of scanning electron microscope and electron microprobe images of pore profiles exposed in cross-section. The program isolates and traces the cross-sectional profiles of exposed pores and computes the Richardson fractal dimension for each pore. Other programs in the set provide for image calibration, display, and statistical analysis of the computed dimensions for highly complex porous materials. Requirements: IBM PC or compatible; minimum 640 K RAM; mathcoprocessor; SVGA graphics board providing mode 103 display.

Integrated quantitative fractal polarimetric analysis of monolayer lung cancer cells

NASA Astrophysics Data System (ADS)

Shrestha, Suman; Zhang, Lin; Quang, Tri; Farrahi, Tannaz; Narayan, Chaya; Deshpande, Aditi; Na, Ying; Blinzler, Adam; Ma, Junyu; Liu, Bo; Giakos, George C.

2014-05-01

Digital diagnostic pathology has become one of the most valuable and convenient advancements in technology over the past years. It allows us to acquire, store and analyze pathological information from the images of histological and immunohistochemical glass slides which are scanned to create digital slides. In this study, efficient fractal, wavelet-based polarimetric techniques for histological analysis of monolayer lung cancer cells will be introduced and different monolayer cancer lines will be studied. The outcome of this study indicates that application of fractal, wavelet polarimetric principles towards the analysis of squamous carcinoma and adenocarcinoma cancer cell lines may be proved extremely useful in discriminating among healthy and lung cancer cells as well as differentiating among different lung cancer cells.

Quantitative characterization of the regressive ecological succession by fractal analysis of plant spatial patterns

USGS Publications Warehouse

Alados, C.L.; Pueyo, Y.; Giner, M.L.; Navarro, T.; Escos, J.; Barroso, F.; Cabezudo, B.; Emlen, J.M.

2003-01-01

We studied the effect of grazing on the degree of regression of successional vegetation dynamic in a semi-arid Mediterranean matorral. We quantified the spatial distribution patterns of the vegetation by fractal analyses, using the fractal information dimension and spatial autocorrelation measured by detrended fluctuation analyses (DFA). It is the first time that fractal analysis of plant spatial patterns has been used to characterize the regressive ecological succession. Plant spatial patterns were compared over a long-term grazing gradient (low, medium and heavy grazing pressure) and on ungrazed sites for two different plant communities: A middle dense matorral of Chamaerops and Periploca at Sabinar-Romeral and a middle dense matorral of Chamaerops, Rhamnus and Ulex at Requena-Montano. The two communities differed also in the microclimatic characteristics (sea oriented at the Sabinar-Romeral site and inland oriented at the Requena-Montano site). The information fractal dimension increased as we moved from a middle dense matorral to discontinuous and scattered matorral and, finally to the late regressive succession, at Stipa steppe stage. At this stage a drastic change in the fractal dimension revealed a change in the vegetation structure, accurately indicating end successional vegetation stages. Long-term correlation analysis (DFA) revealed that an increase in grazing pressure leads to unpredictability (randomness) in species distributions, a reduction in diversity, and an increase in cover of the regressive successional species, e.g. Stipa tenacissima L. These comparisons provide a quantitative characterization of the successional dynamic of plant spatial patterns in response to grazing perturbation gradient. ?? 2002 Elsevier Science B.V. All rights reserved.

Spectral scalability and optical spectra of fractal multilayer structures: FDTD analysis

NASA Astrophysics Data System (ADS)

Simsek, Sevket; Palaz, Selami; Mamedov, Amirullah M.; Ozbay, Ekmel

2017-01-01

An investigation of the optical properties and band structures for the conventional and Fibonacci photonic crystals (PCs) based on SrTiO3 and Sb2Te3 is made in the present research. Here, we use one-dimensional SrTiO3- and Sb2Te3-based layers. We have theoretically calculated the photonic band structure and transmission spectra of SrTiO3- and Sb2Te3-based PC superlattices. The position of minima in the transmission spectrum correlates with the gaps obtained in the calculation. The intensity of the transmission depths is more intense in the case of higher refractive index contrast between the layers.

Application of fractal and grey level co-occurrence matrix analysis in evaluation of brain corpus callosum and cingulum architecture.

PubMed

Pantic, Igor; Dacic, Sanja; Brkic, Predrag; Lavrnja, Irena; Pantic, Senka; Jovanovic, Tomislav; Pekovic, Sanja

2014-10-01

This aim of this study was to assess the discriminatory value of fractal and grey level co-occurrence matrix (GLCM) analysis methods in standard microscopy analysis of two histologically similar brain white mass regions that have different nerve fiber orientation. A total of 160 digital micrographs of thionine-stained rat brain white mass were acquired using a Pro-MicroScan DEM-200 instrument. Eighty micrographs from the anterior corpus callosum and eighty from the anterior cingulum areas of the brain were analyzed. The micrographs were evaluated using the National Institutes of Health ImageJ software and its plugins. For each micrograph, seven parameters were calculated: angular second moment, inverse difference moment, GLCM contrast, GLCM correlation, GLCM variance, fractal dimension, and lacunarity. Using the Receiver operating characteristic analysis, the highest discriminatory value was determined for inverse difference moment (IDM) (area under the receiver operating characteristic (ROC) curve equaled 0.925, and for the criterion IDM≤0.610 the sensitivity and specificity were 82.5 and 87.5%, respectively). Most of the other parameters also showed good sensitivity and specificity. The results indicate that GLCM and fractal analysis methods, when applied together in brain histology analysis, are highly capable of discriminating white mass structures that have different axonal orientation.

PHYSICAL EFFECTS OCCURRING DURING GENERATION AND AMPLIFICATION OF LASER RADIATION: Dynamic chaos in a laser with a bleachable filter and dimensionality

NASA Astrophysics Data System (ADS)

Samson, A. M.; Kotomtseva, L. A.; Grigor'eva, E. V.

1989-02-01

A theoretical study of the dynamics of a laser with a bleachable filter revealed chaotic lasing regimes and ranges of bistable states of parameters close to those found in reality. It is shown how a transition to chaos occurs as a result of period-doubling bifurcation. A study is reported of the degree of chaos and of the structure of the resultant strange attractor by calculation of its fractal dimensionality and of the Lyapunov indices.

Fractal Dimension Analysis of Subcortical Gray Matter Structures in Schizophrenia

PubMed Central

Sehatpour, Pejman; Long, Jun; Gui, Weihua; Qiao, Jianping; Javitt, Daniel C.; Wang, Zhishun

2016-01-01

A failure of adaptive inference—misinterpreting available sensory information for appropriate perception and action—is at the heart of clinical manifestations of schizophrenia, implicating key subcortical structures in the brain including the hippocampus. We used high-resolution, three-dimensional (3D) fractal geometry analysis to study subtle and potentially biologically relevant structural alterations (in the geometry of protrusions, gyri and indentations, sulci) in subcortical gray matter (GM) in patients with schizophrenia relative to healthy individuals. In particular, we focus on utilizing Fractal Dimension (FD), a compact shape descriptor that can be computed using inputs with irregular (i.e., not necessarily smooth) surfaces in order to quantify complexity (of geometrical properties and configurations of structures across spatial scales) of subcortical GM in this disorder. Probabilistic (entropy-based) information FD was computed based on the box-counting approach for each of the seven subcortical structures, bilaterally, as well as the brainstem from high-resolution magnetic resonance (MR) images in chronic patients with schizophrenia (n = 19) and age-matched healthy controls (n = 19) (age ranges: patients, 22.7–54.3 and healthy controls, 24.9–51.6 years old). We found a significant reduction of FD in the left hippocampus (median: 2.1460, range: 2.07–2.18 vs. median: 2.1730, range: 2.15–2.23, p<0.001; Cohen’s effect size, U3 = 0.8158 (95% Confidence Intervals, CIs: 0.6316, 1.0)), the right hippocampus (median: 2.1430, range: 2.05–2.19 vs. median: 2.1760, range: 2.12–2.21, p = 0.004; U3 = 0.8421 (CIs: 0.5263, 1)), as well as left thalamus (median: 2.4230, range: 2.40–2.44, p = 0.005; U3 = 0.7895 (CIs: 0.5789, 0.9473)) in schizophrenia patients, relative to healthy individuals. Our findings provide in-vivo quantitative evidence for reduced surface complexity of hippocampus, with reduced FD indicating a less complex, less regular GM surface detected in schizophrenia. PMID:27176232

A system framework of inter-enterprise machining quality control based on fractal theory

NASA Astrophysics Data System (ADS)

Zhao, Liping; Qin, Yongtao; Yao, Yiyong; Yan, Peng

2014-03-01

In order to meet the quality control requirement of dynamic and complicated product machining processes among enterprises, a system framework of inter-enterprise machining quality control based on fractal was proposed. In this system framework, the fractal-specific characteristic of inter-enterprise machining quality control function was analysed, and the model of inter-enterprise machining quality control was constructed by the nature of fractal structures. Furthermore, the goal-driven strategy of inter-enterprise quality control and the dynamic organisation strategy of inter-enterprise quality improvement were constructed by the characteristic analysis on this model. In addition, the architecture of inter-enterprise machining quality control based on fractal was established by means of Web service. Finally, a case study for application was presented. The result showed that the proposed method was available, and could provide guidance for quality control and support for product reliability in inter-enterprise machining processes.

Fractal based modelling and analysis of electromyography (EMG) to identify subtle actions.

PubMed

Arjunan, Sridhar P; Kumar, Dinesh K

2007-01-01

The paper reports the use of fractal theory and fractal dimension to study the non-linear properties of surface electromyogram (sEMG) and to use these properties to classify subtle hand actions. The paper reports identifying a new feature of the fractal dimension, the bias that has been found to be useful in modelling the muscle activity and of sEMG. Experimental results demonstrate that the feature set consisting of bias values and fractal dimension of the recordings is suitable for classification of sEMG against the different hand gestures. The scatter plots demonstrate the presence of simple relationships of these features against the four hand gestures. The results indicate that there is small inter-experimental variation but large inter-subject variation. This may be due to differences in the size and shape of muscles for different subjects. The possible applications of this research include use in developing prosthetic hands, controlling machines and computers.

Fractal analysis of mandibular trabecular bone: optimal tile sizes for the tile counting method.

PubMed

Huh, Kyung-Hoe; Baik, Jee-Seon; Yi, Won-Jin; Heo, Min-Suk; Lee, Sam-Sun; Choi, Soon-Chul; Lee, Sun-Bok; Lee, Seung-Pyo

2011-06-01

This study was performed to determine the optimal tile size for the fractal dimension of the mandibular trabecular bone using a tile counting method. Digital intraoral radiographic images were obtained at the mandibular angle, molar, premolar, and incisor regions of 29 human dry mandibles. After preprocessing, the parameters representing morphometric characteristics of the trabecular bone were calculated. The fractal dimensions of the processed images were analyzed in various tile sizes by the tile counting method. The optimal range of tile size was 0.132 mm to 0.396 mm for the fractal dimension using the tile counting method. The sizes were closely related to the morphometric parameters. The fractal dimension of mandibular trabecular bone, as calculated with the tile counting method, can be best characterized with a range of tile sizes from 0.132 to 0.396 mm.

Fractal analysis of mandibular trabecular bone: optimal tile sizes for the tile counting method

PubMed Central

Huh, Kyung-Hoe; Baik, Jee-Seon; Heo, Min-Suk; Lee, Sam-Sun; Choi, Soon-Chul; Lee, Sun-Bok; Lee, Seung-Pyo

2011-01-01

Purpose This study was performed to determine the optimal tile size for the fractal dimension of the mandibular trabecular bone using a tile counting method. Materials and Methods Digital intraoral radiographic images were obtained at the mandibular angle, molar, premolar, and incisor regions of 29 human dry mandibles. After preprocessing, the parameters representing morphometric characteristics of the trabecular bone were calculated. The fractal dimensions of the processed images were analyzed in various tile sizes by the tile counting method. Results The optimal range of tile size was 0.132 mm to 0.396 mm for the fractal dimension using the tile counting method. The sizes were closely related to the morphometric parameters. Conclusion The fractal dimension of mandibular trabecular bone, as calculated with the tile counting method, can be best characterized with a range of tile sizes from 0.132 to 0.396 mm. PMID:21977478

Advances in the Quantitative Characterization of the Shape of Ash-Sized Pyroclast Populations: Fractal Analyses Coupled to Micro- and Nano-Computed Tomography Techniques

NASA Astrophysics Data System (ADS)

Rausch, J.; Vonlanthen, P.; Grobety, B. H.

2014-12-01

The quantification of shape parameters in pyroclasts is fundamental to infer the dominant type of magma fragmentation (magmatic vs. phreatomagmatic), as well as the behavior of volcanic plumes and clouds in the atmosphere. In a case study aiming at reconstructing the fragmentation mechanisms triggering maar eruptions in two geologically and compositionally distinctive volcanic fields (West and East Eifel, Germany), the shapes of a large number of ash particle contours obtained from SEM images were analyzed by a dilation-based fractal method. Volcanic particle contours are pseudo-fractals showing mostly two distinct slopes in Richardson plots related to the fractal dimensions D1 (small-scale "textural" dimension) and D2 (large-scale "morphological" dimension). The validity of the data obtained from 2D sections was tested by analysing SEM micro-CT slices of one particle cut in different orientations and positions. Results for West Eifel maar particles yield large D1 values (> 1.023), resembling typical values of magmatic particles, which are characterized by a complex shape, especially at small scales. In contrast, the D1 values of ash particles from one East Eifel maar deposit are much smaller, coinciding with the fractal dimensions obtained from phreatomagmatic end-member particles. These quantitative morphological analyses suggest that the studied maar eruptions were triggered by two different fragmentation processes: phreatomagmatic in the East Eifel and magmatic in the West Eifel. The application of fractal analysis to quantitatively characterize the shape of pyroclasts and the linking of fractal dimensions to specific fragmentation processes has turned out to be a very promising tool for studying the fragmentation history of any volcanic eruption. The next step is to extend morphological analysis of volcanic particles to 3 dimensions. SEM micro-CT, already applied in this study, offers the required resolution, but is not suitable for the analysis of a large number of particles. Newly released nano CT-scanners, however, allows the simultaneous analysis of a statistically relevant number of particles (in the hundreds range). Preliminary results of a first trial will be presented.

Conductivity fluctuations in polymer's networks

NASA Astrophysics Data System (ADS)

Samukhin, A. N.; Prigodin, V. N.; Jastrabík, L.

1998-01-01

A Polymer network is treated as an anisotropic fractal with fractional dimensionality D = 1 + ε close to one. Percolation model on such a fractal is studied. Using real space renormalization group approach of Migdal and Kadanoff, we find the threshold value and all the critical exponents in the percolation model to be strongly nonanalytic functions of ε, e.g. the critical exponent of the conductivity was obtained to be ε-2 exp (-1 - 1/ε). The main part of the finite-size conductivities distribution function at the threshold was found to be universal if expressed in terms of the fluctuating variable which is proportional to a large power of the conductivity, but with ε-dependent low-conductivity cut-off. Its reduced central momenta are of the order of e -1/ε up to a very high order.

Nonlinear anomalous diffusion equation and fractal dimension: exact generalized Gaussian solution.

PubMed

Pedron, I T; Mendes, R S; Malacarne, L C; Lenzi, E K

2002-04-01

In this work we incorporate, in a unified way, two anomalous behaviors, the power law and stretched exponential ones, by considering the radial dependence of the N-dimensional nonlinear diffusion equation partial differential rho/ partial differential t=nabla.(Knablarho(nu))-nabla.(muFrho)-alpharho, where K=Dr(-theta), nu, theta, mu, and D are real parameters, F is the external force, and alpha is a time-dependent source. This equation unifies the O'Shaughnessy-Procaccia anomalous diffusion equation on fractals (nu=1) and the spherical anomalous diffusion for porous media (theta=0). An exact spherical symmetric solution of this nonlinear Fokker-Planck equation is obtained, leading to a large class of anomalous behaviors. Stationary solutions for this Fokker-Planck-like equation are also discussed by introducing an effective potential.

A fractal analysis of protein to DNA binding kinetics using biosensors.

PubMed

Sadana, Ajit

2003-08-01

A fractal analysis of a confirmative nature only is presented for the binding of estrogen receptor (ER) in solution to its corresponding DNA (estrogen response element, ERE) immobilized on a sensor chip surface [J. Biol. Chem. 272 (1997) 11384], and for the cooperative binding of human 1,25-dihydroxyvitamin D(3) receptor (VDR) to DNA with the 9-cis-retinoic acid receptor (RXR) [Biochemistry 35 (1996) 3309]. Ligands were also used to modulate the first reaction. Data taken from the literature may be modeled by using a single- or a dual-fractal analysis. Relationships are presented for the binding rate coefficient as a function of either the analyte concentration in solution or the fractal dimension that exists on the biosensor surface. The binding rate expressions developed exhibit a wide range of dependence on the degree of heterogeneity that exists on the surface, ranging from sensitive (order of dependence equal to 1.202) to very sensitive (order of dependence equal to 12.239). In general, the binding rate coefficient increases as the degree of heterogeneity or the fractal dimension of the surface increases. The predictive relationships presented provide further physical insights into the reactions occurring on the biosensor surface. Even though these reactions are occurring on the biosensor surface, the relationships presented should assist in understanding and in possibly manipulating the reactions occurring on cellular surfaces.

Does fractality in heart rate variability indicate the development of fetal neural processes?

NASA Astrophysics Data System (ADS)

Echeverría, J. C.; Woolfson, M. S.; Crowe, J. A.; Hayes-Gill, B. R.; Piéri, Jean F.; Spencer, C. J.; James, D. K.

2004-10-01

By using an improved detrended fluctuation analysis we studied the scaling behaviour of 53 long-term series of fetal heart rate fluctuations. Our results suggest that fractality begins to arise around 24 weeks of normal human gestation and that this condition, showing some additional developments, seems to be preserved during gestation. This may provide new evidence of a role played by cortical-to-subcortical pathways in the long-term fractal nature of heart rate variability data.

Analysis of the fractal dimension of volcano geomorphology through Synthetic Aperture Radar (SAR) amplitude images acquired in C and X band.

NASA Astrophysics Data System (ADS)

Pepe, S.; Di Martino, G.; Iodice, A.; Manzo, M.; Pepe, A.; Riccio, D.; Ruello, G.; Sansosti, E.; Tizzani, P.; Zinno, I.

2012-04-01

In the last two decades several aspects relevant to volcanic activity have been analyzed in terms of fractal parameters that effectively describe natural objects geometry. More specifically, these researches have been aimed at the identification of (1) the power laws that governed the magma fragmentation processes, (2) the energy of explosive eruptions, and (3) the distribution of the associated earthquakes. In this paper, the study of volcano morphology via satellite images is dealt with; in particular, we use the complete forward model developed by some of the authors (Di Martino et al., 2012) that links the stochastic characterization of amplitude Synthetic Aperture Radar (SAR) images to the fractal dimension of the imaged surfaces, modelled via fractional Brownian motion (fBm) processes. Based on the inversion of such a model, a SAR image post-processing has been implemented (Di Martino et al., 2010), that allows retrieving the fractal dimension of the observed surfaces, dictating the distribution of the roughness over different spatial scales. The fractal dimension of volcanic structures has been related to the specific nature of materials and to the effects of active geodynamic processes. Hence, the possibility to estimate the fractal dimension from a single amplitude-only SAR image is of fundamental importance for the characterization of volcano structures and, moreover, can be very helpful for monitoring and crisis management activities in case of eruptions and other similar natural hazards. The implemented SAR image processing performs the extraction of the point-by-point fractal dimension of the scene observed by the sensor, providing - as an output product - the map of the fractal dimension of the area of interest. In this work, such an analysis is performed on Cosmo-SkyMed, ERS-1/2 and ENVISAT images relevant to active stratovolcanoes in different geodynamic contexts, such as Mt. Somma-Vesuvio, Mt. Etna, Vulcano and Stromboli in Southern Italy, Shinmoe in Japan, Merapi in Indonesia. Preliminary results reveal that the fractal dimension of natural areas, being related only to the roughness of the observed surface, is very stable as the radar illumination geometry, the resolution and the wavelength change, thus holding a very unique property in SAR data inversion. Such a behavior is not verified in case of non-natural objects. As a matter of fact, when the fractal estimation is performed in the presence of either man-made objects or SAR image features depending on geometrical distortions due to the SAR system acquisition (i.e. layover, shadowing), fractal dimension (D) values outside the range of fractality of natural surfaces (2 < D < 3) are retrieved. These non-fractal characteristics show to be heavily dependent on sensor acquisition parameters (e.g. view angle, resolution). In this work, the behaviour of the maps generated starting from the C- and X- band SAR data, relevant to all the considered volcanoes, is analyzed: the distribution of the obtained fractal dimension values is investigated on different zones of the maps. In particular, it is verified that the fore-slope and back-slope areas of the image share a very similar fractal dimension distribution that is placed around the mean value of D=2.3. We conclude that, in this context, the fractal dimension could be considered as a signature of the identification of the volcano growth as a natural process. The COSMO-SkyMed data used in this study have been processed at IREA-CNR within the SAR4Volcanoes project under Italian Space Agency agreement n. I/034/11/0.

Fractal Dimensions of Umbral and Penumbral Regions of Sunspots

NASA Astrophysics Data System (ADS)

Rajkumar, B.; Haque, S.; Hrudey, W.

2017-11-01

The images of sunspots in 16 active regions taken at the University College of the Cayman Islands (UCCI) Observatory on Grand Cayman during June-November 2015 were used to determine their fractal dimensions using the perimeter-area method for the umbral and the penumbral region. Scale-free fractal dimensions of 2.09 ±0.42 and 1.72 ±0.4 were found, respectively. This value was higher than the value determined by Chumak and Chumak ( Astron. Astrophys. Trans. 10, 329, 1996), who used a similar method, but only for the penumbral region of their sample set. The umbral and penumbral fractal dimensions for the specific sunspots are positively correlated with r = 0.58. Furthermore, a similar time-series analysis was performed on eight images of AR 12403, from 21 August 2015 to 28 August 2015 taken from the Debrecen Photoheliographic Data (DPD). The correlation is r = 0.623 between the umbral and penumbral fractal dimensions in the time series, indicating that the complexity in morphology indicated by the fractal dimension between the umbra and penumbra followed each other in time as well.

When human walking becomes random walking: fractal analysis and modeling of gait rhythm fluctuations

NASA Astrophysics Data System (ADS)

Hausdorff, Jeffrey M.; Ashkenazy, Yosef; Peng, Chang-K.; Ivanov, Plamen Ch.; Stanley, H. Eugene; Goldberger, Ary L.

2001-12-01

We present a random walk, fractal analysis of the stride-to-stride fluctuations in the human gait rhythm. The gait of healthy young adults is scale-free with long-range correlations extending over hundreds of strides. This fractal scaling changes characteristically with maturation in children and older adults and becomes almost completely uncorrelated with certain neurologic diseases. Stochastic modeling of the gait rhythm dynamics, based on transitions between different “neural centers”, reproduces distinctive statistical properties of the gait pattern. By tuning one model parameter, the hopping (transition) range, the model can describe alterations in gait dynamics from childhood to adulthood - including a decrease in the correlation and volatility exponents with maturation.

Fractal characterization of a fractured chalk reservoir - The Laegerdorf case

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stoelum, H.H.; Koestler, A.G.; Feder, J.

1991-03-01

What is the matrix block size distribution of a fractured reservoir In order to answer this question and assess the potential of fractal geometry as a method of characterization of fracture networks, a pilot study has been done of the fractured chalk quarry in Laegerdorf. The fractures seen on the quarry walls were traced in the field for a total area of {approximately}200 {times} 45 m. The digitized pictures have been analyzed by a standard box-counting method. This analysis gave a fractal dimension of similarity varying from 1.33 for fractured areas between faults, to 1.43 for the fault zone, andmore » 1.53 for the highly deformed fault gouge. The amplitude showed a similar trend. The fractal dimension for the whole system of fractures is {approximately}1.55. In other words, fracture networks in chalk have a nonlinear, fractal geometry, and so matrix block size is a scaling property of chalk reservoirs. In terms of rock mechanics, the authors interpret the variation of the fractal dimension as follows: A small fractal dimension and amplitude are associated with brittle deformation in the elastic regime, while a large fractal dimension and amplitude are associated with predominantly ductile, strain softening deformation in the plastic regime. The interaction between the two regimes of deformation in the rock body is a key element of successful characterization and may be approached by seeing the rock as a non-Newtonian viscoelastic medium. The fractal dimension for the whole is close to a material independent limit that constrains the development of fractures.« less

Trabecular morphometry by fractal signature analysis is a novel marker of osteoarthritis progression.

PubMed

Kraus, Virginia Byers; Feng, Sheng; Wang, ShengChu; White, Scott; Ainslie, Maureen; Brett, Alan; Holmes, Anthony; Charles, H Cecil

2009-12-01

To evaluate the effectiveness of using subchondral bone texture observed on a radiograph taken at baseline to predict progression of knee osteoarthritis (OA) over a 3-year period. A total of 138 participants in the Prediction of Osteoarthritis Progression study were evaluated at baseline and after 3 years. Fractal signature analysis (FSA) of the medial subchondral tibial plateau was performed on fixed flexion radiographs of 248 nonreplaced knees, using a commercially available software tool. OA progression was defined as a change in joint space narrowing (JSN) or osteophyte formation of 1 grade according to a standardized knee atlas. Statistical analysis of fractal signatures was performed using a new model based on correlating the overall shape of a fractal dimension curve with radius. Fractal signature of the medial tibial plateau at baseline was predictive of medial knee JSN progression (area under the curve [AUC] 0.75, of a receiver operating characteristic curve) but was not predictive of osteophyte formation or progression of JSN in the lateral compartment. Traditional covariates (age, sex, body mass index, knee pain), general bone mineral content, and joint space width at baseline were no more effective than random variables for predicting OA progression (AUC 0.52-0.58). The predictive model with maximum effectiveness combined fractal signature at baseline, knee alignment, traditional covariates, and bone mineral content (AUC 0.79). We identified a prognostic marker of OA that is readily extracted from a plain radiograph using FSA. Although the method needs to be validated in a second cohort, our results indicate that the global shape approach to analyzing these data is a potentially efficient means of identifying individuals at risk of knee OA progression.

Postural control strategies during single limb stance following acute lateral ankle sprain.

PubMed

Doherty, Cailbhe; Bleakley, Chris; Hertel, Jay; Caulfield, Brian; Ryan, John; Delahunt, Eamonn

2014-06-01

Single-limb stance is maintained via the integration of visual, vestibular and somatosensory afferents. Musculoskeletal injury challenges the somatosensory system to reweight distorted sensory afferents. This investigation supplements kinetic analysis of eyes-open and eyes-closed single-limb stance tasks with a kinematic profile of lower limb postural orientation in an acute lateral ankle sprain group to assess the adaptive capacity of the sensorimotor system to injury. Sixty-six participants with first-time acute lateral ankle sprain completed a 20-second eyes-open single-limb stance task on their injured and non-injured limbs (task 1). Twenty-three of these participants successfully completed the same 20-second single-limb stance task with their eyes closed (task 2). A non-injured control group of 19 participants completed task 1, with 16 completing task 2. 3-dimensional kinematics of the hip, knee and ankle joints, as well as associated fractal dimension of the center-of-pressure path were determined for each limb during these tasks. Between trial analyses revealed significant differences in stance limb kinematics and fractal dimension of the center-of-pressure path for task 2 only. The control group bilaterally assumed a position of greater hip flexion compared to injured participants on their side-matched "involved"(7.41 [6.1°] vs 1.44 [4.8]°; η(2)=.34) and "uninvolved" (9.59 [8.5°] vs 2.16 [5.6°]; η(2)=.31) limbs, with a greater fractal dimension of the center-of-pressure path (involved limb=1.39 [0.16°] vs 1.25 [0.14°]; uninvolved limb=1.37 [0.21°] vs 1.23 [0.14°]). Bilateral impairment in postural control strategies present following a first time acute lateral ankle sprain. Copyright © 2014 Elsevier Ltd. All rights reserved.

The Analysis of Leaf Shape Using Fractal Geometry.

ERIC Educational Resources Information Center

Hartvigsen, Gregg

2000-01-01

Describes ways to examine leaf structure and shape using fractal geometry. Students can test hypotheses using the leaves of replicated plants to look for non-linear trends in leaf shape along the stems of plants, across species, and under different environmental growth conditions. (SAH)

Fractal analysis of Xylella fastidiosa biofilm formation

NASA Astrophysics Data System (ADS)

Moreau, A. L. D.; Lorite, G. S.; Rodrigues, C. M.; Souza, A. A.; Cotta, M. A.

2009-07-01

We have investigated the growth process of Xylella fastidiosa biofilms inoculated on a glass. The size and the distance between biofilms were analyzed by optical images; a fractal analysis was carried out using scaling concepts and atomic force microscopy images. We observed that different biofilms show similar fractal characteristics, although morphological variations can be identified for different biofilm stages. Two types of structural patterns are suggested from the observed fractal dimensions Df. In the initial and final stages of biofilm formation, Df is 2.73±0.06 and 2.68±0.06, respectively, while in the maturation stage, Df=2.57±0.08. These values suggest that the biofilm growth can be understood as an Eden model in the former case, while diffusion-limited aggregation (DLA) seems to dominate the maturation stage. Changes in the correlation length parallel to the surface were also observed; these results were correlated with the biofilm matrix formation, which can hinder nutrient diffusion and thus create conditions to drive DLA growth.

Effect of hydrogen addition on soot formation in an ethylene/air premixed flame

NASA Astrophysics Data System (ADS)

De Iuliis, S.; Maffi, S.; Migliorini, F.; Cignoli, F.; Zizak, G.

2012-03-01

The effect of hydrogen addition to fuel in soot formation and growth mechanisms is investigated in a rich ethylene/air premixed flame. To this purpose, three-angle scattering and extinction measurements are carried out in flames with different hydrogen contents. By applying the Rayleigh-Debye-Gans theory and the fractal-like description, soot concentration and morphology, with the evaluation of radius of gyration, volume-mean diameter and primary particle diameter are retrieved. To derive fractal parameters such as fractal dimension and fractal prefactor to be used for optical measurements, sampling technique and TEM analysis are performed. In addition, data concerning soot morphology obtained from TEM analysis are compared with the optical results. A good agreement in the value of the primary particle diameter between optical and ex-situ measurements is found. Significant effects of hydrogen addition are detected and presented in this work. In particular, hydrogen addition to fuel is responsible for a reduction in soot concentration, radius of gyration and primary particle diameter.

An "ASYMPTOTIC FRACTAL" Approach to the Morphology of Malignant Cell Nuclei

NASA Astrophysics Data System (ADS)

Landini, Gabriel; Rippin, John W.

To investigate quantitatively nuclear membrane irregularity, 672 nuclei from 10 cases of oral cancer (squamous cell carcinoma) and normal cells from oral mucosa were studied in transmission electron micrographs. The nuclei were photographed at ×1400 magnification and transferred to computer memory (1 pixel = 35 nm). The perimeter of the profiles was analysed using the "yardstick method" of fractal dimension estimation, and the log-log plot of ruler size vs. boundary length demonstrated that there exists a significant effect of resolution on length measurement. However, this effect seems to disappear at higher resolutions. As this observation is compatible with the concept of asymptotic fractal, we estimated the parameters c, L and Bm from the asymptotic fractal formula Br = Bm {1 + (r / L)c}-1 , where Br is the boundary length measured with a ruler of size r, Bm is the maximum boundary for r → 0, L is a constant, and c = asymptotic fractal dimension minus topological dimension (D - Dt) for r → ∞. Analyses of variance showed c to be significantly higher in the normal than malignant cases (P < 0.001), but log(L) and Bm to be significantly higher in the malignant cases (P < 0.001). A multivariate linear discrimination analysis on c, log(L) and Bm re-classified 76.6% of the cells correctly (84.8% of the normal and 67.5% of the tumor). Furthermore, this shows that asymptotic fractal analysis applied to nuclear profiles has great potential for shape quantification in diagnosis of oral cancer.

Fractal structure of sequential behaviour patterns: an indicator of stress

USGS Publications Warehouse

Alados, C.L.; Escos, J.M; Emlen, J.M.

1996-01-01

The detection of stress arising from parasitic infection bySarcoptes scabieisand from pregnancy is explored, using a fractal analysis of head lifting behaviour and feeding–non-feeding activity sequences in female Spanish ibex,Capra pyrenaica, under natural conditions. Because organisms under stress increase their metabolic rate and, in consequence, energy consumption, it follows that stress will, generally, lead to a reduction in complexity (fractal dimension) of exploratory behaviour. In the present study the fractal dimension of the three measures of complexity used declined with stress, both from pregnancy and from parasitic infection. This observation provides a new and effective way to assess the general state of animals’ health in the field, without the need for capture and handling.

[Simulation of three-dimensional green biomass of urban forests in Shenyang City and the factors affecting the biomass].

PubMed

Liu, Chang-Fu; He, Xing-Yuan; Chen, Wei; Zhao, Gui-Ling; Xue, Wen-Duo

2008-06-01

Based on the fractal theory of forest growth, stepwise regression was employed to pursue a convenient and efficient method of measuring the three-dimensional green biomass (TGB) of urban forests in small area. A total of thirteen simulation equations of TGB of urban forests in Shenyang City were derived, with the factors affecting the TGB analyzed. The results showed that the coefficients of determination (R2) of the 13 simulation equations ranged from 0.612 to 0.842. No evident pattern was shown in residual analysis, and the precisions were all higher than 87% (alpha = 0.05) and 83% (alpha = 0.01). The most convenient simulation equation was ln Y = 7.468 + 0.926 lnx1, where Y was the simulated TGB and x1 was basal area at breast height per hectare (SDB). The correlations between the standard regression coefficients of the simulation equations and 16 tree characteristics suggested that SDB was the main factor affecting the TGB of urban forests in Shenyang.

Skin inspired fractal strain sensors using a copper nanowire and graphite microflake hybrid conductive network.

PubMed

Jason, Naveen N; Wang, Stephen J; Bhanushali, Sushrut; Cheng, Wenlong

2016-09-22

This work demonstrates a facile "paint-on" approach to fabricate highly stretchable and highly sensitive strain sensors by combining one-dimensional copper nanowire networks with two-dimensional graphite microflakes. This paint-on approach allows for the fabrication of electronic skin (e-skin) patches which can directly replicate with high fidelity the human skin surface they are on, regardless of the topological complexity. This leads to high accuracy for detecting biometric signals for applications in personalised wearable sensors. The copper nanowires contribute to high stretchability and the graphite flakes offer high sensitivity, and their hybrid coating offers the advantages of both. To understand the topological effects on the sensing performance, we utilized fractal shaped elastomeric substrates and systematically compared their stretchability and sensitivity. We could achieve a high stretchability of up to 600% and a maximum gauge factor of 3000. Our simple yet efficient paint-on approach enabled facile fine-tuning of sensitivity/stretchability simply by adjusting ratios of 1D vs. 2D materials in the hybrid coating, and the topological structural designs. This capability leads to a wide range of biomedical sensors demonstrated here, including pulse sensors, prosthetic hands, and a wireless ankle motion sensor.

Terahertz response of fractal meta-atoms based on concentric rectangular square resonators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Song, Zhiqiang; Zhao, Zhenyu, E-mail: zyzhao@shnu.edu.cn; Shi, Wangzhou

We investigate the terahertz electromagnetic responses of fractal meta-atoms (MAs) induced by different mode coupling mechanisms. Two types of MAs based on concentric rectangular square (CRS) resonators are presented: independent CRS (I-CRS) and junctional-CRS (J-CRS). In I-CRS, each resonator works as an independent dipole so as to result in the multiple resonance modes when the fractal level is above 1. In J-CRS, however, the generated layer is rotated by π/2 radius to the adjacent CRS in one MA. The multiple resonance modes are coupled into a single mode resonance. The fractal level increasing induces resonance modes redshift in I-CRS whilemore » blueshift in J-CRS. When the fractal level is below 4, the mode Q factor of J-CRS is in between the two modes of I-CRS; when the fractal level is 4 or above, the mode Q factor of J-CRS exceeds the two modes of I-CRS. Furthermore, the modulation depth (MD) decreases in I-CRS while it increases in J-CRS with the increase in fractal levels. The surface currents analysis reveals that the capacitive coupling of modes in I-CRS results in the modes redshift, while the conductive coupling of modes in J-CRS induces the mode blueshift. A high Q mode with large MD can be achieved via conductive coupling between the resonators of different scales in a fractal MA.« less

Nonlinear Field Equations and Solitons as Particles

NASA Astrophysics Data System (ADS)

Maccari, Attilio

2006-05-01

Profound advances have recently interested nonlinear field theories and their exact or approximate solutions. We review the last results and point out some important unresolved questions. It is well known that quantum field theories are based upon Fourier series and the identification of plane waves with free particles. On the contrary, nonlinear field theories admit the existence of coherent solutions (dromions, solitons and so on). Moreover, one can construct lower dimensional chaotic patterns, periodic-chaotic patterns, chaotic soliton and dromion patterns. In a similar way, fractal dromion and lump patterns as well as stochastic fractal excitations can appear in the solution. We discuss in some detail a nonlinear Dirac field and a spontaneous symmetry breaking model that are reduced by means of the asymptotic perturbation method to a system of nonlinear evolution equations integrable via an appropriate change of variables. Their coherent, chaotic and fractal solutions are examined in some detail. Finally, we consider the possible identification of some types of coherent solutions with extended particles along the de Broglie-Bohm theory. However, the last findings suggest an inadequacy of the particle concept that appears only as a particular case of nonlinear field theories excitations.

High-Directivity Emissions with Flexible Beam Numbers and Beam Directions Using Gradient-Refractive-Index Fractal Metamaterial

PubMed Central

Xu, He-Xiu; Wang, Guang-Ming; Tao, Zui; Cui, Tie Jun

2014-01-01

A three-dimensional (3D) highly-directive emission system is proposed to enable beam shaping and beam steering capabilities in wideband frequencies. It is composed of an omnidirectional source antenna and several 3D gradient-refractive-index (GRIN) lenses. To engineer a broadband impedance match, the design method for these 3D lenses is established under the scenario of free-space excitation by using a planar printed monopole. For realizations and demonstrations, a kind of GRIN metamaterial is proposed, which is constructed by non-uniform fractal geometries. Due to the non-resonant and deep-subwavelength features of the fractal elements, the resulting 3D GRIN metamaterial lenses have extra wide bandwidth (3 to 7.5 GHz), and are capable of manipulating electromagnetic wavefronts accurately, advancing the state of the art of available GRIN lenses. The proposal for the versatile highly-directive emissions has been confirmed by simulations and measurements, showing that not only the number of beams can be arbitrarily tailored but also the beam directions can be steerable. The proposal opens a new way to control broadband highly-directive emissions with pre-designed directions, promising great potentials in modern wireless communication systems. PMID:25034268

Seasonal cycles on Titan from a Coupled Aerosol Microphysical and Global Circulation Model

NASA Astrophysics Data System (ADS)

Larson, Erik J.; Toon, Owen B.

2010-04-01

Understanding the aerosols on Titan is imperative for understanding the atmosphere as a whole. The aerosols affect the albedo, optical depth, and heating and cooling rates which in turn affects the winds on Titan. Correctly representing them in atmospheric models is crucial to understanding this atmosphere. Several groups have used GCMs to model Titan's atmosphere. Hourdin et al. (1995) were able to reproduce the super-rotating prograde winds. Rannou et al. (2004) found the aerosols accumulated at the poles, which increased the temperature gradient. The increased temperature gradient intensified the zonal winds. Friedson et al. (2009) produced a three- dimensional model for Titan using the NCAR CAM3 model, to which we coupled the aerosol microphysics model CARMA. Until now, there has not been a three- dimensional model that couples radiation, dynamics and aerosol microphysics to study the atmospheric properties of Titan. We have also made the aerosols produced by CARMA interactive with the radiation code in CAM. Preliminary results show that this model is capable of reproducing the seasonal changes in aerosols on Titan and many of the associated phenomena. For instance, the radiatively interactive aerosols are lifted more in the summer hemisphere than the non-interactive aerosols, which is necessary to reproduce the observed seasonal cycle of the albedo (Hutzell et al 1996). However, treating aerosols as spheres with Mie theory is inconsistent with laboratory and observational data that suggest the aerosols are fractal aggregates. We are currently incorporating fractal particle physics into the model. Changing the particles to fractals will affect the radiative properties of the particles, their distribution in the atmosphere, and should improve our fits to the data.

Multifractal analysis of mobile social networks

NASA Astrophysics Data System (ADS)

Zheng, Wei; Zhang, Zifeng; Deng, Yufan

2017-09-01

As Wireless Fidelity (Wi-Fi)-enabled handheld devices have been widely used, the mobile social networks (MSNs) has been attracting extensive attention. Fractal approaches have also been widely applied to characterierize natural networks as useful tools to depict their spatial distribution and scaling properties. Moreover, when the complexity of the spatial distribution of MSNs cannot be properly charaterized by single fractal dimension, multifractal analysis is required. For further research, we introduced a multifractal analysis method based on box-covering algorithm to describe the structure of MSNs. Using this method, we find that the networks are multifractal at different time interval. The simulation results demonstrate that the proposed method is efficient for analyzing the multifractal characteristic of MSNs, which provides a distribution of singularities adequately describing both the heterogeneity of fractal patterns and the statistics of measurements across spatial scales in MSNs.

Characterization of postural control deficit in whiplash patients by means of linear and nonlinear analyses - A pilot study.

PubMed

Madeleine, Pascal; Nielsen, Mogens; Arendt-Nielsen, Lars

2011-04-01

The ability to maintain balance is diminished in patients suffering from a whiplash injury. The aim of this study was to characterize the variability of postural control in patients with chronic whiplash injury. For this purpose, we analyzed static postural recordings from 11 whiplash patients and sex- and age-matched asymptomatic healthy volunteers. Static postural recordings were performed randomly with eyes open, eyes closed, and eyes open and speaking (dual task). Spatial-temporal changes of the center of pressure displacement were analyzed to assess the amplitude and structure of postural variability by computing, respectively, the standard deviation/coefficient of variation and sample entropy/fractal dimension of the time series. The amplitude of variability of the center of pressure was larger among whiplash patients compared with controls (P<0.001) while fractal dimension was lower (P<0.001). The sample entropy increased during both eyes closed and a simple dual task compared with eyes open (P<0.05). The analysis of postural control dynamics revealed increased amplitude of postural variability and decreased signal dimensionality related to the deficit in postural stability found in whiplash patients. Linear and nonlinear analyses can thus be helpful for the quantification of postural control in normal and pathological conditions. Copyright © 2010 Elsevier Ltd. All rights reserved.

A Brief Historical Introduction to Fractals and Fractal Geometry

ERIC Educational Resources Information Center

Debnath, Lokenath

2006-01-01

This paper deals with a brief historical introduction to fractals, fractal dimension and fractal geometry. Many fractals including the Cantor fractal, the Koch fractal, the Minkowski fractal, the Mandelbrot and Given fractal are described to illustrate self-similar geometrical figures. This is followed by the discovery of dynamical systems and…

Fractal dimension based damage identification incorporating multi-task sparse Bayesian learning

NASA Astrophysics Data System (ADS)

Huang, Yong; Li, Hui; Wu, Stephen; Yang, Yongchao

2018-07-01

Sensitivity to damage and robustness to noise are critical requirements for the effectiveness of structural damage detection. In this study, a two-stage damage identification method based on the fractal dimension analysis and multi-task Bayesian learning is presented. The Higuchi’s fractal dimension (HFD) based damage index is first proposed, directly examining the time-frequency characteristic of local free vibration data of structures based on the irregularity sensitivity and noise robustness analysis of HFD. Katz’s fractal dimension is then presented to analyze the abrupt irregularity change of the spatial curve of the displacement mode shape along the structure. At the second stage, the multi-task sparse Bayesian learning technique is employed to infer the final damage localization vector, which borrow the dependent strength of the two fractal dimension based damage indication information and also incorporate the prior knowledge that structural damage occurs at a limited number of locations in a structure in the absence of its collapse. To validate the capability of the proposed method, a steel beam and a bridge, named Yonghe Bridge, are analyzed as illustrative examples. The damage identification results demonstrate that the proposed method is capable of localizing single and multiple damages regardless of its severity, and show superior robustness under heavy noise as well.

Majorana Zero-Energy Mode and Fractal Structure in Fibonacci-Kitaev Chain

NASA Astrophysics Data System (ADS)

Ghadimi, Rasoul; Sugimoto, Takanori; Tohyama, Takami

2017-11-01

We theoretically study a Kitaev chain with a quasiperiodic potential, where the quasiperiodicity is introduced by a Fibonacci sequence. Based on an analysis of the Majorana zero-energy mode, we find the critical p-wave superconducting pairing potential separating a topological phase and a non-topological phase. The topological phase diagram with respect to Fibonacci potentials follow a self-similar fractal structure characterized by the box-counting dimension, which is an example of the interplay of fractal and topology like the Hofstadter's butterfly in quantum Hall insulators.

Fractal markets hypothesis and the global financial crisis: wavelet power evidence.

PubMed

Kristoufek, Ladislav

2013-10-04

We analyze whether the prediction of the fractal markets hypothesis about a dominance of specific investment horizons during turbulent times holds. To do so, we utilize the continuous wavelet transform analysis and obtained wavelet power spectra which give the crucial information about the variance distribution across scales and its evolution in time. We show that the most turbulent times of the Global Financial Crisis can be very well characterized by the dominance of short investment horizons which is in hand with the assertions of the fractal markets hypothesis.

Fractal Markets Hypothesis and the Global Financial Crisis: Wavelet Power Evidence

NASA Astrophysics Data System (ADS)

Kristoufek, Ladislav

2013-10-01

We analyze whether the prediction of the fractal markets hypothesis about a dominance of specific investment horizons during turbulent times holds. To do so, we utilize the continuous wavelet transform analysis and obtained wavelet power spectra which give the crucial information about the variance distribution across scales and its evolution in time. We show that the most turbulent times of the Global Financial Crisis can be very well characterized by the dominance of short investment horizons which is in hand with the assertions of the fractal markets hypothesis.

Fractal Markets Hypothesis and the Global Financial Crisis: Wavelet Power Evidence

PubMed Central

Kristoufek, Ladislav

2013-01-01

We analyze whether the prediction of the fractal markets hypothesis about a dominance of specific investment horizons during turbulent times holds. To do so, we utilize the continuous wavelet transform analysis and obtained wavelet power spectra which give the crucial information about the variance distribution across scales and its evolution in time. We show that the most turbulent times of the Global Financial Crisis can be very well characterized by the dominance of short investment horizons which is in hand with the assertions of the fractal markets hypothesis. PMID:24091386

Fractal mechanisms and heart rate dynamics. Long-range correlations and their breakdown with disease

NASA Technical Reports Server (NTRS)

Peng, C. K.; Havlin, S.; Hausdorff, J. M.; Mietus, J. E.; Stanley, H. E.; Goldberger, A. L.

1995-01-01

Under healthy conditions, the normal cardiac (sinus) interbeat interval fluctuates in a complex manner. Quantitative analysis using techniques adapted from statistical physics reveals the presence of long-range power-law correlations extending over thousands of heartbeats. This scale-invariant (fractal) behavior suggests that the regulatory system generating these fluctuations is operating far from equilibrium. In contrast, it is found that for subjects at high risk of sudden death (e.g., congestive heart failure patients), these long-range correlations break down. Application of fractal scaling analysis and related techniques provides new approaches to assessing cardiac risk and forecasting sudden cardiac death, as well as motivating development of novel physiologic models of systems that appear to be heterodynamic rather than homeostatic.

Low-dimensional chaos in magnetospheric activity from AE time series

NASA Technical Reports Server (NTRS)

Vassiliadis, D. V.; Sharma, A. S.; Eastman, T. E.; Papadopoulos, K.

1990-01-01

The magnetospheric response to the solar-wind input, as represented by the time-series measurements of the auroral electrojet (AE) index, has been examined using phase-space reconstruction techniques. The system was found to behave as a low-dimensional chaotic system with a fractal dimension of 3.6 and has Kolmogorov entropy less than 0.2/min. These indicate that the dynamics of the system can be adequately described by four independent variables, and that the corresponding intrinsic time scale is of the order of 5 min. The relevance of the results to magnetospheric modeling is discussed.

Retinal vasculature classification using novel multifractal features

NASA Astrophysics Data System (ADS)

Ding, Y.; Ward, W. O. C.; Duan, Jinming; Auer, D. P.; Gowland, Penny; Bai, L.

2015-11-01

Retinal blood vessels have been implicated in a large number of diseases including diabetic retinopathy and cardiovascular diseases, which cause damages to retinal blood vessels. The availability of retinal vessel imaging provides an excellent opportunity for monitoring and diagnosis of retinal diseases, and automatic analysis of retinal vessels will help with the processes. However, state of the art vascular analysis methods such as counting the number of branches or measuring the curvature and diameter of individual vessels are unsuitable for the microvasculature. There has been published research using fractal analysis to calculate fractal dimensions of retinal blood vessels, but so far there has been no systematic research extracting discriminant features from retinal vessels for classifications. This paper introduces new methods for feature extraction from multifractal spectra of retinal vessels for classification. Two publicly available retinal vascular image databases are used for the experiments, and the proposed methods have produced accuracies of 85.5% and 77% for classification of healthy and diabetic retinal vasculatures. Experiments show that classification with multiple fractal features produces better rates compared with methods using a single fractal dimension value. In addition to this, experiments also show that classification accuracy can be affected by the accuracy of vessel segmentation algorithms.

Visual information processing; Proceedings of the Meeting, Orlando, FL, Apr. 20-22, 1992

NASA Technical Reports Server (NTRS)

Huck, Friedrich O. (Editor); Juday, Richard D. (Editor)

1992-01-01

Topics discussed in these proceedings include nonlinear processing and communications; feature extraction and recognition; image gathering, interpolation, and restoration; image coding; and wavelet transform. Papers are presented on noise reduction for signals from nonlinear systems; driving nonlinear systems with chaotic signals; edge detection and image segmentation of space scenes using fractal analyses; a vision system for telerobotic operation; a fidelity analysis of image gathering, interpolation, and restoration; restoration of images degraded by motion; and information, entropy, and fidelity in visual communication. Attention is also given to image coding methods and their assessment, hybrid JPEG/recursive block coding of images, modified wavelets that accommodate causality, modified wavelet transform for unbiased frequency representation, and continuous wavelet transform of one-dimensional signals by Fourier filtering.

Nonlinear stochastic interacting dynamics and complexity of financial gasket fractal-like lattice percolation

NASA Astrophysics Data System (ADS)

Zhang, Wei; Wang, Jun

2018-05-01

A novel nonlinear stochastic interacting price dynamics is proposed and investigated by the bond percolation on Sierpinski gasket fractal-like lattice, aim to make a new approach to reproduce and study the complexity dynamics of real security markets. Fractal-like lattices correspond to finite graphs with vertices and edges, which are similar to fractals, and Sierpinski gasket is a well-known example of fractals. Fractional ordinal array entropy and fractional ordinal array complexity are introduced to analyze the complexity behaviors of financial signals. To deeper comprehend the fluctuation characteristics of the stochastic price evolution, the complexity analysis of random logarithmic returns and volatility are preformed, including power-law distribution, fractional sample entropy and fractional ordinal array complexity. For further verifying the rationality and validity of the developed stochastic price evolution, the actual security market dataset are also studied with the same statistical methods for comparison. The empirical results show that this stochastic price dynamics can reconstruct complexity behaviors of the actual security markets to some extent.

The Fractal-based Analysis of the Regulation of Vascular Remodeling in the Quail Chorioallantoic Membrane

NASA Technical Reports Server (NTRS)

Smith, Genee S.

2004-01-01

Critical to the advancement of space exploration is the safety and well being of astronauts while in space. This study focuses on the second highest of NASA-defined risk categories for human space exploration, cardiovascular alterations. Current research of this problem is being tackled by investigating angiogenesis through vascular remodeling. Angiogenesis is the growth and formation of new blood vessels. Angiogenesis is an important part of maintaining normal development and bodily functions. The loss of control of this process, either insufficient or excessive vascular growth, is considered a common denominator in many diseases, such as cancer, diabetes, and coronary artery disease. Objectives are presently being met by observing the effects of various regulators, like thrombospondin 1 (TSP-1) and a novel vessel tortuosity factor (TF), through the use of the chorioallantoic membrane (CAM) of Japanese quail embryos, which enables the direct optical imaging of 2-dimensional vascular branching trees. Research within the CAM is being performed to deduce numerous methods of regulating vessel growth. This project centers on the ability of a novel vessel regulator to affect angiogenesis. For example, it is hypothesized that the TSP-1 will inhibit the growth of CAM vasculature. Fractal/VESGEN-based techniques and PTV analysis are the methodologies used to investigate vascular differentiation. This tactic is used to quantify results and measure the growth patterns and morphology of blood vessels. The regulatory mechanisms posed by this vessel regulator can be deduced by alterations found within the vasculature patterns of quail embryos.

The Calculation of Fractal Dimension in the Presence of Non-Fractal Clutter

NASA Technical Reports Server (NTRS)

Herren, Kenneth A.; Gregory, Don A.

1999-01-01

The area of information processing has grown dramatically over the last 50 years. In the areas of image processing and information storage the technology requirements have far outpaced the ability of the community to meet demands. The need for faster recognition algorithms and more efficient storage of large quantities of data has forced the user to accept less than lossless retrieval of that data for analysis. In addition to clutter that is not the object of interest in the data set, often the throughput requirements forces the user to accept "noisy" data and to tolerate the clutter inherent in that data. It has been shown that some of this clutter, both the intentional clutter (clouds, trees, etc) as well as the noise introduced on the data by processing requirements can be modeled as fractal or fractal-like. Traditional methods using Fourier deconvolution on these sources of noise in frequency space leads to loss of signal and can, in many cases, completely eliminate the target of interest. The parameters that characterize fractal-like noise (predominately the fractal dimension) have been investigated and a technique to reduce or eliminate noise from real scenes has been developed. Examples of clutter reduced images are presented.

Fractal Feature of Particle-Size Distribution in the Rhizospheres and Bulk Soils during Natural Recovery on the Loess Plateau, China

PubMed Central

Song, Zilin; Zhang, Chao; Liu, Guobin; Qu, Dong; Xue, Sha

2015-01-01

The application of fractal geometry to describe soil structure is an increasingly useful tool for better understanding the performance of soil systems. Only a few studies, however, have focused on the structure of rhizospheric zones, where energy flow and nutrient recycling most frequently occur. We used fractal dimensions to investigate the characteristics of particle-size distribution (PSD) in the rhizospheres and bulk soils of six croplands abandoned for 1, 5, 10, 15, 20, and 30 years on the Loess Plateau of China and evaluated the changes over successional time. The PSDs of the rhizospheres and the fractal dimensions between rhizosphere soil and bulk soils during the natural succession differed significantly due to the influence of plant roots. The rhizospheres had higher sand (0.05–1.00 mm) contents, lower silt (<0.002 mm) contents, and lower fractal dimensions than the bulk soils during the early and intermediate successional stages (1–15 years). The fractal dimensions of the rhizosphere soil and bulk soil ranged from 2.102 to 2.441 and from 2.214 to 2.459, respectively, during the 30-year restoration. Rhizospheric clay and silt contents and fractal dimension tended to be higher and sand content tended to be lower as abandonment age increased, but the bulk soils had the opposite trend. Linear regression analysis indicated that the fractal dimensions of both the rhizospheres and bulk soils were significantly linearly correlated with clay, sand, organic-carbon, and total-nitrogen contents, with R 2 ranging from 0.526 to 0.752 (P<0.001). In conclusion, PSD differed significantly between the rhizosphere soil and bulk soil. The fractal dimension was a sensitive and useful index for quantifying changes in the properties of the different soil zones. This study will greatly aid the application of the fractal method for describing soil structure and nutrient status and the understanding of the performance of rhizospheric zones during ecological restoration. PMID:26368339

Analysis of coined quantum walks with renormalization

NASA Astrophysics Data System (ADS)

Boettcher, Stefan; Li, Shanshan

2018-01-01

We introduce a framework to analyze quantum algorithms with the renormalization group (RG). To this end, we present a detailed analysis of the real-space RG for discrete-time quantum walks on fractal networks and show how deep insights into the analytic structure as well as generic results about the long-time behavior can be extracted. The RG flow for such a walk on a dual Sierpinski gasket and a Migdal-Kadanoff hierarchical network is obtained explicitly from elementary algebraic manipulations, after transforming the unitary evolution equation into Laplace space. Unlike for classical random walks, we find that the long-time asymptotics for the quantum walk requires consideration of a diverging number of Laplace poles, which we demonstrate exactly for the closed-form solution available for the walk on a one-dimensional loop. In particular, we calculate the probability of the walk to overlap with its starting position, which oscillates with a period that scales as NdwQ/df with system size N . While the largest Jacobian eigenvalue λ1 of the RG flow merely reproduces the fractal dimension, df=log2λ1 , the asymptotic analysis shows that the second Jacobian eigenvalue λ2 becomes essential to determine the dimension of the quantum walk via dwQ=log2√{λ1λ2 } . We trace this fact to delicate cancellations caused by unitarity. We obtain identical relations for other networks, although the details of the RG analysis may exhibit surprisingly distinct features. Thus, our conclusions—which trivially reproduce those for regular lattices with translational invariance with df=d and dwQ=1 —appear to be quite general and likely apply to networks beyond those studied here.

Fractal analysis of polyferric chloride-humic acid (PFC-HA) flocs in different topological spaces.

PubMed

Wang, Yili; Lu, Jia; Baiyu, Du; Shi, Baoyou; Wang, Dongsheng

2009-01-01

The fractal dimensions in different topological spaces of polyferric chloride-humic acid (PFC-HA) flocs, formed in flocculating different kinds of humic acids (HA) water at different initial pH (9.0, 7.0, 5.0) and PFC dosages, were calculated by effective density-maximum diameter, image analysis, and N2 absorption-desorption methods, respectively. The mass fractal dimensions (Df) of PFC-HA flocs were calculated by bi-logarithm relation of effective density with maximum diameter and Logan empirical equation. The Df value was more than 2.0 at initial pH of 7.0, which was 11% and 13% higher than those at pH 9.0 and 5.0, respectively, indicating the most compact flocs formed in flocculated HA water at initial pH of 7.0. The image analysis for those flocs indicates that after flocculating the HA water at initial pH greater than 7.0 with PFC flocculant, the fractal dimensions of D2 (logA vs. logdL) and D3 (logVsphere VS. logdL) of PFC-HA flocs decreased with the increase of PFC dosages, and PFC-HA flocs showed a gradually looser structure. At the optimum dosage of PFC, the D2 (logA vs. logdL) values of the flocs show 14%-43% difference with their corresponding Df, and they even had different tendency with the change of initial pH values. However, the D2 values of the flocs formed at three different initial pH in HA solution had a same tendency with the corresponding Dr. Based on fractal Frenkel-Halsey-Hill (FHH) adsorption and desorption equations, the pore surface fractal dimensions (Ds) for dried powders of PFC-HA flocs formed in HA water with initial pH 9.0 and 7.0 were all close to 2.9421, and the Ds values of flocs formed at initial pH 5.0 were less than 2.3746. It indicated that the pore surface fractal dimensions of PFC-HA flocs dried powder mainly show the irregularity from the mesopore-size distribution and marcopore-size distribution.

Communication: Dimensionality of the ionic conduction pathways in glass and the mixed-alkali effect.

PubMed

Novy, Melissa; Avila-Paredes, Hugo; Kim, Sangtae; Sen, Sabyasachi

2015-12-28

A revised empirical relationship between the power law exponent of ac conductivity dispersion and the dimensionality of the ionic conduction pathway is established on the basis of electrical impedance spectroscopic (EIS) measurements on crystalline ionic conductors. These results imply that the "universal" ac conductivity dispersion observed in glassy solids is associated with ionic transport along fractal pathways. EIS measurements on single-alkali glasses indicate that the dimensionality of this pathway D is ∼2.5, while in mixed-alkali glasses, D is lower and goes through a minimum value of ∼2.2 when the concentrations of the two alkalis become equal. D and σ display similar variation with alkali composition, thus suggesting a topological origin of the mixed-alkali effect.

Procedure for estimating fracture energy from fracture surface roughness

DOEpatents

Williford, Ralph E.

1989-01-01

The fracture energy of a material is determined by first measuring the length of a profile of a section through a fractured surface of the material taken on a plane perpendicular to the mean plane of that surface, then determining the fractal dimensionality of the surface. From this, the yield strength of the material, and the Young's Modulus of that material, the fracture energy is calculated.

Polarimetric Wavelet Fractal Remote Sensing Principles for Space Materials (Preprint)

DTIC Science & Technology

2012-06-04

previously introduced 9-10, 28. The combination of polarimetry and wavelet-fractal analysis yields enhanced knowledge of the spatial-temporal-frequency...applications in situations that require analysis over very short time durations or where information is localized, and have been combined with polarimetry ...and D.B. Chenault, “Near Infrared Imaging Polarimetry ”, Proc. SPIE 4481, pp. 30-31, 2001. [8] A.B. Mahler, P. Smith, R. Chipman, G. Smith, N

Proteins as sponges: a statistical journey along protein structure organization principles.

PubMed

Paola, Luisa Di; Paci, Paola; Santoni, Daniele; Ruvo, Micol De; Giuliani, Alessandro

2012-02-27

The analysis of a large database of protein structures by means of topological and shape indexes inspired by complex network and fractal analysis shed light on some organizational principles of proteins. Proteins appear much more similar to "fractal" sponges than to closely packed spheres, casting doubts on the tenability of the hydrophobic core concept. Principal component analysis highlighted three main order parameters shaping the protein universe: (1) "size", with the consequent generation of progressively less dense and more empty structures at an increasing number of residues, (2) "microscopic structuring", linked to the existence of a spectrum going from the prevalence of heterologous (different hydrophobicity) to the prevalence of homologous (similar hydrophobicity) contacts, and (3) "fractal shape", an organizing protein data set along a continuum going from approximately linear to very intermingled structures. Perhaps the time has come for seriously taking into consideration the real relevance of time-honored principles like the hydrophobic core and hydrophobic effect.

Delineation of geochemical anomalies based on stream sediment data utilizing fractal modeling and staged factor analysis

NASA Astrophysics Data System (ADS)

Afzal, Peyman; Mirzaei, Misagh; Yousefi, Mahyar; Adib, Ahmad; Khalajmasoumi, Masoumeh; Zarifi, Afshar Zia; Foster, Patrick; Yasrebi, Amir Bijan

2016-07-01

Recognition of significant geochemical signatures and separation of geochemical anomalies from background are critical issues in interpretation of stream sediment data to define exploration targets. In this paper, we used staged factor analysis in conjunction with the concentration-number (C-N) fractal model to generate exploration targets for prospecting Cr and Fe mineralization in Balvard area, SE Iran. The results show coexistence of derived multi-element geochemical signatures of the deposit-type sought and ultramafic-mafic rocks in the NE and northern parts of the study area indicating significant chromite and iron ore prospects. In this regard, application of staged factor analysis and fractal modeling resulted in recognition of significant multi-element signatures that have a high spatial association with host lithological units of the deposit-type sought, and therefore, the generated targets are reliable for further prospecting of the deposit in the study area.

Mapping of the Bak, Tang, and Wiesenfeld sandpile model on a two-dimensional Ising-correlated percolation lattice to the two-dimensional self-avoiding random walk.

PubMed

Cheraghalizadeh, J; Najafi, M N; Dashti-Naserabadi, H; Mohammadzadeh, H

2017-11-01

The self-organized criticality on the random fractal networks has many motivations, like the movement pattern of fluid in the porous media. In addition to the randomness, introducing correlation between the neighboring portions of the porous media has some nontrivial effects. In this paper, we consider the Ising-like interactions between the active sites as the simplest method to bring correlations in the porous media, and we investigate the statistics of the BTW model in it. These correlations are controlled by the artificial "temperature" T and the sign of the Ising coupling. Based on our numerical results, we propose that at the Ising critical temperature T_{c} the model is compatible with the universality class of two-dimensional (2D) self-avoiding walk (SAW). Especially the fractal dimension of the loops, which are defined as the external frontier of the avalanches, is very close to D_{f}^{SAW}=4/3. Also, the corresponding open curves has conformal invariance with the root-mean-square distance R_{rms}∼t^{3/4} (t being the parametrization of the curve) in accordance with the 2D SAW. In the finite-size study, we observe that at T=T_{c} the model has some aspects compatible with the 2D BTW model (e.g., the 1/log(L)-dependence of the exponents of the distribution functions) and some in accordance with the Ising model (e.g., the 1/L-dependence of the fractal dimensions). The finite-size scaling theory is tested and shown to be fulfilled for all statistical observables in T=T_{c}. In the off-critical temperatures in the close vicinity of T_{c} the exponents show some additional power-law behaviors in terms of T-T_{c} with some exponents that are reported in the text. The spanning cluster probability at the critical temperature also scales with L^{1/2}, which is different from the regular 2D BTW model.

Assessment of changes in crystallization properties of pressurized milk fat.

PubMed

Staniewski, Bogusław; Smoczyński, Michał; Staniewska, Katarzyna; Baranowska, Maria; Kiełczewska, Katarzyna; Zulewska, Justyna

2015-04-01

The aim of the study was to demonstrate the use of fractal image analysis as a possible tool to monitor the effect of pressurization on the crystallization pattern of anhydrous milk fat. This approach can be useful when developing new products based on milk fat. The samples were subjected to different hydrostatic pressure (100, 200, 300, and 400 MPa) and temperature (10 and 40 °C) treatments. The crystallization microphotographs were taken with a scanning electron microscope. The image analysis of scanning electron microscope photographs was done to determine a fractal dimension. Milk-fat pressurization under the applied parameters resulted in slight, but statistically significant, changes in the course of crystallization curves, related to the triacylglycerol fraction crystallizing in the lowest temperature (I exothermic effect). These changes were dependent on the value of pressure but not dependent on the temperatures applied during the process of pressurization (at either 10 or 40 °C). In turn, significant differences were observed in crystallization images of milk-fat samples subjected to this process compared with the control sample. The results of additional fractal analysis additionally demonstrated the highest degree of irregularity of the surface of the crystalline form for the nonpressurized sample and the samples pressurized at 200 and 300 MPa at 10 °C. The lowest value of fractal dimension-indicative of the least irregularity-was achieved for the fat samples pressurized at 400 MPa, 10 °C and at 100 MPa, 40 °C. The possibilities of wider application of the fractal analysis for the evaluation of effects of parameters of various technological processes on crystallization properties of milk fat require further extensive investigations. Copyright © 2015 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

Diagnosis of Lung Cancer by Fractal Analysis of Damaged DNA

PubMed Central

Namazi, Hamidreza; Kiminezhadmalaie, Mona

2015-01-01

Cancer starts when cells in a part of the body start to grow out of control. In fact cells become cancer cells because of DNA damage. A DNA walk of a genome represents how the frequency of each nucleotide of a pairing nucleotide couple changes locally. In this research in order to study the cancer genes, DNA walk plots of genomes of patients with lung cancer were generated using a program written in MATLAB language. The data so obtained was checked for fractal property by computing the fractal dimension using a program written in MATLAB. Also, the correlation of damaged DNA was studied using the Hurst exponent measure. We have found that the damaged DNA sequences are exhibiting higher degree of fractality and less correlation compared with normal DNA sequences. So we confirmed this method can be used for early detection of lung cancer. The method introduced in this research not only is useful for diagnosis of lung cancer but also can be applied for detection and growth analysis of different types of cancers. PMID:26539245

Analysis of Geographical Distribution Patterns in Plants Using Fractals

NASA Astrophysics Data System (ADS)

Bari, A.; Ayad, G.; Padulosi, S.; Hodgkin, T.; Martin, A.; Gonzalez-Andujar, J. L.; Brown, A. H. D.

Geographical distribution patterns in plants have been observed since primeval times and have been used by plant explorers to trace the origin of plants species. These patterns embody the effects of fundamental law-like processes. Diversity in plants has also been found to be proportionate with the area, and this scaling behavior is also known as fractal behavior. In the present study, we use fractal geometry to analyze the distribution patterns of wild taxa of cowpea with the objective to locate where their diversity would be the highest to aid in the planning of targeted explorations and conservation measures.

Fractal model of polarization switching kinetics in ferroelectrics under nonequilibrium conditions of electron irradiation

NASA Astrophysics Data System (ADS)

Maslovskaya, A. G.; Barabash, T. K.

2018-03-01

The paper presents the results of the fractal and multifractal analysis of polarization switching current in ferroelectrics under electron irradiation, which allows statistical memory effects to be estimated at dynamics of domain structure. The mathematical model of formation of electron beam-induced polarization current in ferroelectrics was suggested taking into account the fractal nature of domain structure dynamics. In order to realize the model the computational scheme was constructed using the numerical solution approximation of fractional differential equation. Evidences of electron beam-induced polarization switching process in ferroelectrics were specified at a variation of control model parameters.

Nonlinear dynamics, fractals, cardiac physiology and sudden death

NASA Technical Reports Server (NTRS)

Goldberger, Ary L.

1987-01-01

The authors propose a diametrically opposite viewpoint to the generally accepted tendency of equating healthy function with order and disease with chaos. With regard to the question of sudden cardiac death and chaos, it is suggested that certain features of dynamical chaos related to fractal structure and fractal dynamics may be important organizing principles in normal physiology and that certain pathologies, including ventricular fibrillation, represent a class of 'pathological periodicities'. Some laboratory work bearing on the relation of nonlinear analysis to physiological and pathophysiological data is briefly reviewed, with tentative theories and models described in reference to the mechanism of ventricular fibrillation.

Fractal analysis of the hydraulic conductivity on a sandy porous media reproduced in a laboratory facility.

NASA Astrophysics Data System (ADS)

de Bartolo, S.; Fallico, C.; Straface, S.; Troisi, S.; Veltri, M.

2009-04-01

The complexity characterization of the porous media structure, in terms of the "pore" phase and the "solid" phase, can be carried out by means of the fractal geometry which is able to put in relationship the soil structural properties and the water content. It is particularly complicated to describe analytically the hydraulic conductivity for the irregularity of the porous media structure. However these can be described by many fractal models considering the soil structure as the distribution of particles dimensions, the distribution of the solid aggregates, the surface of the pore-solid interface and the fractal mass of the "pore" and "solid" phases. In this paper the fractal model of Yu and Cheng (2002) and Yu and Liu (2004), for a saturated bidispersed porous media, was considered. This model, using the Sierpinsky-type gasket scheme, doesn't contain empiric constants and furnishes a well accord with the experimental data. For this study an unconfined aquifer was reproduced by means of a tank with a volume of 10 Ã- 7 Ã- 3 m3, filled with a homogeneous sand (95% of SiO2), with a high percentage (86.4%) of grains between 0.063mm and 0.125mm and a medium-high permeability. From the hydraulic point of view, 17 boreholes, a pumping well and a drainage ring around its edge were placed. The permeability was measured utilizing three different methods, consisting respectively in pumping test, slug test and laboratory analysis of an undisturbed soil cores, each of that involving in the measurement a different support volume. The temporal series of the drawdown obtained by the pumping test were analyzed by the Neuman-type Curve method (1972), because the saturated part above the bottom of the facility represents an unconfined aquifer. The data analysis of the slug test were performed by the Bouwer & Rice (1976) method and the laboratory analysis were performed on undisturbed saturated soil samples utilizing a falling head permeameter. The obtained values either of the fractal dimension of the area of the pores (Df) or of the fractal dimension of capillary tortuosity (DT), very similar to those reported in literature (Yu and Cheng, 2002; Yu and Liu, 2004; Yu, 2005) and falling in the range of definition (1 < Df < 2), resulted very close to those carried out in a previous study performed on the same apparatus but with a limited number of values (De Bartolo et al., in review). In fact in the present study the laboratory analysis were performed on other 10 undisturbed soil samples and moreover three new values of slug test and 12 new of pumping test were considered. Moreover the trend of DT growing with the scale length (L) was confirmed, as well as the invariability of, due to the homogeneity of the considered porous media. The linear scaling law of the permeability (k) close to scale length was investigated furnishing more reliable results. However for a better definition of a law of scale for Df, DT and k several number of scale length are need and a greater number of experimental data should be carried out. For this purpose the considered experimental apparatus is limited from its restricted dimensions and geometric bounds; therefore further investigations in experimental field are desirable. Bibliografy Bouwer, H. & Rice, R. C. 1976. A Slug Test for Hydraulic Conductivity of Unconfined Aquifers With Completely or Partially Penetrating Wells, Water Resources Research, 12(3). De Bartolo, S., Fallico, C., Straface, S., Troisi, S. & Veltri M. (in review). Scaling of the hydraulic conductivity measurements by a fractal analysis on an unconfined aquifer reproduced in a laboratory facility, Geoderma Special Issue 2008. Neuman, S.P. 1972. Theory of flow in unconfined aquifers considering delayed response of the water table, Water Resources Research, 8(4), 1031-1045. Yu, B.M. 2005. Fractal Character for Tortuous Streamtubes in Porous Media, Chin. Phis. Lett., 22(1), 158. Yu, B.M. & Cheng, P. 2002. A Fractal Permeability Model for Bi-Dispersed Porous Media, Int. J. Heat Mass Transfer 45(14), 2983. Yu, B.M. & Liu W. 2004. Fractal Analysis of Permeabilities for Porous Media, American Institute of Chemical Engineers 50(1), 46-57.

A fractal nature for polymerized laminin.

PubMed

Hochman-Mendez, Camila; Cantini, Marco; Moratal, David; Salmeron-Sanchez, Manuel; Coelho-Sampaio, Tatiana

2014-01-01

Polylaminin (polyLM) is a non-covalent acid-induced nano- and micro-structured polymer of the protein laminin displaying distinguished biological properties. Polylaminin stimulates neuritogenesis beyond the levels achieved by ordinary laminin and has been shown to promote axonal regeneration in animal models of spinal cord injury. Here we used confocal fluorescence microscopy (CFM), scanning electron microscopy (SEM) and atomic force microscopy (AFM) to characterize its three-dimensional structure. Renderization of confocal optical slices of immunostained polyLM revealed the aspect of a loose flocculated meshwork, which was homogeneously stained by the antibody. On the other hand, an ordinary matrix obtained upon adsorption of laminin in neutral pH (LM) was constituted of bulky protein aggregates whose interior was not accessible to the same anti-laminin antibody. SEM and AFM analyses revealed that the seed unit of polyLM was a flat polygon formed in solution whereas the seed structure of LM was highly heterogeneous, intercalating rod-like, spherical and thin spread lamellar deposits. As polyLM was visualized at progressively increasing magnifications, we observed that the morphology of the polymer was alike independently of the magnification used for the observation. A search for the Hausdorff dimension in images of the two matrices showed that polyLM, but not LM, presented fractal dimensions of 1.55, 1.62 and 1.70 after 1, 8 and 12 hours of adsorption, respectively. Data in the present work suggest that the intrinsic fractal nature of polymerized laminin can be the structural basis for the fractal-like organization of basement membranes in the neurogenic niches of the central nervous system.

Fractal correlation properties of R-R interval dynamics and mortality in patients with depressed left ventricular function after an acute myocardial infarction

NASA Technical Reports Server (NTRS)

Huikuri, H. V.; Makikallio, T. H.; Peng, C. K.; Goldberger, A. L.; Hintze, U.; Moller, M.

2000-01-01

BACKGROUND: Preliminary data suggest that the analysis of R-R interval variability by fractal analysis methods may provide clinically useful information on patients with heart failure. The purpose of this study was to compare the prognostic power of new fractal and traditional measures of R-R interval variability as predictors of death after acute myocardial infarction. METHODS AND RESULTS: Time and frequency domain heart rate (HR) variability measures, along with short- and long-term correlation (fractal) properties of R-R intervals (exponents alpha(1) and alpha(2)) and power-law scaling of the power spectra (exponent beta), were assessed from 24-hour Holter recordings in 446 survivors of acute myocardial infarction with a depressed left ventricular function (ejection fraction

Multitemporal and Multiscaled Fractal Analysis of Landsat Satellite Data Using the Image Characterization and Modeling System (ICAMS)

NASA Technical Reports Server (NTRS)

Quattrochi, Dale A.; Emerson, Charles W.; Lam, Nina Siu-Ngan; Laymon, Charles A.

1997-01-01

The Image Characterization And Modeling System (ICAMS) is a public domain software package that is designed to provide scientists with innovative spatial analytical tools to visualize, measure, and characterize landscape patterns so that environmental conditions or processes can be assessed and monitored more effectively. In this study ICAMS has been used to evaluate how changes in fractal dimension, as a landscape characterization index, and resolution, are related to differences in Landsat images collected at different dates for the same area. Landsat Thematic Mapper (TM) data obtained in May and August 1993 over a portion of the Great Basin Desert in eastern Nevada were used for analysis. These data represent contrasting periods of peak "green-up" and "dry-down" for the study area. The TM data sets were converted into Normalized Difference Vegetation Index (NDVI) images to expedite analysis of differences in fractal dimension between the two dates. These NDVI images were also resampled to resolutions of 60, 120, 240, 480, and 960 meters from the original 30 meter pixel size, to permit an assessment of how fractal dimension varies with spatial resolution. Tests of fractal dimension for two dates at various pixel resolutions show that the D values in the August image become increasingly more complex as pixel size increases to 480 meters. The D values in the May image show an even more complex relationship to pixel size than that expressed in the August image. Fractal dimension for a difference image computed for the May and August dates increase with pixel size up to a resolution of 120 meters, and then decline with increasing pixel size. This means that the greatest complexity in the difference images occur around a resolution of 120 meters, which is analogous to the operational domain of changes in vegetation and snow cover that constitute differences between the two dates.

Morphology and Fractal Characterization of Multiscale Pore Structures for Organic-Rich Lacustrine Shale Reservoirs

NASA Astrophysics Data System (ADS)

Wang, Yang; Wu, Caifang; Zhu, Yanming; Chen, Shangbin; Liu, Shimin; Zhang, Rui

Lacustrine shale gas has received considerable attention and has been playing an important role in unconventional natural gas production in China. In this study, multiple techniques, including total organic carbon (TOC) analysis, X-ray diffraction (XRD) analysis, field emission scanning electron microscopy (FE-SEM), helium pycnometry and low-pressure N2 adsorption have been applied to characterize the pore structure of lacustrine shale of Upper Triassic Yanchang Formation from the Ordos Basin. The results show that organic matter (OM) pores are the most important type dominating the pore system, while interparticle (interP) pores, intraparticle (intraP) and microfractures are also usually observed between or within different minerals. The shapes of OM pores are less complex compared with the other two pore types based on the Image-Pro Plus software analysis. In addition, the specific surface area ranges from 2.76m2/g to 10.26m2/g and the pore volume varies between 0.52m3/100g and 1.31m3/100g. Two fractal dimensions D1 and D2 were calculated using Frenkel-Halsey-Hill (FHH) method, with D1 varying between 2.510 and 2.632, and D2 varying between 2.617 and 2.814. Further investigation indicates that the fractal dimensions exhibit positive correlations with TOC contents, whereas there is no definite relationship observed between fractal dimensions and clay minerals. Meanwhile, the fractal dimensions increase with the increase in specific surface area, and is negatively correlated with the pore size.

Morphometrical differences between resectable and non-resectable pancreatic cancer: a fractal analysis.

PubMed

Vasilescu, Catalin; Giza, Dana Elena; Petrisor, Petre; Dobrescu, Radu; Popescu, Irinel; Herlea, Vlad

2012-01-01

Pancreatic cancer is a highly aggressive cancer with a rising incidence and poor prognosis despite active surgical treatment. Candidates for surgical resection should be carefully selected. In order to avoid unnecessary laparotomy it is useful to identify reliable factors that may predict resectability. Nuclear morphometry and fractal dimension of pancreatic nuclear features could provide important preoperative information in assessing pancreas resectability. Sixty-one patients diagnosed with pancreatic cancer were enrolled in this retrospective study between 2003 and 2005. Patients were divided into two groups: one resectable cancer group and one with non-resectable pancreatic cancer. Morphometric parameters measured were: nuclear area, length of minor axis and length of major axis. Nuclear shape and chromatin distribution of the pancreatic tumor cells were both estimated using fractal dimension. Morphometric measurements have shown significant differences between the nuclear area of the resectable group and the non-resectable group (61.9 ± 19.8µm vs. 42.2 ± 15.6µm). Fractal dimension of the nuclear outlines and chromatin distribution was found to have a higher value in the non-resectable group (p<0.05). Objective measurements should be performed to improve risk assessment and therapeutic decisions in pancreatic cancer. Nuclear morphometry of the pancreatic nuclear features can provide important pre-operative information in resectability assessment. The fractal dimension of the nuclear shape and chromatin distribution may be considered a new promising adjunctive tool for conventional pathological analysis.

A Note on the Fractal Behavior of Hydraulic Conductivity and Effective Porosity for Experimental Values in a Confined Aquifer

PubMed Central

De Bartolo, Samuele; Fallico, Carmine; Veltri, Massimo

2013-01-01

Hydraulic conductivity and effective porosity values for the confined sandy loam aquifer of the Montalto Uffugo (Italy) test field were obtained by laboratory and field measurements; the first ones were carried out on undisturbed soil samples and the others by slug and aquifer tests. A direct simple-scaling analysis was performed for the whole range of measurement and a comparison among the different types of fractal models describing the scale behavior was made. Some indications about the largest pore size to utilize in the fractal models were given. The results obtained for a sandy loam soil show that it is possible to obtain global indications on the behavior of the hydraulic conductivity versus the porosity utilizing a simple scaling relation and a fractal model in coupled manner. PMID:24385876

Active tectonics on Deception Island (West-Antarctica): A new approach by using the fractal anisotropy of lineaments, fault slip measurements and the caldera collapse shape

USGS Publications Warehouse

Pérez-López, R.; Giner-Robles, J.L.; Martínez-Díaz, J.J.; Rodríguez-Pascua, M.A.; Bejar, M.; Paredes, C.; González-Casado, J.M.

2007-01-01

The tectonic field on Deception Island (South Shetlands, West Antarctica) is determined from structural and fractal analyses. Three different analyses are applied to the study of the strain and stress fields in the area: (1) field measurements of faults (strain analysis), (2) fractal geometry of the spatial distribution of lineaments and (3) the caldera shape (stress analyses). In this work, the identified strain field is extensional with the maximum horizontal shortening trending NE-SW and NW-SE. The fractal technique applied to the spatial distribution of lineaments indicates a stress field with SHMAX oriented NE-SW. The elliptical caldera of Deception Island, determined from field mapping, satellite imagery, vents and fissure eruptions, has an elongate shape and a stress field with SHMAX trending NE-SW.

Fractal Branching in Vascular Trees and Networks by VESsel GENeration Analysis (VESGEN)

NASA Technical Reports Server (NTRS)

Parsons-Wingerter, Patricia A.

2016-01-01

Vascular patterning offers an informative multi-scale, fractal readout of regulatory signaling by complex molecular pathways. Understanding such molecular crosstalk is important for physiological, pathological and therapeutic research in Space Biology and Astronaut countermeasures. When mapped out and quantified by NASA's innovative VESsel GENeration Analysis (VESGEN) software, remodeling vascular patterns become useful biomarkers that advance out understanding of the response of biology and human health to challenges such as microgravity and radiation in space environments.

Applicability of Complexity Theory to Martian Fluvial Systems: A Preliminary Analysis

NASA Technical Reports Server (NTRS)

Rosenshein, E. B.

2003-01-01

In the last 15 years, terrestrial geomorphology has been revolutionized by the theories of chaotic systems, fractals, self-organization, and selforganized criticality. Except for the application of fractal theory to the analysis of lava flows and rampart craters on Mars, these theories have not yet been applied to problems of Martian landscape evolution. These complexity theories are elucidated below, along with the methods used to relate these theories to the realities of Martian fluvial systems.

Nonlinear analysis of gait kinematics to track changes in oxygen consumption in prolonged load carriage walking: a pilot study.

PubMed

Schiffman, Jeffrey M; Chelidze, David; Adams, Albert; Segala, David B; Hasselquist, Leif

2009-09-18

Linking human mechanical work to physiological work for the purpose of developing a model of physical fatigue is a complex problem that cannot be solved easily by conventional biomechanical analysis. The purpose of the study was to determine if two nonlinear analysis methods can address the fundamental issue of utilizing kinematic data to track oxygen consumption from a prolonged walking trial: we evaluated the effectiveness of dynamical systems and fractal analysis in this study. Further, we selected, oxygen consumption as a measure to represent the underlying physiological measure of fatigue. Three male US Army Soldier volunteers (means: 23.3 yr; 1.80 m; 77.3 kg) walked for 120 min at 1.34 m/s with a 40-kg load on a level treadmill. Gait kinematic data and oxygen consumption (VO(2)) data were collected over the 120-min period. For the fractal analysis, utilizing stride interval data, we calculated fractal dimension. For the dynamical systems analysis, kinematic angle time series were used to estimate phase space warping based features at uniform time intervals: smooth orthogonal decomposition (SOD) was used to extract slowly time-varying trends from these features. Estimated fractal dimensions showed no apparent trend or correlation with independently measured VO(2). While inter-individual difference did exist in the VO(2) data, dominant SOD time trends tracked and correlated with the VO(2) for all volunteers. Thus, dynamical systems analysis using gait kinematics may be suitable to develop a model to predict physiologic fatigue based on biomechanical work.

Multifractal analysis of 2001 Mw 7 . 7 Bhuj earthquake sequence in Gujarat, Western India

NASA Astrophysics Data System (ADS)

Aggarwal, Sandeep Kumar; Pastén, Denisse; Khan, Prosanta Kumar

2017-12-01

The 2001 Mw 7 . 7 Bhuj mainshock seismic sequence in the Kachchh area, occurring during 2001 to 2012, has been analyzed using mono-fractal and multi-fractal dimension spectrum analysis technique. This region was characterized by frequent moderate shocks of Mw ≥ 5 . 0 for more than a decade since the occurrence of 2001 Bhuj earthquake. The present study is therefore important for precursory analysis using this sequence. The selected long-sequence has been investigated first time for completeness magnitude Mc 3.0 using the maximum curvature method. Multi-fractal Dq spectrum (Dq ∼ q) analysis was carried out using effective window-length of 200 earthquakes with a moving window of 20 events overlapped by 180 events. The robustness of the analysis has been tested by considering the magnitude completeness correction term of 0.2 to Mc 3.0 as Mc 3.2 and we have tested the error in the calculus of Dq for each magnitude threshold. On the other hand, the stability of the analysis has been investigated down to the minimum magnitude of Mw ≥ 2 . 6 in the sequence. The analysis shows the multi-fractal dimension spectrum Dq decreases with increasing of clustering of events with time before a moderate magnitude earthquake in the sequence, which alternatively accounts for non-randomness in the spatial distribution of epicenters and its self-organized criticality. Similar behavior is ubiquitous elsewhere around the globe, and warns for proximity of a damaging seismic event in an area. OS: Please confirm math roman or italics in abs.

Fractal Physiology and the Fractional Calculus: A Perspective

PubMed Central

West, Bruce J.

2010-01-01

This paper presents a restricted overview of Fractal Physiology focusing on the complexity of the human body and the characterization of that complexity through fractal measures and their dynamics, with fractal dynamics being described by the fractional calculus. Not only are anatomical structures (Grizzi and Chiriva-Internati, 2005), such as the convoluted surface of the brain, the lining of the bowel, neural networks and placenta, fractal, but the output of dynamical physiologic networks are fractal as well (Bassingthwaighte et al., 1994). The time series for the inter-beat intervals of the heart, inter-breath intervals and inter-stride intervals have all been shown to be fractal and/or multifractal statistical phenomena. Consequently, the fractal dimension turns out to be a significantly better indicator of organismic functions in health and disease than the traditional average measures, such as heart rate, breathing rate, and stride rate. The observation that human physiology is primarily fractal was first made in the 1980s, based on the analysis of a limited number of datasets. We review some of these phenomena herein by applying an allometric aggregation approach to the processing of physiologic time series. This straight forward method establishes the scaling behavior of complex physiologic networks and some dynamic models capable of generating such scaling are reviewed. These models include simple and fractional random walks, which describe how the scaling of correlation functions and probability densities are related to time series data. Subsequently, it is suggested that a proper methodology for describing the dynamics of fractal time series may well be the fractional calculus, either through the fractional Langevin equation or the fractional diffusion equation. A fractional operator (derivative or integral) acting on a fractal function, yields another fractal function, allowing us to construct a fractional Langevin equation to describe the evolution of a fractal statistical process. Control of physiologic complexity is one of the goals of medicine, in particular, understanding and controlling physiological networks in order to ensure their proper operation. We emphasize the difference between homeostatic and allometric control mechanisms. Homeostatic control has a negative feedback character, which is both local and rapid. Allometric control, on the other hand, is a relatively new concept that takes into account long-time memory, correlations that are inverse power law in time, as well as long-range interactions in complex phenomena as manifest by inverse power-law distributions in the network variable. We hypothesize that allometric control maintains the fractal character of erratic physiologic time series to enhance the robustness of physiological networks. Moreover, allometric control can often be described using the fractional calculus to capture the dynamics of complex physiologic networks. PMID:21423355

Effect of Fractal Dimension on the Strain Behavior of Particulate Media

NASA Astrophysics Data System (ADS)

Altun, Selim; Sezer, Alper; Goktepe, A. Burak

2016-12-01

In this study, the influence of several fractal identifiers of granular materials on dynamic behavior of a flexible pavement structure as a particulate stratum is considered. Using experimental results and numerical methods as well, 15 different grain-shaped sands obtained from 5 different sources were analyzed as pavement base course materials. Image analyses were carried out by use of a stereomicroscope on 15 different samples to obtain quantitative particle shape information. Furthermore, triaxial compression tests were conducted to determine stress-strain and shear strength parameters of sands. Additionally, the dynamic response of the particulate media to standard traffic loads was computed using finite element modeling (FEM) technique. Using area-perimeter, line divider and box counting methods, over a hundred grains for each sand type were subjected to fractal analysis. Relationships among fractal dimension descriptors and dynamic strain levels were established for assessment of importance of shape descriptors of sands at various scales on the dynamic behavior. In this context, the advantage of fractal geometry concept to describe irregular and fractured shapes was used to characterize the sands used as base course materials. Results indicated that fractal identifiers can be preferred to analyze the effect of shape properties of sands on dynamic behavior of pavement base layers.

Quantification of structural changes in acute inflammation by fractal dimension, angular second moment and correlation.

PubMed

Stankovic, Marija; Pantic, Igor; De Luka, Silvio R; Puskas, Nela; Zaletel, Ivan; Milutinovic-Smiljanic, Sanja; Pantic, Senka; Trbovich, Alexander M

2016-03-01

The aim of the study was to examine alteration and possible application of fractal dimension, angular second moment, and correlation for quantification of structural changes in acutely inflamed tissue. Acute inflammation was induced by injection of turpentine oil into the right and left hind limb muscles of mice, whereas control animals received intramuscular saline injection. After 12 h, animals were anesthetised and treated muscles collected. The tissue was stained by hematoxylin and eosin, digital micrographs produced, enabling determination of fractal dimension of the cells, angular second moment and correlation of studied tissue. Histopathological analysis showed presence of inflammatory infiltrate and tissue damage in inflammatory group, whereas tissue structure in control group was preserved, devoid of inflammatory infiltrate. Fractal dimension of the cells, angular second moment and correlation of treated tissue in inflammatory group decreased in comparison to the control group. In this study, we were first to observe and report that fractal dimension of the cells, angular second moment, and correlation were reduced in acutely inflamed tissue, indicating loss of overall complexity of the cells in the tissue, the tissue uniformity and structure regularity. Fractal dimension, angular second moment and correlation could be useful methods for quantification of structural changes in acute inflammation. © 2015 The Authors Journal of Microscopy © 2015 Royal Microscopical Society.

Fractal properties and denoising of lidar signals from cirrus clouds

NASA Astrophysics Data System (ADS)

van den Heuvel, J. C.; Driesenaar, M. L.; Lerou, R. J. L.

2000-02-01

Airborne lidar signals of cirrus clouds are analyzed to determine the cloud structure. Climate modeling and numerical weather prediction benefit from accurate modeling of cirrus clouds. Airborne lidar measurements of the European Lidar in Space Technology Experiment (ELITE) campaign were analyzed by combining shots to obtain the backscatter at constant altitude. The signal at high altitude was analyzed for horizontal structure of cirrus clouds. The power spectrum and the structure function show straight lines on a double logarithmic plot. This behavior is characteristic for a Brownian fractal. Wavelet analysis using the Haar wavelet confirms the fractal aspects. It is shown that the horizontal structure of cirrus can be described by a fractal with a dimension of 1.8 over length scales that vary 4 orders of magnitude. We use the fractal properties in a new denoising method. Denoising is required for future lidar measurements from space that have a low signal to noise ratio. Our wavelet denoising is based on the Haar wavelet and uses the statistical fractal properties of cirrus clouds in a method based on the maximum a posteriori (MAP) probability. This denoising based on wavelets is tested on airborne lidar signals from ELITE using added Gaussian noise. Superior results with respect to averaging are obtained.

Buried mine detection using fractal geometry analysis to the LWIR successive line scan data image

NASA Astrophysics Data System (ADS)

Araki, Kan

2012-06-01

We have engaged in research on buried mine/IED detection by remote sensing method using LWIR camera. A IR image of a ground, containing buried objects can be assumed as a superimposed pattern including thermal scattering which may depend on the ground surface roughness, vegetation canopy, and effect of the sun light, and radiation due to various heat interaction caused by differences in specific heat, size, and buried depth of the objects and local temperature of their surrounding environment. In this cumbersome environment, we introduce fractal geometry for analyzing from an IR image. Clutter patterns due to these complex elements have oftentimes low ordered fractal dimension of Hausdorff Dimension. On the other hand, the target patterns have its tendency of obtaining higher ordered fractal dimension in terms of Information Dimension. Random Shuffle Surrogate method or Fourier Transform Surrogate method is used to evaluate fractional statistics by applying shuffle of time sequence data or phase of spectrum. Fractal interpolation to each line scan was also applied to improve the signal processing performance in order to evade zero division and enhance information of data. Some results of target extraction by using relationship between low and high ordered fractal dimension are to be presented.

Efficient fractal-based mutation in evolutionary algorithms from iterated function systems

NASA Astrophysics Data System (ADS)

Salcedo-Sanz, S.; Aybar-Ruíz, A.; Camacho-Gómez, C.; Pereira, E.

2018-03-01

In this paper we present a new mutation procedure for Evolutionary Programming (EP) approaches, based on Iterated Function Systems (IFSs). The new mutation procedure proposed consists of considering a set of IFS which are able to generate fractal structures in a two-dimensional phase space, and use them to modify a current individual of the EP algorithm, instead of using random numbers from different probability density functions. We test this new proposal in a set of benchmark functions for continuous optimization problems. In this case, we compare the proposed mutation against classical Evolutionary Programming approaches, with mutations based on Gaussian, Cauchy and chaotic maps. We also include a discussion on the IFS-based mutation in a real application of Tuned Mass Dumper (TMD) location and optimization for vibration cancellation in buildings. In both practical cases, the proposed EP with the IFS-based mutation obtained extremely competitive results compared to alternative classical mutation operators.

Fractal analysis of MRI data for the characterization of patients with schizophrenia and bipolar disorder.

PubMed

Squarcina, Letizia; De Luca, Alberto; Bellani, Marcella; Brambilla, Paolo; Turkheimer, Federico E; Bertoldo, Alessandra

2015-02-21

Fractal geometry can be used to analyze shape and patterns in brain images. With this study we use fractals to analyze T1 data of patients affected by schizophrenia or bipolar disorder, with the aim of distinguishing between healthy and pathological brains using the complexity of brain structure, in particular of grey matter, as a marker of disease. 39 healthy volunteers, 25 subjects affected by schizophrenia and 11 patients affected by bipolar disorder underwent an MRI session. We evaluated fractal dimension of the brain cortex and its substructures, calculated with an algorithm based on the box-count algorithm. We modified this algorithm, with the aim of avoiding the segmentation processing step and using all the information stored in the image grey levels. Moreover, to increase sensitivity to local structural changes, we computed a value of fractal dimension for each slice of the brain or of the particular structure. To have reference values in comparing healthy subjects with patients, we built a template by averaging fractal dimension values of the healthy volunteers data. Standard deviation was evaluated and used to create a confidence interval. We also performed a slice by slice t-test to assess the difference at slice level between the three groups. Consistent average fractal dimension values were found across all the structures in healthy controls, while in the pathological groups we found consistent differences, indicating a change in brain and structures complexity induced by these disorders.

Fractal analysis of MRI data for the characterization of patients with schizophrenia and bipolar disorder

NASA Astrophysics Data System (ADS)

Squarcina, Letizia; De Luca, Alberto; Bellani, Marcella; Brambilla, Paolo; Turkheimer, Federico E.; Bertoldo, Alessandra

2015-02-01

Fractal geometry can be used to analyze shape and patterns in brain images. With this study we use fractals to analyze T1 data of patients affected by schizophrenia or bipolar disorder, with the aim of distinguishing between healthy and pathological brains using the complexity of brain structure, in particular of grey matter, as a marker of disease. 39 healthy volunteers, 25 subjects affected by schizophrenia and 11 patients affected by bipolar disorder underwent an MRI session. We evaluated fractal dimension of the brain cortex and its substructures, calculated with an algorithm based on the box-count algorithm. We modified this algorithm, with the aim of avoiding the segmentation processing step and using all the information stored in the image grey levels. Moreover, to increase sensitivity to local structural changes, we computed a value of fractal dimension for each slice of the brain or of the particular structure. To have reference values in comparing healthy subjects with patients, we built a template by averaging fractal dimension values of the healthy volunteers data. Standard deviation was evaluated and used to create a confidence interval. We also performed a slice by slice t-test to assess the difference at slice level between the three groups. Consistent average fractal dimension values were found across all the structures in healthy controls, while in the pathological groups we found consistent differences, indicating a change in brain and structures complexity induced by these disorders.

The use of fractal dimension analysis in estimation of blood vessels shape in transplantable mammary adenocarcinoma in Wistar rats after photodynamic therapy combined with cysteine protease inhibitors.

PubMed

Jurczyszyn, Kamil; Osiecka, Beata J; Ziółkowski, Piotr

2012-01-01

Fractal dimension analysis (FDA) is modern mathematical method widely used to describing of complex and chaotic shapes when classic methods fail. The main aim of this study was evaluating the influence of photodynamic therapy (PDT) with cystein proteases inhibitors (CPI) on the number and morphology of blood vessels inside tumor and on increase of effectiveness of combined therapy in contrast to PDT and CPI used separately. Animals were divided into four groups: control, treated using only PDT, treated using only CPI and treated using combined therapy, PDT and CPI. Results showed that time of animal survival and depth of necrosis inside tumor were significantly higher in CPI+PDT group in contrast to other groups. The higher value of fractal dimension (FD) was observed in control group, while the lowest value was found in the group which was treated by cystein protease inhibitors. The differences between FD were observed in CPI group and PDT+CPI group in comparison to control group. Our results revealed that fractal dimension analysis is a very useful tool in estimating differences between irregular shapes like blood vessels in PDT treated tumors. Thus, the implementation of FDA algorithms could be useful method in evaluating the efficacy of PDT.

The Use of Fractal Dimension Analysis in Estimation of Blood Vessels Shape in Transplantable Mammary Adenocarcinoma in Wistar Rats after Photodynamic Therapy Combined with Cysteine Protease Inhibitors

PubMed Central

Jurczyszyn, Kamil; Osiecka, Beata J.; Ziółkowski, Piotr

2012-01-01

Fractal dimension analysis (FDA) is modern mathematical method widely used to describing of complex and chaotic shapes when classic methods fail. The main aim of this study was evaluating the influence of photodynamic therapy (PDT) with cystein proteases inhibitors (CPI) on the number and morphology of blood vessels inside tumor and on increase of effectiveness of combined therapy in contrast to PDT and CPI used separately. Animals were divided into four groups: control, treated using only PDT, treated using only CPI and treated using combined therapy, PDT and CPI. Results showed that time of animal survival and depth of necrosis inside tumor were significantly higher in CPI+PDT group in contrast to other groups. The higher value of fractal dimension (FD) was observed in control group, while the lowest value was found in the group which was treated by cystein protease inhibitors. The differences between FD were observed in CPI group and PDT+CPI group in comparison to control group. Our results revealed that fractal dimension analysis is a very useful tool in estimating differences between irregular shapes like blood vessels in PDT treated tumors. Thus, the implementation of FDA algorithms could be useful method in evaluating the efficacy of PDT. PMID:22991578

Fractal Dynamics of Heartbeat Interval Fluctuations in Health and Disease

NASA Astrophysics Data System (ADS)

Meyer, M.; Marconi, C.; Rahmel, A.; Grassi, B.; Ferretti, G.; Skinner, J. E.; Cerretelli, P.

The dynamics of heartbeat interval time series were studied by a modified random walk analysis recently introduced as Detrended Fluctuation Analysis. In this analysis, the intrinsic fractal long-range power-law correlation properties of beat-to-beat fluctuations generated by the dynamical system (i.e. cardiac rhythm generator), after decomposition from extrinsic uncorrelated sources, can be quantified by the scaling exponent which, in healthy subjects, is about 1.0. The finding of a scaling coefficient of 1.0, indicating scale-invariant long-range power-law correlations (1/ƒnoise) of heartbeat fluctuations, would reflect a genuinely self-similar fractal process that typically generates fluctuations on a wide range of time scales. Lack of a characteristic time scale suggests that the neuroautonomic system underlying the control of heart rate dynamics helps prevent excessive mode-locking (error tolerance) that would restrict its functional responsiveness (plasticity) to environmental stimuli. The 1/ƒ dynamics of heartbeat interval fluctuations are unaffected by exposure to chronic hypoxia suggesting that the neuroautonomic cardiac control system is preadapted to hypoxia. Functional (hypothermia, cardiac disease) and/or structural (cardiac transplantation, early cardiac development) inactivation of neuroautonomic control is associated with the breakdown or absence of fractal complexity reflected by anticorrelated random walk-like dynamics, indicating that in these conditions the heart is unadapted to its environment.

The Application of Fractal and Multifractal Theory in Hydraulic-Flow-Unit Characterization and Permeability Estimation

NASA Astrophysics Data System (ADS)

Chen, X.; Yao, G.; Cai, J.

2017-12-01

Pore structure characteristics are important factors in influencing the fluid transport behavior of porous media, such as pore-throat ratio, pore connectivity and size distribution, moreover, wettability. To accurately characterize the diversity of pore structure among HFUs, five samples selected from different HFUs (porosities are approximately equal, however permeability varies widely) were chosen to conduct micro-computerized tomography test to acquire direct 3D images of pore geometries and to perform mercury injection experiments to obtain the pore volume-radii distribution. To characterize complex and high nonlinear pore structure of all samples, three classic fractal geometry models were applied. Results showed that each HFU has similar box-counting fractal dimension and generalized fractal dimension in the number-area model, but there are significant differences in multifractal spectrums. In the radius-volume model, there are three obvious linear segments, corresponding to three fractal dimension values, and the middle one is proved as the actual fractal dimension according to the maximum radius. In the number-radius model, the spherical-pore size distribution extracted by maximum ball algorithm exist a decrease in the number of small pores compared with the fractal power rate rather than the traditional linear law. Among the three models, only multifractal analysis can classify the HFUs accurately. Additionally, due to the tightness and low-permeability in reservoir rocks, connate water film existing in the inner surface of pore channels commonly forms bound water. The conventional model which is known as Yu-Cheng's model has been proved to be typically not applicable. Considering the effect of irreducible water saturation, an improved fractal permeability model was also deduced theoretically. The comparison results showed that the improved model can be applied to calculate permeability directly and accurately in such unconventional rocks.

Analysis of regional deformation and strain accumulation data adjacent to the San Andreas fault

NASA Technical Reports Server (NTRS)

Turcotte, Donald L.

1991-01-01

A new approach to the understanding of crustal deformation was developed under this grant. This approach combined aspects of fractals, chaos, and self-organized criticality to provide a comprehensive theory for deformation on distributed faults. It is hypothesized that crustal deformation is an example of comminution: Deformation takes place on a fractal distribution of faults resulting in a fractal distribution of seismicity. Our primary effort under this grant was devoted to developing an understanding of distributed deformation in the continental crust. An initial effort was carried out on the fractal clustering of earthquakes in time. It was shown that earthquakes do not obey random Poisson statistics, but can be approximated in many cases by coupled, scale-invariant fractal statistics. We applied our approach to the statistics of earthquakes in the New Hebrides region of the southwest Pacific because of the very high level of seismicity there. This work was written up and published in the Bulletin of the Seismological Society of America. This approach was also applied to the statistics of the seismicity on the San Andreas fault system.

Universality of Critically Pinned Interfaces in Two-Dimensional Isotropic Random Media

NASA Astrophysics Data System (ADS)

Grassberger, Peter

2018-05-01

Based on extensive simulations, we conjecture that critically pinned interfaces in two-dimensional isotropic random media with short-range correlations are always in the universality class of ordinary percolation. Thus, in contrast to interfaces in >2 dimensions, there is no distinction between fractal (i.e., percolative) and rough but nonfractal interfaces. Our claim includes interfaces in zero-temperature random field Ising models (both with and without spontaneous nucleation), in heterogeneous bootstrap percolation, and in susceptible-weakened-infected-removed epidemics. It does not include models with long-range correlations in the randomness and models where overhangs are explicitly forbidden (which would imply nonisotropy of the medium).

A new characterization of three-dimensional conductivity backbone above and below the percolation threshold

NASA Astrophysics Data System (ADS)

Skal, Asya S.

1996-08-01

A new definition of three-dimensional conductivity backbone, obtained from a distribution function of Joule heat and the Hall coefficient is introduced. The fractal dimension d fB = d - ( {g}/{v}) = 2.25 of conductivity backbone for both sides of the threshold is obtained from a critical exponent of the Hall coefficient g = 0.6. This allows one to construct, below the threshold, a new order parameter of metal-conductor transition—the two-component infinite conductivity back-bone and tested scaling relation, proposed by Alexander and Orbach [ J. Phys. Rev. Lett.43, 1982, L625] for both sides of a threshold.

Unification of two fractal families

NASA Astrophysics Data System (ADS)

Liu, Ying

1995-06-01

Barnsley and Hurd classify the fractal images into two families: iterated function system fractals (IFS fractals) and fractal transform fractals, or local iterated function system fractals (LIFS fractals). We will call IFS fractals, class 2 fractals and LIFS fractals, class 3 fractals. In this paper, we will unify these two approaches plus another family of fractals, the class 5 fractals. The basic idea is given as follows: a dynamical system can be represented by a digraph, the nodes in a digraph can be divided into two parts: transient states and persistent states. For bilevel images, a persistent node is a black pixel. A transient node is a white pixel. For images with more than two gray levels, a stochastic digraph is used. A transient node is a pixel with the intensity of 0. The intensity of a persistent node is determined by a relative frequency. In this way, the two families of fractals can be generated in a similar way. In this paper, we will first present a classification of dynamical systems and introduce the transformation based on digraphs, then we will unify the two approaches for fractal binary images. We will compare the decoding algorithms of the two families. Finally, we will generalize the discussion to continuous-tone images.

Study on the Quality and Performance of CoCrMo Alloy Parts Manufactured by Selective Laser Melting

NASA Astrophysics Data System (ADS)

Guoqing, Zhang; Yongqiang, Yang; Hui, Lin; Changhui, Song; Zimian, Zhang

2017-05-01

To obtain medical implants with better performance, it is necessary to conduct studies on the quality and other performances of the selective laser melting (SLM) manufacturing parts. Interior defects in CoCrMo parts manufactured by SLM were detected using x-ray radiographic inspection, and the manufactured parts compared with three-dimensional models to assess manufacturing quality. Impact tests were employed to establish the mechanical properties of the manufactured parts. With the aim of studying the mechanism of fracture of the parts, we utilized a metalloscope and SEM to observe the surface and fractal theory was used to analyze the appearance of fractures. The results show that part defects manifested in an increase in transmittance caused by the non-uniform distribution of density, resulting in variation in the residual stresses of the parts. The density of the parts was more uniform following heat treatment. Internal residual stress of the manufactured parts enhanced their impact toughness. There was a ductile-brittle transition temperature between the two annealing temperatures. We determined that the fracture mechanism was brittle fracture. Fractures exhibited significant fractal behavior. The impact energy and fractal dimension were positively correlated, which provided good support for using selective laser melting manufacturing of CoCrMo alloy in medical implants.

Fusion of multiscale wavelet-based fractal analysis on retina image for stroke prediction.

PubMed

Che Azemin, M Z; Kumar, Dinesh K; Wong, T Y; Wang, J J; Kawasaki, R; Mitchell, P; Arjunan, Sridhar P

2010-01-01

In this paper, we present a novel method of analyzing retinal vasculature using Fourier Fractal Dimension to extract the complexity of the retinal vasculature enhanced at different wavelet scales. Logistic regression was used as a fusion method to model the classifier for 5-year stroke prediction. The efficacy of this technique has been tested using standard pattern recognition performance evaluation, Receivers Operating Characteristics (ROC) analysis and medical prediction statistics, odds ratio. Stroke prediction model was developed using the proposed system.

Morphology and Three-Dimensional Inhalation Flow in Human Airways in Healthy and Diseased Subjects

NASA Astrophysics Data System (ADS)

Van de Moortele, Tristan

We investigate experimentally the relation between anatomical structure and respiratory function in healthy and diseased airways. Computed Tomography (CT) scans of human lungs are analyzed from the data base of a large multi-institution clinical study on Chronic Obstructive Pulmonary Disease (COPD). Through segmentation, the 3D volumes of the airways are determined at total lung capacity. A geometric analysis provides data on the morphometry of the airways, including the length and diameter of branches, the child-to-parent diameter ratio, and branching angles. While several geometric parameters are confirmed to match past studies for healthy subjects, previously unreported trends are reported on the length of branches. Specifically, in most dichotomous airway bifurcation, the branch of smaller diameter tends to be significantly longer than the one of larger diameter. Additionally, the branch diameter tends to be smaller in diseased airways than in healthy airways up to the 7th generation of bronchial branching. 3D fractal analysis is also performed on the airway volume. Fractal dimensions of 1.89 and 1.83 are found for healthy non-smokers and declining COPD subjects, respectively, furthering the belief that COPD (and lung disease in general) significantly affects the morphometry of the airways already in early stages of the disease. To investigate the inspiratory flow, 3D flow models of the airways are generated using Computer Aided Design (CAD) software and 3D printed. Using Magnetic Resonance Velocimetry (MRV), 3-component 3D flow fields are acquired for steady inhalation at Reynolds number Re 2000 defined at the trachea. Analysis of the flow data reveals that diseased subjects may experience greater secondary flow strength in their conducting airways, especially in deeper generations.

Fractals: To Know, to Do, to Simulate.

ERIC Educational Resources Information Center

Talanquer, Vicente; Irazoque, Glinda

1993-01-01

Discusses the development of fractal theory and suggests fractal aggregates as an attractive alternative for introducing fractal concepts. Describes methods for producing metallic fractals and a computer simulation for drawing fractals. (MVL)

Selective modulation of cell response on engineered fractal silicon substrates

PubMed Central

Gentile, Francesco; Medda, Rebecca; Cheng, Ling; Battista, Edmondo; Scopelliti, Pasquale E.; Milani, Paolo; Cavalcanti-Adam, Elisabetta A.; Decuzzi, Paolo

2013-01-01

A plethora of work has been dedicated to the analysis of cell behavior on substrates with ordered topographical features. However, the natural cell microenvironment is characterized by biomechanical cues organized over multiple scales. Here, randomly rough, self-affinefractal surfaces are generated out of silicon,where roughness Ra and fractal dimension Df are independently controlled. The proliferation rates, the formation of adhesion structures, and the morphology of 3T3 murine fibroblasts are monitored over six different substrates. The proliferation rate is maximized on surfaces with moderate roughness (Ra ~ 40 nm) and large fractal dimension (Df ~ 2.4); whereas adhesion structures are wider and more stable on substrates with higher roughness (Ra ~ 50 nm) and lower fractal dimension (Df ~ 2.2). Higher proliferation occurson substrates exhibiting densely packed and sharp peaks, whereas more regular ridges favor adhesion. These results suggest that randomly roughtopographies can selectively modulate cell behavior. PMID:23492898

Fractal patterns of fracture in sandwich composite materials under biaxial tension

NASA Astrophysics Data System (ADS)

Fang, Jing; Yao, Xuefeng; Qi, Jia

1996-04-01

The paper presents a successful experiment to generate a fractal pattern of branching cracks in a brittle material sandwiched in ductile plates. A glass sheet bonded between two polycarbonate plates was heated at different levels of temperatures and the stress field due to the difference of thermal coefficients of the materials was solved by combining the results from isochromatic fringes and thermal stress analysis. At a critical degree of temperature, a crack was initiated at a point and soon produced crack branches to release the stored energy. A tree—like fractal patterns of the branch cracks was then developed with the growth of the branches that subsequently produced more branches on their ways of propagation. The fractal dimension of the fracture pattern was evaluated and the mechanism of the fragmentation was analyzed with the help of the residual stress field of isochromatic and isoclinic patterns.

The fractal based analysis of human face and DNA variations during aging.

PubMed

Namazi, Hamidreza; Akrami, Amin; Hussaini, Jamal; Silva, Osmar N; Wong, Albert; Kulish, Vladimir V

2017-01-16

Human DNA is the main unit that shapes human characteristics and features such as behavior. Thus, it is expected that changes in DNA (DNA mutation) influence human characteristics and features. Face is one of the human features which is unique and also dependent on his gen. In this paper, for the first time we analyze the variations of human DNA and face simultaneously. We do this job by analyzing the fractal dimension of DNA walk and face during human aging. The results of this study show the human DNA and face get more complex by aging. These complexities are mapped on fractal exponents of DNA walk and human face. The method discussed in this paper can be further developed in order to investigate the direct influence of DNA mutation on the face variations during aging, and accordingly making a model between human face fractality and the complexity of DNA walk.

Fractal dimension of microbead assemblies used for protein detection.

PubMed

Hecht, Ariel; Commiskey, Patrick; Lazaridis, Filippos; Argyrakis, Panos; Kopelman, Raoul

2014-11-10

We use fractal analysis to calculate the protein concentration in a rotating magnetic assembly of microbeads of size 1 μm, which has optimized parameters of sedimentation, binding sites and magnetic volume. We utilize the original Forrest-Witten method, but due to the relatively small number of bead particles, which is of the order of 500, we use a large number of origins and also a large number of algorithm iterations. We find a value of the fractal dimension in the range 1.70-1.90, as a function of the thrombin concentration, which plays the role of binding the microbeads together. This is in good agreement with previous results from magnetorotation studies. The calculation of the fractal dimension using multiple points of reference can be used for any assembly with a relatively small number of particles. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Fractal serpentine-shaped design for stretchable wireless strain sensors

NASA Astrophysics Data System (ADS)

Dong, Wentao; Cheng, Xiao; Wang, Xiaoming; Zhang, Hailiang

2018-07-01

Stretchable sensors have been widely applied to biological fields due to their unique capacity to integrate with soft materials and curvilinear surfaces. The article presents the fractal serpentine-shaped design for stretchable wireless strain sensor which is operating around 1.6 GHz. The wireless passive LC sensor is formed by a fractal serpentine-shaped inductor coil and a concentric coplanar capacitor. The inductance of the fractal serpentine-shaped coil varies with the deformation of the wireless sensor, and the resonance frequency also varies with the applied strain of the wireless sensor embedded in soft substrate. The 40% stretchability of wireless sensor is verified by finite element analysis (FEA). Strain response of the stretchable wireless sensor has been characterized by experiments and demonstrates high strain responsivity about 6.74 MHz/1%. The stretchable wireless sensor has the potential to be used in biological and wearable applications.

Use of sEMG in identification of low level muscle activities: features based on ICA and fractal dimension.

PubMed

Naik, Ganesh R; Kumar, Dinesh K; Arjunan, Sridhar

2009-01-01

This paper has experimentally verified and compared features of sEMG (Surface Electromyogram) such as ICA (Independent Component Analysis) and Fractal Dimension (FD) for identification of low level forearm muscle activities. The fractal dimension was used as a feature as reported in the literature. The normalized feature values were used as training and testing vectors for an Artificial neural network (ANN), in order to reduce inter-experimental variations. The identification accuracy using FD of four channels sEMG was 58%, and increased to 96% when the signals are separated to their independent components using ICA.

a New Method for Calculating Fractal Dimensions of Porous Media Based on Pore Size Distribution

NASA Astrophysics Data System (ADS)

Xia, Yuxuan; Cai, Jianchao; Wei, Wei; Hu, Xiangyun; Wang, Xin; Ge, Xinmin

Fractal theory has been widely used in petrophysical properties of porous rocks over several decades and determination of fractal dimensions is always the focus of researches and applications by means of fractal-based methods. In this work, a new method for calculating pore space fractal dimension and tortuosity fractal dimension of porous media is derived based on fractal capillary model assumption. The presented work establishes relationship between fractal dimensions and pore size distribution, which can be directly used to calculate the fractal dimensions. The published pore size distribution data for eight sandstone samples are used to calculate the fractal dimensions and simultaneously compared with prediction results from analytical expression. In addition, the proposed fractal dimension method is also tested through Micro-CT images of three sandstone cores, and are compared with fractal dimensions by box-counting algorithm. The test results also prove a self-similar fractal range in sandstone when excluding smaller pores.

Test-retest reliability of muscle fiber conduction velocity and fractal dimension of surface EMG during isometric contractions.

PubMed

Beretta-Piccoli, Matteo; D'Antona, Giuseppe; Zampella, Cristian; Barbero, Marco; Clijsen, Ron; Cescon, Corrado

2017-04-01

The aim of this study was to determine the test-retest reliability of muscle fiber conduction velocity (CV) and fractal dimension (FD) obtained from multichannel surface electromyographic (sEMG) recordings. Forty healthy recreationally active subjects (20 men and 20 women) performed two elbow flexions on two trials with a 1 week interval. The first was a 20% maximal voluntary contraction (MVC) of 120 s, and the second at 60% MVC held until exhaustion. sEMG signals were detected from the biceps brachii, using bi-dimensional arrays. Initial values and slope of CV and FD were used for the reliability analysis. The intraclass correlation coefficient (ICC) values for the isometric contraction at 20% MVC were (-0.09) and 0.67 for CV and FD respectively; whereas the ICC values at 60% MVC were 0.78 and 0.82 for CV and FD respectively. The Bland Altman plots for the two isometric contractions showed a mean difference close to zero, with no evident outliers between the repeated measurements: at 20% MVC 0.001 53 for FD and  -0.0277 for CV, and at 60% MVC 0.006 66 for FD and 0.009 07 for CV. Overall, our findings suggest that during isometric fatiguing contractions, CV and FD slopes are reliable variables, with potential application in clinical populations.

Renormalization of the unitary evolution equation for coined quantum walks

NASA Astrophysics Data System (ADS)

Boettcher, Stefan; Li, Shanshan; Portugal, Renato

2017-03-01

We consider discrete-time evolution equations in which the stochastic operator of a classical random walk is replaced by a unitary operator. Such a problem has gained much attention as a framework for coined quantum walks that are essential for attaining the Grover limit for quantum search algorithms in physically realizable, low-dimensional geometries. In particular, we analyze the exact real-space renormalization group (RG) procedure recently introduced to study the scaling of quantum walks on fractal networks. While this procedure, when implemented numerically, was able to provide some deep insights into the relation between classical and quantum walks, its analytic basis has remained obscure. Our discussion here is laying the groundwork for a rigorous implementation of the RG for this important class of transport and algorithmic problems, although some instances remain unresolved. Specifically, we find that the RG fixed-point analysis of the classical walk, which typically focuses on the dominant Jacobian eigenvalue {λ1} , with walk dimension dw\\text{RW}={{log}2}{λ1} , needs to be extended to include the subdominant eigenvalue {λ2} , such that the dimension of the quantum walk obtains dw\\text{QW}={{log}2}\\sqrt{{λ1}{λ2}} . With that extension, we obtain analytically previously conjectured results for dw\\text{QW} of Grover walks on all but one of the fractal networks that have been considered.

Analysis of chitin particle size on maximum power generation, power longevity, and Coulombic efficiency in solid-substrate microbial fuel cells

NASA Astrophysics Data System (ADS)

Rezaei, Farzaneh; Richard, Tom L.; Logan, Bruce E.

Microbial fuel cells (MFCs) produce bioelectricity from a wide variety of organic and inorganic substrates. Chitin can be used as a slowly degrading substrate in MFCs and thus as a long-term fuel to sustain power by these devices in remote locations. However, little is known about the effects of particle size on power density and length of the power cycle (longevity). We therefore examined power generation from chitin particles sieved to produce three average particle sizes (0.28, 0.46 and 0.78 mm). The longevity increased from 9 to 33 days with an increase in the particle diameter from 0.28 to 0.78 mm. Coulombic efficiency also increased with particle size from 18% to 56%. The maximum power density was lower for the largest (0.78 mm) particles (176 mW m -2), with higher power densities for the 0.28 mm (272 mW m -2) and 0.46 mm (252 mW m -2) particle sizes. The measured lifetimes of these particles scaled with particle diameter to the 1.3 power. Application of a fractal dissolution model indicates chitin particles had a three-dimensional fractal dimension between 2 and 2.3. These results demonstrate particles can be used as a sustainable fuel in MFCs, but that particle sizes will need to be controlled to achieve desired power levels.

Effects of autonomic ganglion blockade on fractal and spectral components of blood pressure and heart rate variability in free-moving rats.

PubMed

Castiglioni, Paolo; Di Rienzo, Marco; Radaelli, Alberto

2013-11-01

Fractal analysis is a promising tool for assessing autonomic influences on heart rate (HR) and blood pressure (BP) variability. The temporal spectrum of scale coefficients, α(t), was recently proposed to describe the cardiovascular fractal dynamics. Aim of our work is to evaluate sympathetic influences on cardiovascular variability analyzing α(t) and spectral powers of HR and BP after ganglionic blockade. BP was recorded in 11 rats before and after autonomic blockade by hexamethonium infusion (HEX). Systolic and diastolic BP, pulse pressure and pulse interval were derived beat-by-beat. Segments longer than 5 min were selected at baseline and HEX to estimate power spectra and α(t). Comparisons were made by paired t-test. HEX reduced all spectral components of systolic and diastolic BP, the reduction being particularly significant around the frequency of Mayer waves; it induced a reduction on α(t) coefficients at t<2s and an increase on coefficients at t>8s. HEX reduced only slower components of pulse interval power spectrum, but decreased significantly faster scale coefficients (t<8s). HEX only marginally affected pulse pressure variability. Results indicate that the sympathetic outflow contributes to BP fractal dynamics with fractional Gaussian noise (α<1) at longer scales and fractional Brownian motion (α>1) at shorter scales. Ganglionic blockade also removes a fractional Brownian motion component at shorter scales from HR dynamics. Results may be explained by the characteristic time constants between sympathetic efferent activity and cardiovascular effectors. Therefore fractal analysis may complete spectral analysis with information on the correlation structure of the data. Copyright © 2013 Elsevier B.V. All rights reserved.

Classification of diabetic retinopathy using fractal dimension analysis of eye fundus image

NASA Astrophysics Data System (ADS)

Safitri, Diah Wahyu; Juniati, Dwi

2017-08-01

Diabetes Mellitus (DM) is a metabolic disorder when pancreas produce inadequate insulin or a condition when body resist insulin action, so the blood glucose level is high. One of the most common complications of diabetes mellitus is diabetic retinopathy which can lead to a vision problem. Diabetic retinopathy can be recognized by an abnormality in eye fundus. Those abnormalities are characterized by microaneurysms, hemorrhage, hard exudate, cotton wool spots, and venous's changes. The diabetic retinopathy is classified depends on the conditions of abnormality in eye fundus, that is grade 1 if there is a microaneurysm only in the eye fundus; grade 2, if there are a microaneurysm and a hemorrhage in eye fundus; and grade 3: if there are microaneurysm, hemorrhage, and neovascularization in the eye fundus. This study proposed a method and a process of eye fundus image to classify of diabetic retinopathy using fractal analysis and K-Nearest Neighbor (KNN). The first phase was image segmentation process using green channel, CLAHE, morphological opening, matched filter, masking, and morphological opening binary image. After segmentation process, its fractal dimension was calculated using box-counting method and the values of fractal dimension were analyzed to make a classification of diabetic retinopathy. Tests carried out by used k-fold cross validation method with k=5. In each test used 10 different grade K of KNN. The accuracy of the result of this method is 89,17% with K=3 or K=4, it was the best results than others K value. Based on this results, it can be concluded that the classification of diabetic retinopathy using fractal analysis and KNN had a good performance.

Fractal analysis of the susceptibility weighted imaging patterns in malignant brain tumors during antiangiogenic treatment: technical report on four cases serially imaged by 7 T magnetic resonance during a period of four weeks.

PubMed

Di Ieva, Antonio; Matula, Christian; Grizzi, Fabio; Grabner, Günther; Trattnig, Siegfried; Tschabitscher, Manfred

2012-01-01

The need for new and objective indexes for the neuroradiologic follow-up of brain tumors and for monitoring the effects of antiangiogenic strategies in vivo led us to perform a technical study on four patients who received computerized analysis of tumor-associated vasculature with ultra-high-field (7 T) magnetic resonance imaging (MRI). The image analysis involved the application of susceptibility weighted imaging (SWI) to evaluate vascular structures. Four patients affected by recurrent malignant brain tumors were enrolled in the present study. After the first 7-T SWI MRI procedure, the patients underwent antiangiogenic treatment with bevacizumab. The imaging was repeated every 2 weeks for a period of 4 weeks. The SWI patterns visualized in the three MRI temporal sequences were analyzed by means of a computer-aided fractal-based method to objectively quantify their geometric complexity. In two clinically deteriorating patients we found an increase of the geometric complexity of the space-filling properties of the SWI patterns over time despite the antiangiogenic treatment. In one patient, who showed improvement with the therapy, the fractal dimension of the intratumoral structure decreased, whereas in the fourth patient, no differences were found. The qualitative changes of the intratumoral SWI patterns during a period of 4 weeks were quantified with the fractal dimension. Because SWI patterns are also related to the presence of vascular structures, the quantification of their space-filling properties with fractal dimension seemed to be a valid tool for the in vivo neuroradiologic follow-up of brain tumors. Copyright © 2012 Elsevier Inc. All rights reserved.

Internal structure of the upwelling events at Punta Gallinas (Colombian Caribbean) from modis-sst imagery

NASA Astrophysics Data System (ADS)

Alonso, J.; Blázquez, E.; Isaza-Toro, E.; Vidal, J.

2015-10-01

The upwelling at Punta Gallinas in the Guajira Peninsula (Colombian Caribbean) was studied from the point of view of the Mathematical Morphology using 10 years of monthly composite MODIS-SST imagery. Among all the morphological operators, the skeleton is widely used to compute the axis of the of the SST fields for the observed upwelling events. The skeleton is characterized by means of the Geometrical Theory of Measurement using the fractal dimension. The upwelling in the area is driven by the dynamic of the ITCZ (InterTropical Convergence Zone) and the relationship between the area and the East-West component of the trade winds has a lag of about 4 months. It has been found that the fractal dimension of the skeleton and the area of the upwelling are related. Some relationship was found between the fractal dimension of the skeleton (its complexity) and the Southern Oscillation Index by means of linear regression and cross-spectral analysis finding coherent energy at 1 year, 6 months and in the low frequency band. Finally, a sensitivity analysis between fractal dimension and threshold SST points out to take an extreme care at the time of fixing the last one.

Single-Image Super-Resolution Based on Rational Fractal Interpolation.

PubMed

Zhang, Yunfeng; Fan, Qinglan; Bao, Fangxun; Liu, Yifang; Zhang, Caiming

2018-08-01

This paper presents a novel single-image super-resolution (SR) procedure, which upscales a given low-resolution (LR) input image to a high-resolution image while preserving the textural and structural information. First, we construct a new type of bivariate rational fractal interpolation model and investigate its analytical properties. This model has different forms of expression with various values of the scaling factors and shape parameters; thus, it can be employed to better describe image features than current interpolation schemes. Furthermore, this model combines the advantages of rational interpolation and fractal interpolation, and its effectiveness is validated through theoretical analysis. Second, we develop a single-image SR algorithm based on the proposed model. The LR input image is divided into texture and non-texture regions, and then, the image is interpolated according to the characteristics of the local structure. Specifically, in the texture region, the scaling factor calculation is the critical step. We present a method to accurately calculate scaling factors based on local fractal analysis. Extensive experiments and comparisons with the other state-of-the-art methods show that our algorithm achieves competitive performance, with finer details and sharper edges.

Using fractal analysis of thermal signatures for thyroid disease evaluation

NASA Astrophysics Data System (ADS)

Gavriloaia, Gheorghe; Sofron, Emil; Gavriloaia, Mariuca-Roxana; Ghemigean, Adina-Mariana

2010-11-01

The skin is the largest organ of the body and it protects against heat, light, injury and infection. Skin temperature is an important parameter for diagnosing diseases. Thermal analysis is non-invasive, painless, and relatively inexpensive, showing a great potential research. Since the thyroid regulates metabolic rate it is intimately connected to body temperature, more than, any modification of its function generates a specific thermal image on the neck skin. The shapes of thermal signatures are often irregular in size and shape. Euclidean geometry is not able to evaluate their shape for different thyroid diseases, and fractal geometry is used in this paper. Different thyroid diseases generate different shapes, and their complexity are evaluated by specific mathematical approaches, fractal analysis, in order to the evaluate selfsimilarity and lacunarity. Two kinds of thyroid diseases, hyperthyroidism and papillary cancer are analyzed in this paper. The results are encouraging and show the ability to continue research for thermal signature to be used in early diagnosis of thyroid diseases.

Radiomics-based differentiation of lung disease models generated by polluted air based on X-ray computed tomography data.

PubMed

Szigeti, Krisztián; Szabó, Tibor; Korom, Csaba; Czibak, Ilona; Horváth, Ildikó; Veres, Dániel S; Gyöngyi, Zoltán; Karlinger, Kinga; Bergmann, Ralf; Pócsik, Márta; Budán, Ferenc; Máthé, Domokos

2016-02-11

Lung diseases (resulting from air pollution) require a widely accessible method for risk estimation and early diagnosis to ensure proper and responsive treatment. Radiomics-based fractal dimension analysis of X-ray computed tomography attenuation patterns in chest voxels of mice exposed to different air polluting agents was performed to model early stages of disease and establish differential diagnosis. To model different types of air pollution, BALBc/ByJ mouse groups were exposed to cigarette smoke combined with ozone, sulphur dioxide gas and a control group was established. Two weeks after exposure, the frequency distributions of image voxel attenuation data were evaluated. Specific cut-off ranges were defined to group voxels by attenuation. Cut-off ranges were binarized and their spatial pattern was associated with calculated fractal dimension, then abstracted by the fractal dimension -- cut-off range mathematical function. Nonparametric Kruskal-Wallis (KW) and Mann-Whitney post hoc (MWph) tests were used. Each cut-off range versus fractal dimension function plot was found to contain two distinctive Gaussian curves. The ratios of the Gaussian curve parameters are considerably significant and are statistically distinguishable within the three exposure groups. A new radiomics evaluation method was established based on analysis of the fractal dimension of chest X-ray computed tomography data segments. The specific attenuation patterns calculated utilizing our method may diagnose and monitor certain lung diseases, such as chronic obstructive pulmonary disease (COPD), asthma, tuberculosis or lung carcinomas.

Fractal analysis of seafloor textures for target detection in synthetic aperture sonar imagery

NASA Astrophysics Data System (ADS)

Nabelek, T.; Keller, J.; Galusha, A.; Zare, A.

2018-04-01

Fractal analysis of an image is a mathematical approach to generate surface related features from an image or image tile that can be applied to image segmentation and to object recognition. In undersea target countermeasures, the targets of interest can appear as anomalies in a variety of contexts, visually different textures on the seafloor. In this paper, we evaluate the use of fractal dimension as a primary feature and related characteristics as secondary features to be extracted from synthetic aperture sonar (SAS) imagery for the purpose of target detection. We develop three separate methods for computing fractal dimension. Tiles with targets are compared to others from the same background textures without targets. The different fractal dimension feature methods are tested with respect to how well they can be used to detect targets vs. false alarms within the same contexts. These features are evaluated for utility using a set of image tiles extracted from a SAS data set generated by the U.S. Navy in conjunction with the Office of Naval Research. We find that all three methods perform well in the classification task, with a fractional Brownian motion model performing the best among the individual methods. We also find that the secondary features are just as useful, if not more so, in classifying false alarms vs. targets. The best classification accuracy overall, in our experimentation, is found when the features from all three methods are combined into a single feature vector.

Histomorphometric, fractal and lacunarity comparative analysis of sheep (Ovis aries), goat (Capra hircus) and roe deer (Capreolus capreolus) compact bone samples.

PubMed

Gudea, A I; Stefan, A C

2013-08-01

Quantitative and qualitative studies dealing with histomorphometry of the bone tissue play a new role in modern legal medicine/forensic medicine and archaeozoology nowadays. This study deals with the differences found in case of humerus and metapodial bones of recent sheep (Ovis aries), goat (Capra hircus) and roedeer (Capreolus capreolus) specimens, both from a qualitative point of view, but mainly from a quantitative perspective. A novel perspective given by the fractal analysis performed on the digital histological images is approached. This study shows that the qualitative assessment may not be a reliable one due to the close resemblance of the structures. From the quantitative perspective (several measurements performed on osteonal units and statistical processing of data),some of the elements measured show significant differences among 3 species(the primary osteonal diameter, etc.). The fractal analysis and the lacunarity of the images show a great deal of potential, proving that this type of analysis can be of great help in the separation of the material from this perspective.

Latent heat induced rotation limited aggregation in 2D ice nanocrystals.

PubMed

Bampoulis, Pantelis; Siekman, Martin H; Kooij, E Stefan; Lohse, Detlef; Zandvliet, Harold J W; Poelsema, Bene

2015-07-21

The basic science responsible for the fascinating shapes of ice crystals and snowflakes is still not understood. Insufficient knowledge of the interaction potentials and the lack of relevant experimental access to the growth process are to blame for this failure. Here, we study the growth of fractal nanostructures in a two-dimensional (2D) system, intercalated between mica and graphene. Based on our scanning tunneling spectroscopy data, we provide compelling evidence that these fractals are 2D ice. They grow while they are in material contact with the atmosphere at 20 °C and without significant thermal contact to the ambient. The growth is studied in situ, in real time and space at the nanoscale. We find that the growing 2D ice nanocrystals assume a fractal shape, which is conventionally attributed to Diffusion Limited Aggregation (DLA). However, DLA requires a low mass density mother phase, in contrast to the actual currently present high mass density mother phase. Latent heat effects and consequent transport of heat and molecules are found to be key ingredients for understanding the evolution of the snow (ice) flakes. We conclude that not the local availability of water molecules (DLA), but rather them having the locally required orientation is the key factor for incorporation into the 2D ice nanocrystal. In combination with the transport of latent heat, we attribute the evolution of fractal 2D ice nanocrystals to local temperature dependent rotation limited aggregation. The ice growth occurs under extreme supersaturation, i.e., the conditions closely resemble the natural ones for the growth of complex 2D snow (ice) flakes and we consider our findings crucial for solving the "perennial" snow (ice) flake enigma.

Beyond maximum entropy: Fractal Pixon-based image reconstruction

NASA Technical Reports Server (NTRS)

Puetter, Richard C.; Pina, R. K.

1994-01-01

We have developed a new Bayesian image reconstruction method that has been shown to be superior to the best implementations of other competing methods, including Goodness-of-Fit methods such as Least-Squares fitting and Lucy-Richardson reconstruction, as well as Maximum Entropy (ME) methods such as those embodied in the MEMSYS algorithms. Our new method is based on the concept of the pixon, the fundamental, indivisible unit of picture information. Use of the pixon concept provides an improved image model, resulting in an image prior which is superior to that of standard ME. Our past work has shown how uniform information content pixons can be used to develop a 'Super-ME' method in which entropy is maximized exactly. Recently, however, we have developed a superior pixon basis for the image, the Fractal Pixon Basis (FPB). Unlike the Uniform Pixon Basis (UPB) of our 'Super-ME' method, the FPB basis is selected by employing fractal dimensional concepts to assess the inherent structure in the image. The Fractal Pixon Basis results in the best image reconstructions to date, superior to both UPB and the best ME reconstructions. In this paper, we review the theory of the UPB and FPB pixon and apply our methodology to the reconstruction of far-infrared imaging of the galaxy M51. The results of our reconstruction are compared to published reconstructions of the same data using the Lucy-Richardson algorithm, the Maximum Correlation Method developed at IPAC, and the MEMSYS ME algorithms. The results show that our reconstructed image has a spatial resolution a factor of two better than best previous methods (and a factor of 20 finer than the width of the point response function), and detects sources two orders of magnitude fainter than other methods.

Fractal-Inspired Subwavelength Geometric Inclusions for Improvement of High-Frequency Electromagnetic Devices

NASA Astrophysics Data System (ADS)

Smith, Kathryn Leigh

This dissertation presents research results demonstrating the efficacy of fractal-inspired subwavelength geometric inclusions for improvement of high-frequency electromagnetic devices. It begins with a review of the open literature in the area of fractal applications in antennas and metamaterials. This is followed by a detailed discussion of three high-frequency electromagnetic devices that demonstrate performance improvement through incorporation of subwavelength geometric design elements. The first of these devices is a spherical spiral metamaterial unit cell that was developed as a three-dimensional fractal expansion of the traditional split ring resonator, and is shown to be capable of producing broadband negative permeability, negative permittivity, or both, depending solely on the orientation of the unit cells with respect to the incident electric field. The second device is a ringed rectangular patch antenna that has four resonant frequencies. All four of these operative frequencies are shown to produce similar radiation patterns, which also closely match the pattern of a traditional patch antenna. Several minor geometric modifications of the basic shape of the device are also presented, and are shown to enable modification of the number of resonances, as well as tuning of frequencies of resonance. The third and final topic is a modified horn antenna that incorporates a spiral metamaterial as a phase-shifting device in order to achieve circularly polarized radiation. The handedness of the radiated wave is shown to be tunable through simple reorientation of the loading unit cells. In each of these cases, electrically-small geometric modification of existing device geometries is shown to greatly affect performance, either by increasing bandwidth, by inducing multiband behavior, or by enabling exotic radiation characteristics.

Latent heat induced rotation limited aggregation in 2D ice nanocrystals

NASA Astrophysics Data System (ADS)

Bampoulis, Pantelis; Siekman, Martin H.; Kooij, E. Stefan; Lohse, Detlef; Zandvliet, Harold J. W.; Poelsema, Bene

2015-07-01

The basic science responsible for the fascinating shapes of ice crystals and snowflakes is still not understood. Insufficient knowledge of the interaction potentials and the lack of relevant experimental access to the growth process are to blame for this failure. Here, we study the growth of fractal nanostructures in a two-dimensional (2D) system, intercalated between mica and graphene. Based on our scanning tunneling spectroscopy data, we provide compelling evidence that these fractals are 2D ice. They grow while they are in material contact with the atmosphere at 20 °C and without significant thermal contact to the ambient. The growth is studied in situ, in real time and space at the nanoscale. We find that the growing 2D ice nanocrystals assume a fractal shape, which is conventionally attributed to Diffusion Limited Aggregation (DLA). However, DLA requires a low mass density mother phase, in contrast to the actual currently present high mass density mother phase. Latent heat effects and consequent transport of heat and molecules are found to be key ingredients for understanding the evolution of the snow (ice) flakes. We conclude that not the local availability of water molecules (DLA), but rather them having the locally required orientation is the key factor for incorporation into the 2D ice nanocrystal. In combination with the transport of latent heat, we attribute the evolution of fractal 2D ice nanocrystals to local temperature dependent rotation limited aggregation. The ice growth occurs under extreme supersaturation, i.e., the conditions closely resemble the natural ones for the growth of complex 2D snow (ice) flakes and we consider our findings crucial for solving the "perennial" snow (ice) flake enigma.

Analysis of Resting-State fMRI Topological Graph Theory Properties in Methamphetamine Drug Users Applying Box-Counting Fractal Dimension.

PubMed

Siyah Mansoory, Meysam; Oghabian, Mohammad Ali; Jafari, Amir Homayoun; Shahbabaie, Alireza

2017-01-01

Graph theoretical analysis of functional Magnetic Resonance Imaging (fMRI) data has provided new measures of mapping human brain in vivo. Of all methods to measure the functional connectivity between regions, Linear Correlation (LC) calculation of activity time series of the brain regions as a linear measure is considered the most ubiquitous one. The strength of the dependence obligatory for graph construction and analysis is consistently underestimated by LC, because not all the bivariate distributions, but only the marginals are Gaussian. In a number of studies, Mutual Information (MI) has been employed, as a similarity measure between each two time series of the brain regions, a pure nonlinear measure. Owing to the complex fractal organization of the brain indicating self-similarity, more information on the brain can be revealed by fMRI Fractal Dimension (FD) analysis. In the present paper, Box-Counting Fractal Dimension (BCFD) is introduced for graph theoretical analysis of fMRI data in 17 methamphetamine drug users and 18 normal controls. Then, BCFD performance was evaluated compared to those of LC and MI methods. Moreover, the global topological graph properties of the brain networks inclusive of global efficiency, clustering coefficient and characteristic path length in addict subjects were investigated too. Compared to normal subjects by using statistical tests (P<0.05), topological graph properties were postulated to be disrupted significantly during the resting-state fMRI. Based on the results, analyzing the graph topological properties (representing the brain networks) based on BCFD is a more reliable method than LC and MI.

Fractal scaling analysis of groundwater dynamics in confined aquifers

NASA Astrophysics Data System (ADS)

Tu, Tongbi; Ercan, Ali; Kavvas, M. Levent

2017-10-01

Groundwater closely interacts with surface water and even climate systems in most hydroclimatic settings. Fractal scaling analysis of groundwater dynamics is of significance in modeling hydrological processes by considering potential temporal long-range dependence and scaling crossovers in the groundwater level fluctuations. In this study, it is demonstrated that the groundwater level fluctuations in confined aquifer wells with long observations exhibit site-specific fractal scaling behavior. Detrended fluctuation analysis (DFA) was utilized to quantify the monofractality, and multifractal detrended fluctuation analysis (MF-DFA) and multiscale multifractal analysis (MMA) were employed to examine the multifractal behavior. The DFA results indicated that fractals exist in groundwater level time series, and it was shown that the estimated Hurst exponent is closely dependent on the length and specific time interval of the time series. The MF-DFA and MMA analyses showed that different levels of multifractality exist, which may be partially due to a broad probability density distribution with infinite moments. Furthermore, it is demonstrated that the underlying distribution of groundwater level fluctuations exhibits either non-Gaussian characteristics, which may be fitted by the Lévy stable distribution, or Gaussian characteristics depending on the site characteristics. However, fractional Brownian motion (fBm), which has been identified as an appropriate model to characterize groundwater level fluctuation, is Gaussian with finite moments. Therefore, fBm may be inadequate for the description of physical processes with infinite moments, such as the groundwater level fluctuations in this study. It is concluded that there is a need for generalized governing equations of groundwater flow processes that can model both the long-memory behavior and the Brownian finite-memory behavior.

Characterizing Tityus discrepans scorpion venom from a fractal perspective: Venom complexity, effects of captivity, sexual dimorphism, differences among species.

PubMed

D'Suze, Gina; Sandoval, Moisés; Sevcik, Carlos

2015-12-15

A characteristic of venom elution patterns, shared with many other complex systems, is that many their features cannot be properly described with statistical or euclidean concepts. The understanding of such systems became possible with Mandelbrot's fractal analysis. Venom elution patterns were produced using the reversed phase high performance liquid chromatography (HPLC) with 1 mg of venom. One reason for the lack of quantitative analyses of the sources of venom variability is parametrizing the venom chromatograms' complexity. We quantize this complexity by means of an algorithm which estimates the contortedness (Q) of a waveform. Fractal analysis was used to compare venoms and to measure inter- and intra-specific venom variability. We studied variations in venom complexity derived from gender, seasonal and environmental factors, duration of captivity in the laboratory, technique used to milk venom. Copyright © 2015 Elsevier Ltd. All rights reserved.

Applications of Fractal Analytical Techniques in the Estimation of Operational Scale

NASA Technical Reports Server (NTRS)

Emerson, Charles W.; Quattrochi, Dale A.

2000-01-01

The observational scale and the resolution of remotely sensed imagery are essential considerations in the interpretation process. Many atmospheric, hydrologic, and other natural and human-influenced spatial phenomena are inherently scale dependent and are governed by different physical processes at different spatial domains. This spatial and operational heterogeneity constrains the ability to compare interpretations of phenomena and processes observed in higher spatial resolution imagery to similar interpretations obtained from lower resolution imagery. This is a particularly acute problem, since longterm global change investigations will require high spatial resolution Earth Observing System (EOS), Landsat 7, or commercial satellite data to be combined with lower resolution imagery from older sensors such as Landsat TM and MSS. Fractal analysis is a useful technique for identifying the effects of scale changes on remotely sensed imagery. The fractal dimension of an image is a non-integer value between two and three which indicates the degree of complexity in the texture and shapes depicted in the image. A true fractal surface exhibits self-similarity, a property of curves or surfaces where each part is indistinguishable from the whole, or where the form of the curve or surface is invariant with respect to scale. Theoretically, if the digital numbers of a remotely sensed image resemble an ideal fractal surface, then due to the self-similarity property, the fractal dimension of the image will not vary with scale and resolution, and the slope of the fractal dimension-resolution relationship would be zero. Most geographical phenomena, however, are not self-similar at all scales, but they can be modeled by a stochastic fractal in which the scaling properties of the image exhibit patterns that can be described by statistics such as area-perimeter ratios and autocovariances. Stochastic fractal sets relax the self-similarity assumption and measure many scales and resolutions to represent the varying form of a phenomenon as the pixel size is increased in a convolution process. We have observed that for images of homogeneous land covers, the fractal dimension varies linearly with changes in resolution or pixel size over the range of past, current, and planned space-borne sensors. This relationship differs significantly in images of agricultural, urban, and forest land covers, with urban areas retaining the same level of complexity, forested areas growing smoother, and agricultural areas growing more complex as small pixels are aggregated into larger, mixed pixels. Images of scenes having a mixture of land covers have fractal dimensions that exhibit a non-linear, complex relationship to pixel size. Measuring the fractal dimension of a difference image derived from two images of the same area obtained on different dates showed that the fractal dimension increased steadily, then exhibited a sharp decrease at increasing levels of pixel aggregation. This breakpoint of the fractal dimension/resolution plot is related to the spatial domain or operational scale of the phenomenon exhibiting the predominant visible difference between the two images (in this case, mountain snow cover). The degree to which an image departs from a theoretical ideal fractal surface provides clues as to how much information is altered or lost in the processes of rescaling and rectification. The measured fractal dimension of complex, composite land covers such as urban areas also provides a useful textural index that can assist image classification of complex scenes.

Alpha-spectrometry and fractal analysis of surface micro-images for characterisation of porous materials used in manufacture of targets for laser plasma experiments

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aushev, A A; Barinov, S P; Vasin, M G

2015-06-30

We present the results of employing the alpha-spectrometry method to determine the characteristics of porous materials used in targets for laser plasma experiments. It is shown that the energy spectrum of alpha-particles, after their passage through porous samples, allows one to determine the distribution of their path length in the foam skeleton. We describe the procedure of deriving such a distribution, excluding both the distribution broadening due to statistical nature of the alpha-particle interaction with an atomic structure (straggling) and hardware effects. The fractal analysis of micro-images is applied to the same porous surface samples that have been studied bymore » alpha-spectrometry. The fractal dimension and size distribution of the number of the foam skeleton grains are obtained. Using the data obtained, a distribution of the total foam skeleton thickness along a chosen direction is constructed. It roughly coincides with the path length distribution of alpha-particles within a range of larger path lengths. It is concluded that the combined use of the alpha-spectrometry method and fractal analysis of images will make it possible to determine the size distribution of foam skeleton grains (or pores). The results can be used as initial data in theoretical studies on propagation of the laser and X-ray radiation in specific porous samples. (laser plasma)« less

Fractal analysis of multiscale spatial autocorrelation among point data

USGS Publications Warehouse

De Cola, L.

1991-01-01

The analysis of spatial autocorrelation among point-data quadrats is a well-developed technique that has made limited but intriguing use of the multiscale aspects of pattern. In this paper are presented theoretical and algorithmic approaches to the analysis of aggregations of quadrats at or above a given density, in which these sets are treated as multifractal regions whose fractal dimension, D, may vary with phenomenon intensity, scale, and location. The technique is illustrated with Matui's quadrat house-count data, which yield measurements consistent with a nonautocorrelated simulated Poisson process but not with an orthogonal unit-step random walk. The paper concludes with a discussion of the implications of such analysis for multiscale geographic analysis systems. -Author

Fractal analysis of heart rate dynamics as a predictor of mortality in patients with depressed left ventricular function after acute myocardial infarction. TRACE Investigators. TRAndolapril Cardiac Evaluation

NASA Technical Reports Server (NTRS)

Makikallio, T. H.; Hoiber, S.; Kober, L.; Torp-Pedersen, C.; Peng, C. K.; Goldberger, A. L.; Huikuri, H. V.

1999-01-01

A number of new methods have been recently developed to quantify complex heart rate (HR) dynamics based on nonlinear and fractal analysis, but their value in risk stratification has not been evaluated. This study was designed to determine whether selected new dynamic analysis methods of HR variability predict mortality in patients with depressed left ventricular (LV) function after acute myocardial infarction (AMI). Traditional time- and frequency-domain HR variability indexes along with short-term fractal-like correlation properties of RR intervals (exponent alpha) and power-law scaling (exponent beta) were studied in 159 patients with depressed LV function (ejection fraction <35%) after an AMI. By the end of 4-year follow-up, 72 patients (45%) had died and 87 (55%) were still alive. Short-term scaling exponent alpha (1.07 +/- 0.26 vs 0.90 +/- 0.26, p <0.001) and power-law slope beta (-1.35 +/- 0.23 vs -1.44 +/- 0.25, p <0.05) differed between survivors and those who died, but none of the traditional HR variability measures differed between these groups. Among all analyzed variables, reduced scaling exponent alpha (<0.85) was the best univariable predictor of mortality (relative risk 3.17, 95% confidence interval 1.96 to 5.15, p <0.0001), with positive and negative predictive accuracies of 65% and 86%, respectively. In the multivariable Cox proportional hazards analysis, mortality was independently predicted by the reduced exponent alpha (p <0.001) after adjustment for several clinical variables and LV function. A short-term fractal-like scaling exponent was the most powerful HR variability index in predicting mortality in patients with depressed LV function. Reduction in fractal correlation properties implies more random short-term HR dynamics in patients with increased risk of death after AMI.

Music and fractals

NASA Astrophysics Data System (ADS)

Wuorinen, Charles

2015-03-01

Any of the arts may produce exemplars that have fractal characteristics. There may be fractal painting, fractal poetry, and the like. But these will always be specific instances, not necessarily displaying intrinsic properties of the art-medium itself. Only music, I believe, of all the arts possesses an intrinsically fractal character, so that its very nature is fractally determined. Thus, it is reasonable to assert that any instance of music is fractal...

Fractal structures and fractal functions as disease indicators

USGS Publications Warehouse

Escos, J.M; Alados, C.L.; Emlen, J.M.

1995-01-01

Developmental instability is an early indicator of stress, and has been used to monitor the impacts of human disturbance on natural ecosystems. Here we investigate the use of different measures of developmental instability on two species, green peppers (Capsicum annuum), a plant, and Spanish ibex (Capra pyrenaica), an animal. For green peppers we compared the variance in allometric relationship between control plants, and a treatment group infected with the tomato spotted wilt virus. The results show that infected plants have a greater variance about the allometric regression line than the control plants. We also observed a reduction in complexity of branch structure in green pepper with a viral infection. Box-counting fractal dimension of branch architecture declined under stress infection. We also tested the reduction in complexity of behavioral patterns under stress situations in Spanish ibex (Capra pyrenaica). Fractal dimension of head-lift frequency distribution measures predator detection efficiency. This dimension decreased under stressful conditions, such as advanced pregnancy and parasitic infection. Feeding distribution activities reflect food searching efficiency. Power spectral analysis proves to be the most powerful tool for character- izing fractal behavior, revealing a reduction in complexity of time distribution activity under parasitic infection.

Fractal feature of sEMG from Flexor digitorum superficialis muscle correlated with levels of contraction during low-level finger flexions.

PubMed

Arjunan, Sridhar P; Kumar, Dinesh K; Naik, Ganesh R

2010-01-01

This research paper reports an experimental study on identification of the changes in fractal properties of surface Electromyogram (sEMG) with the changes in the force levels during low-level finger flexions. In the previous study, the authors have identified a novel fractal feature, Maximum fractal length (MFL) as a measure of strength of low-level contractions and has used this feature to identify various wrist and finger movements. This study has tested the relationship between the MFL and force of contraction. The results suggest that changes in MFL is correlated with the changes in contraction levels (20%, 50% and 80% maximum voluntary contraction (MVC)) during low-level muscle activation such as finger flexions. From the statistical analysis and by visualisation using box-plot, it is observed that MFL (p ≈ 0.001) is a more correlated to force of contraction compared to RMS (p≈0.05), even when the muscle contraction is less than 50% MVC during low-level finger flexions. This work has established that this fractal feature will be useful in providing information about changes in levels of force during low-level finger movements for prosthetic control or human computer interface.

Analyzing the photonic band gaps in two-dimensional plasma photonic crystals with fractal Sierpinski gasket structure based on the Monte Carlo method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Hai-Feng, E-mail: hanlor@163.com; Key Laboratory of Radar Imaging and Microwave Photonics; Liu, Shao-Bin

2016-08-15

In this paper, the properties of photonic band gaps (PBGs) in two types of two-dimensional plasma-dielectric photonic crystals (2D PPCs) under a transverse-magnetic (TM) wave are theoretically investigated by a modified plane wave expansion (PWE) method where Monte Carlo method is introduced. The proposed PWE method can be used to calculate the band structures of 2D PPCs which possess arbitrary-shaped filler and any lattice. The efficiency and convergence of the present method are discussed by a numerical example. The configuration of 2D PPCs is the square lattices with fractal Sierpinski gasket structure whose constituents are homogeneous and isotropic. The type-1more » PPCs is filled with the dielectric cylinders in the plasma background, while its complementary structure is called type-2 PPCs, in which plasma cylinders behave as the fillers in the dielectric background. The calculated results reveal that the enough accuracy and good convergence can be obtained, if the number of random sampling points of Monte Carlo method is large enough. The band structures of two types of PPCs with different fractal orders of Sierpinski gasket structure also are theoretically computed for a comparison. It is demonstrate that the PBGs in higher frequency region are more easily produced in the type-1 PPCs rather than in the type-2 PPCs. Sierpinski gasket structure introduced in the 2D PPCs leads to a larger cutoff frequency, enhances and induces more PBGs in high frequency region. The effects of configurational parameters of two types of PPCs on the PBGs are also investigated in detail. The results show that the PBGs of the PPCs can be easily manipulated by tuning those parameters. The present type-1 PPCs are more suitable to design the tunable compacted devices.« less

Dynamic Pattern Formation for Wings of Pterygota in an Eclosion ---Pattern Analysis for Wings with the Imago---

NASA Astrophysics Data System (ADS)

Seino, M.; Kakazu, Y.

The vein and cell patterns for the fore and hind wing of Lepidoptera, Hemiptera, Orthoptera and Odonata are analyzed and discussed. For vein patterns of them, the fractal properties are shown and the inequality between four orders is obtained. The nature of wings observed by mass distributions for fractal dimensions of the vein pattern is presented.

Fractal-like thickness and topography of the salt layer in a pillows province of the southern North Sea

NASA Astrophysics Data System (ADS)

Hernandez Maya, K.; Mitchell, N. C.; Huuse, M.

2017-12-01

Salt topography and thickness variations are important for testing theories of how halokinetic deformation proceeds. The ability to predict thickness variations of salt at small scale is also important for reservoir evaluations, as breach of the salt layer can lead to loss of petroleum fluids and can be difficult to evaluate from seismic reflection data. Relevant to these issues, we here report analysis of data on salt layer topography and thickness from the southern North Sea, where the salt is organized into pillows. These data were derived by the Geological Survey of the Netherlands (TNO) from industry 3D seismic reflection data combined with a dense network of well information. Highs and lows in the topography of the upper salt interface occur spaced over a variety of lengthscales. Power spectral analysis of the interface topography reveals a simple inverse power law relationship between power spectral density and spatial wave number. The relationship suggests that the interface is a self-affine fractal with a fractal dimension of 2.85. A similar analysis of the salt layer thickness also suggests a fractal-like power law. Whereas the layer thickness power law is unsurprising as the underlying basement topography dominates the thickness and it also has a fractal-like power spectrum, the salt topography is not so easily explained as not all the basement faults are overlaid by salt pillows, instead some areas of the dataset salt thinning overlies faults. We consider instead whether a spatially varied loading of the salt layer may have caused this fractal-like geometry. Varied density and thickness of overburdening layers seem unlikely causes, as thicknesses of layers and their reflectivities do not vary sympathetically with the topography of the interface. The composition of the salt layer varies with the relative proportions of halite and denser anhydrite and other minerals. Although limited in scope and representing the mobilized salt layer, the information from the well data could potentially support the loading originating initially from within the salt. Such internal loading needs to be considered in modelling salt deformation for a variety of practical and academic purposes.

Global and Local Approaches Describing Critical Phenomena on the Developing and Developed Financial Markets

NASA Astrophysics Data System (ADS)

Grech, Dariusz

We define and confront global and local methods to analyze the financial crash-like events on the financial markets from the critical phenomena point of view. These methods are based respectively on the analysis of log-periodicity and on the local fractal properties of financial time series in the vicinity of phase transitions (crashes). The log-periodicity analysis is made in a daily time horizon, for the whole history (1991-2008) of Warsaw Stock Exchange Index (WIG) connected with the largest developing financial market in Europe. We find that crash-like events on the Polish financial market are described better by the log-divergent price model decorated with log-periodic behavior than by the power-law-divergent price model usually discussed in log-periodic scenarios for developed markets. Predictions coming from log-periodicity scenario are verified for all main crashes that took place in WIG history. It is argued that crash predictions within log-periodicity model strongly depend on the amount of data taken to make a fit and therefore are likely to contain huge inaccuracies. Next, this global analysis is confronted with the local fractal description. To do so, we provide calculation of the so-called local (time dependent) Hurst exponent H loc for the WIG time series and for main US stock market indices like DJIA and S&P 500. We point out dependence between the behavior of the local fractal properties of financial time series and the crashes appearance on the financial markets. We conclude that local fractal method seems to work better than the global approach - both for developing and developed markets. The very recent situation on the market, particularly related to the Fed intervention in September 2007 and the situation immediately afterwards is also analyzed within fractal approach. It is shown in this context how the financial market evolves through different phases of fractional Brownian motion. Finally, the current situation on American market is analyzed in fractal language. This is to show how far we still are from the end of recession and from the beginning of a new boom on US financial market or on other world leading stocks.

An Approach to Study Elastic Vibrations of Fractal Cylinders

NASA Astrophysics Data System (ADS)

Steinberg, Lev; Zepeda, Mario

2016-11-01

This paper presents our study of dynamics of fractal solids. Concepts of fractal continuum and time had been used in definitions of a fractal body deformation and motion, formulation of conservation of mass, balance of momentum, and constitutive relationships. A linearized model, which was written in terms of fractal time and spatial derivatives, has been employed to study the elastic vibrations of fractal circular cylinders. Fractal differential equations of torsional, longitudinal and transverse fractal wave equations have been obtained and solution properties such as size and time dependence have been revealed.

Fractal vector optical fields.

PubMed

Pan, Yue; Gao, Xu-Zhen; Cai, Meng-Qiang; Zhang, Guan-Lin; Li, Yongnan; Tu, Chenghou; Wang, Hui-Tian

2016-07-15

We introduce the concept of a fractal, which provides an alternative approach for flexibly engineering the optical fields and their focal fields. We propose, design, and create a new family of optical fields-fractal vector optical fields, which build a bridge between the fractal and vector optical fields. The fractal vector optical fields have polarization states exhibiting fractal geometry, and may also involve the phase and/or amplitude simultaneously. The results reveal that the focal fields exhibit self-similarity, and the hierarchy of the fractal has the "weeding" role. The fractal can be used to engineer the focal field.

Multi-fractality in aeroelastic response as a precursor to flutter

NASA Astrophysics Data System (ADS)

Venkatramani, J.; Nair, Vineeth; Sujith, R. I.; Gupta, Sayan; Sarkar, Sunetra

2017-01-01

Wind tunnel tests on a NACA 0012 airfoil have been carried out to study the transition in aeroelastic response from an initial state characterised by low-amplitude aperiodic fluctuations to aeroelastic flutter when the system exhibits limit cycle oscillations. An analysis of the aeroelastic measurements reveals multi-fractal characteristics in the pre-flutter regime. This has not been studied in the literature. As the flow velocity approaches the flutter velocity from below, a gradual loss in multi-fractality is observed. Measures based on the generalised Hurst exponents are developed and are shown to have the potential to warn against impending aeroelastic flutter. The results of this study could be useful for health monitoring of aeroelastic structures.

Microstructure of cotton fibrous assemblies based on computed tomography

NASA Astrophysics Data System (ADS)

Jing, Hui; Yu, Weidong

2017-12-01

This paper describes for the first time the analysis of inner microstructure of cotton fibrous assemblies using computed tomography. Microstructure parameters such as packing density, fractal dimension as well as porosity including open porosity, closed porosity and total porosity are calculated based on 2D data from computed tomography. Values of packing density and fractal dimension are stable in random oriented fibrous assemblies, and there exists a satisfactory approximate linear relationship between them. Moreover, poles analysis indicates that porosity represents the tightness of fibrous assemblies and open poles are main existence.

Possibilities of fractal analysis of the competitive dynamics: Approaches and procedures

NASA Astrophysics Data System (ADS)

Zagornaya, T. O.; Medvedeva, M. A.; Panova, V. L.; Isaichik, K. F.; Medvedev, A. N.

2017-11-01

The possibilities of the fractal approach are used for the study of non-linear nature of the competitive dynamics of the market of trading intermediaries. Based on a statistical study of the functioning of retail indicators in the region, the approach to the analysis of the characteristics of the competitive behavior of market participants is developed. The authors postulate the principles of studying the dynamics of competition as a result of changes in the characteristics of the vector and the competitive behavior of market agents.

Human physiological benefits of viewing nature: EEG responses to exact and statistical fractal patterns.

PubMed

Hagerhall, C M; Laike, T; Küller, M; Marcheschi, E; Boydston, C; Taylor, R P

2015-01-01

Psychological and physiological benefits of viewing nature have been extensively studied for some time. More recently it has been suggested that some of these positive effects can be explained by nature's fractal properties. Virtually all studies on human responses to fractals have used stimuli that represent the specific form of fractal geometry found in nature, i.e. statistical fractals, as opposed to fractal patterns which repeat exactly at different scales. This raises the question of whether human responses like preference and relaxation are being driven by fractal geometry in general or by the specific form of fractal geometry found in nature. In this study we consider both types of fractals (statistical and exact) and morph one type into the other. Based on the Koch curve, nine visual stimuli were produced in which curves of three different fractal dimensions evolve gradually from an exact to a statistical fractal. The patterns were shown for one minute each to thirty-five subjects while qEEG was continuously recorded. The results showed that the responses to statistical and exact fractals differ, and that the natural form of the fractal is important for inducing alpha responses, an indicator of a wakefully relaxed state and internalized attention.

Ferroelectric and electrical characterization of multiferroic BiFeO3 at the single nanoparticle level

NASA Astrophysics Data System (ADS)

Vasudevan, R. K.; Bogle, K. A.; Kumar, A.; Jesse, S.; Magaraggia, R.; Stamps, R.; Ogale, S. B.; Potdar, H. S.; Nagarajan, V.

2011-12-01

Ferroelectric BiFeO3 (BFO) nanoparticles deposited on epitaxial substrates of SrRuO3 (SRO) and La1-xSrxMnO3 (LSMO) were studied using band excitation piezoresponse spectroscopy (BEPS), piezoresponse force microscopy (PFM), and ferromagnetic resonance (FMR). BEPS confirms that the nanoparticles are ferroelectric in nature. Switching behavior of nanoparticle clusters were studied and showed evidence for inhomogeneous switching. The dimensionality of domains within nanoparticles was found to be fractal in nature, with a dimensionality constant of ˜1.4, on par with ferroelectric BFO thin-films under 100 nm in thickness. Ferromagnetic resonance studies indicate BFO nanoparticles only weakly affect the magnetic response of LSMO.

Application to recognition of ferrography image with fractal neural network

NASA Astrophysics Data System (ADS)

Tian, Xianzhong; Hu, Tongsen; Zhang, Jian

2005-10-01

Because wear particles have fractal characteristics, it is necessary that adding fractal parameters to studying wear particles and diagnosing machine troubles. This paper discusses fractal parameters of wear particles, presents arithmetic calculating fractal dimension, and constructs a fractal neural network which can recognize wear particles image. It is proved by experiments that this fractal neural network can recognize some characteristics of wear particles image, and can also classify wear types.

Technologically important extremophile 16S rRNA sequence Shannon entropy and fractal property comparison with long term dormant microbes

NASA Astrophysics Data System (ADS)

Holden, Todd; Gadura, N.; Dehipawala, S.; Cheung, E.; Tuffour, M.; Schneider, P.; Tremberger, G., Jr.; Lieberman, D.; Cheung, T.

2011-10-01

Technologically important extremophiles including oil eating microbes, uranium and rocket fuel perchlorate reduction microbes, electron producing microbes and electrode electrons feeding microbes were compared in terms of their 16S rRNA sequences, a standard targeted sequence in comparative phylogeny studies. Microbes that were reported to have survived a prolonged dormant duration were also studied. Examples included the recently discovered microbe that survives after 34,000 years in a salty environment while feeding off organic compounds from other trapped dead microbes. Shannon entropy of the 16S rRNA nucleotide composition and fractal dimension of the nucleotide sequence in terms of its atomic number fluctuation analyses suggest a selected range for these extremophiles as compared to other microbes; consistent with the experience of relatively mild evolutionary pressure. However, most of the microbes that have been reported to survive in prolonged dormant duration carry sequences with fractal dimension between 1.995 and 2.005 (N = 10 out of 13). Similar results are observed for halophiles, red-shifted chlorophyll and radiation resistant microbes. The results suggest that prolonged dormant duration, in analogous to high salty or radiation environment, would select high fractal 16S rRNA sequences. Path analysis in structural equation modeling supports a causal relation between entropy and fractal dimension for the studied 16S rRNA sequences (N = 7). Candidate choices for high fractal 16S rRNA microbes could offer protection for prolonged spaceflights. BioBrick gene network manipulation could include extremophile 16S rRNA sequences in synthetic biology and shed more light on exobiology and future colonization in shielded spaceflights. Whether the high fractal 16S rRNA sequences contain an asteroidlike extra-terrestrial source could be speculative but interesting.

Fractal Theory for Permeability Prediction, Venezuelan and USA Wells

NASA Astrophysics Data System (ADS)

Aldana, Milagrosa; Altamiranda, Dignorah; Cabrera, Ana

2014-05-01

Inferring petrophysical parameters such as permeability, porosity, water saturation, capillary pressure, etc, from the analysis of well logs or other available core data has always been of critical importance in the oil industry. Permeability in particular, which is considered to be a complex parameter, has been inferred using both empirical and theoretical techniques. The main goal of this work is to predict permeability values on different wells using Fractal Theory, based on a method proposed by Pape et al. (1999). This approach uses the relationship between permeability and the geometric form of the pore space of the rock. This method is based on the modified equation of Kozeny-Carman and a fractal pattern, which allows determining permeability as a function of the cementation exponent, porosity and the fractal dimension. Data from wells located in Venezuela and the United States of America are analyzed. Employing data of porosity and permeability obtained from core samples, and applying the Fractal Theory method, we calculated the prediction equations for each well. At the beginning, this was achieved by training with 50% of the data available for each well. Afterwards, these equations were tested inferring over 100% of the data to analyze possible trends in their distribution. This procedure gave excellent results in all the wells in spite of their geographic distance, generating permeability models with the potential to accurately predict permeability logs in the remaining parts of the well for which there are no core samples, using even porority logs. Additionally, empirical models were used to determine permeability and the results were compared with those obtained by applying the fractal method. The results indicated that, although there are empirical equations that give a proper adjustment, the prediction results obtained using fractal theory give a better fit to the core reference data.

Mass fractal dimension and spectral dimension to characterize different horizons in La Herreria (Sierra de Guadarrama, Spain)

NASA Astrophysics Data System (ADS)

Inclan, Rosa Maria

2016-04-01

Knowledge on three dimensional soil pore architecture is important to improve our understanding of the factors that control a number of critical soil processes as it controls biological, chemical and physical processes at various scales. Computed Tomography (CT) images provide increasingly reliable information about the geometry of pores and solids in soils at very small scale with the benefit that is a non-invasive technique. Fractal formalism has revealed as a useful tool in these cases where highly complex and heterogeneous meda are studied. One of these quantifications is mass dimension (Dm) and spectral dimension (d) applied to describe the water and gas diffusion coefficients in soils (Tarquis et al., 2012). In this work, intact soil samples were collected from the first three horizons of La Herreria soil. This station is located in the lowland mountain area of Sierra de Guadarrama (Santolaria et al., 2015) and it represents a highly degraded type of site as a result of the livestock keeping. The 3D images, of 45.1 micro-m resolution (256x256x256 voxels), were obtained and then binarized following the singularity-CA method (Martín-Sotoca et al. 2016). Based on these images Dm and d were estimated. The results showed an statistical difference in porosity, Dm and d for each horizon. This fact has a direct implication in diffusion parameters for a pore network modeling based on both fractal dimensions. These soil parameters will constitute a basis for site characterization for further studies regarding soil degradation; determining the interaction between soil, plant and atmosphere with respect to human induced activities as well as the basis for several nitrogen and carbon cycles modeling. References Martin Sotoca; J.J. Ana M. Tarquis, Antonio Saa Requejo, and Juan B. Grau (2016). Pore detection in Computed Tomography (CT) soil 3D images using singularity map analysis. Geophysical Research Abstracts, 18, EGU2016-829. Santolaria-Canales, Edmundo and the GuMNet Consortium Team (2015). GuMNet - Guadarrama Monitoring Network. Installation and set up of a high altitude monitoring network, north of Madrid. Spain. Geophysical Research Abstracts, 17, EGU2015-13989-2. Tarquis, A. M., Sanchez, M. E., Antón, J. M., Jimenez, J., Saa-Requejo, A., Andina, D., & Crawford, J. W. (2012). Variation in spectral and mass dimension on three-dimensional soil image processing. Soil Science, 177(2), 88-97. Web: http://www.ucm.es/gumnet/

Micro and MACRO Fractals Generated by Multi-Valued Dynamical Systems

NASA Astrophysics Data System (ADS)

Banakh, T.; Novosad, N.

2014-08-01

Given a multi-valued function Φ : X \\mumap X on a topological space X we study the properties of its fixed fractal \\malteseΦ, which is defined as the closure of the orbit Φω(*Φ) = ⋃n∈ωΦn(*Φ) of the set *Φ = {x ∈ X : x ∈ Φ(x)} of fixed points of Φ. A special attention is paid to the duality between micro-fractals and macro-fractals, which are fixed fractals \\maltese Φ and \\maltese {Φ -1} for a contracting compact-valued function Φ : X \\mumap X on a complete metric space X. With help of algorithms (described in this paper) we generate various images of macro-fractals which are dual to some well-known micro-fractals like the fractal cross, the Sierpiński triangle, Sierpiński carpet, the Koch curve, or the fractal snowflakes. The obtained images show that macro-fractals have a large-scale fractal structure, which becomes clearly visible after a suitable zooming.

Temporal fractal analysis of the rs-BOLD signal identifies brain abnormalities in autism spectrum disorder.

PubMed

Dona, Olga; Hall, Geoffrey B; Noseworthy, Michael D

2017-01-01

Brain connectivity in autism spectrum disorders (ASD) has proven difficult to characterize due to the heterogeneous nature of the spectrum. Connectivity in the brain occurs in a complex, multilevel and multi-temporal manner, driving the fluctuations observed in local oxygen demand. These fluctuations can be characterized as fractals, as they auto-correlate at different time scales. In this study, we propose a model-free complexity analysis based on the fractal dimension of the rs-BOLD signal, acquired with magnetic resonance imaging. The fractal dimension can be interpreted as measure of signal complexity and connectivity. Previous studies have suggested that reduction in signal complexity can be associated with disease. Therefore, we hypothesized that a detectable difference in rs-BOLD signal complexity could be observed between ASD patients and Controls. Anatomical and functional data from fifty-five subjects with ASD (12.7 ± 2.4 y/o) and 55 age-matched (14.1 ± 3.1 y/o) healthy controls were accessed through the NITRC database and the ABIDE project. Subjects were scanned using a 3T GE Signa MRI and a 32-channel RF-coil. Axial FSPGR-3D images were used to prescribe rs-BOLD (TE/TR = 30/2000ms) where 300 time points were acquired. Motion correction was performed on the functional data and anatomical and functional images were aligned and spatially warped to the N27 standard brain atlas. Fractal analysis, performed on a grey matter mask, was done by estimating the Hurst exponent in the frequency domain using a power spectral density approach and refining the estimation in the time domain with de-trended fluctuation analysis and signal summation conversion methods. Voxel-wise fractal dimension (FD) was calculated for every subject in the control group and in the ASD group to create ROI-based Z-scores for the ASD patients. Voxel-wise validation of FD normality across controls was confirmed, and non-Gaussian voxels were eliminated from subsequent analysis. To maintain a 95% confidence level, only regions where Z-score values were at least 2 standard deviations away from the mean (i.e. where |Z| > 2.0) were included in the analysis. We found that the main regions, where signal complexity significantly decreased among ASD patients, were the amygdala (p = 0.001), the vermis (p = 0.02), the basal ganglia (p = 0.01) and the hippocampus (p = 0.02). No regions reported significant increase in signal complexity in this study. Our findings were correlated with ADIR and ADOS assessment tools, reporting the highest correlation with the ADOS metrics. Brain connectivity is best modeled as a complex system. Therefore, a measure of complexity as the fractal dimension of fluctuations in brain oxygen demand and utilization could provide important information about connectivity issues in ASD. Moreover, this technique can be used in the characterization of a single subject, with respect to controls, without the need for group analysis. Our novel approach provides an ideal avenue for personalized diagnostics, thus providing unique patient specific assessment that could help in individualizing treatments.

The pore structure and fractal characteristics of shales with low thermal maturity from the Yuqia Coalfield, northern Qaidam Basin, northwestern China

NASA Astrophysics Data System (ADS)

Hou, Haihai; Shao, Longyi; Li, Yonghong; Li, Zhen; Zhang, Wenlong; Wen, Huaijun

2018-03-01

The continental shales from the Middle Jurassic Shimengou Formation of the northern Qaidam Basin, northwestern China, have been investigated in recent years because of their shale gas potential. In this study, a total of twenty-two shale samples were collected from the YQ-1 borehole in the Yuqia Coalfield, northern Qaidam Basin. The total organic carbon (TOC) contents, pore structure parameters, and fractal characteristics of the samples were investigated using TOC analysis, low-temperature nitrogen adsorption experiments, and fractal analysis. The results show that the average pore size of the Shimengou shales varied from 8.149 nm to 20.635 nm with a mean value of 10.74 nm, which is considered mesopore-sized. The pores of the shales are mainly inkbottle- and slit-shaped. The sedimentary environment plays an essential role in controlling the TOC contents of the low maturity shales, with the TOC values of shales from deep to semi-deep lake facies (mean: 5.23%) being notably higher than those of the shore-shallow lake facies (mean: 0.65%). The fractal dimensions range from 2.4639 to 2.6857 with a mean of 2.6122, higher than those of marine shales, which indicates that the pore surface was rougher and the pore structure more complex in these continental shales. The fractal dimensions increase with increasing total pore volume and total specific surface area, and with decreasing average pore size. With increasing TOC contents in shales, the fractal dimensions increase first and then decrease, with the highest value occurring at 2% of TOC content, which is in accordance with the trends between the TOC and both total specific surface area and total pore volume. The pore structure complexity and pore surface roughness of these low-maturity shales would be controlled by the combined effects of both sedimentary environments and the TOC contents.

SU-D-BRA-04: Fractal Dimension Analysis of Edge-Detected Rectal Cancer CTs for Outcome Prediction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhong, H; Wang, J; Hu, W

2015-06-15

Purpose: To extract the fractal dimension features from edge-detected rectal cancer CTs, and to examine the predictability of fractal dimensions to outcomes of primary rectal cancer patients. Methods: Ninety-seven rectal cancer patients treated with neo-adjuvant chemoradiation were enrolled in this study. CT images were obtained before chemoradiotherapy. The primary lesions of the rectal cancer were delineated by experienced radiation oncologists. These images were extracted and filtered by six different Laplacian of Gaussian (LoG) filters with different filter values (0.5–3.0: from fine to coarse) to achieve primary lesions in different anatomical scales. Edges of the original images were found at zero-crossingsmore » of the filtered images. Three different fractal dimensions (box-counting dimension, Minkowski dimension, mass dimension) were calculated upon the image slice with the largest cross-section of the primary lesion. The significance of these fractal dimensions in survival, recurrence and metastasis were examined by Student’s t-test. Results: For a follow-up time of two years, 18 of 97 patients had experienced recurrence, 24 had metastasis, and 18 were dead. Minkowski dimensions under large filter values (2.0, 2.5, 3.0) were significantly larger (p=0.014, 0.006, 0.015) in patients with recurrence than those without. For metastasis, only box-counting dimensions under a single filter value (2.5) showed differences (p=0.016) between patients with and without. For overall survival, box-counting dimensions (filter values = 0.5, 1.0, 1.5), Minkowski dimensions (filter values = 0.5, 1.5, 2.0, 2,5) and mass dimensions (filter values = 1.5, 2.0) were all significant (p<0.05). Conclusion: It is feasible to extract shape information by edge detection and fractal dimensions analysis in neo-adjuvant rectal cancer patients. This information can be used to prognosis prediction.« less

Spatial and velocity statistics of inertial particles in turbulent flows

NASA Astrophysics Data System (ADS)

Bec, J.; Biferale, L.; Cencini, M.; Lanotte, A. S.; Toschi, F.

2011-12-01

Spatial and velocity statistics of heavy point-like particles in incompressible, homogeneous, and isotropic three-dimensional turbulence is studied by means of direct numerical simulations at two values of the Taylor-scale Reynolds number Reλ ~ 200 and Reλ ~ 400, corresponding to resolutions of 5123 and 20483 grid points, respectively. Particles Stokes number values range from St ≈ 0.2 to 70. Stationary small-scale particle distribution is shown to display a singular -multifractal- measure, characterized by a set of generalized fractal dimensions with a strong sensitivity on the Stokes number and a possible, small Reynolds number dependency. Velocity increments between two inertial particles depend on the relative weight between smooth events - where particle velocity is approximately the same of the fluid velocity-, and caustic contributions - when two close particles have very different velocities. The latter events lead to a non-differentiable small-scale behaviour for the relative velocity. The relative weight of these two contributions changes at varying the importance of inertia. We show that moments of the velocity difference display a quasi bi-fractal-behavior and that the scaling properties of velocity increments for not too small Stokes number are in good agreement with a recent theoretical prediction made by K. Gustavsson and B. Mehlig arXiv: 1012.1789v1 [physics.flu-dyn], connecting the saturation of velocity scaling exponents with the fractal dimension of particle clustering.

Synthesis of Polyferrocenylsilane Block Copolymers and their Crystallization-Driven Self-Assembly in Protic Solvents

NASA Astrophysics Data System (ADS)

Zhou, Hang

Quantum walks are the quantum mechanical analogue of classical random walks. Discrete-time quantum walks have been introduced and studied mostly on the line Z or higher dimensional space Zd but rarely defined on graphs with fractal dimensions because the coin operator depends on the position and the Fourier transform on the fractals is not defined. Inspired by its nature of classical walks, different quantum walks will be defined by choosing different shift and coin operators. When the coin operator is uniform, the results of classical walks will be obtained upon measurement at each step. Moreover, with measurement at each step, our results reveal more information about the classical random walks. In this dissertation, two graphs with fractal dimensions will be considered. The first one is Sierpinski gasket, a degree-4 regular graph with Hausdorff dimension of df = ln 3/ ln 2. The second is the Cantor graph derived like Cantor set, with Hausdorff dimension of df = ln 2/ ln 3. The definitions and amplitude functions of the quantum walks will be introduced. The main part of this dissertation is to derive a recursive formula to compute the amplitude Green function. The exiting probability will be computed and compared with the classical results. When the generation of graphs goes to infinity, the recursion of the walks will be investigated and the convergence rates will be obtained and compared with the classical counterparts.

On the question of fractal packing structure in metallic glasses

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ding, Jun; Asta, Mark; Ritchie, Robert O.

2017-07-25

This work addresses the long-standing debate over fractal models of packing structure in metallic glasses (MGs). Through detailed fractal and percolation analyses of MG structures, derived from simulations spanning a range of compositions and quenching rates, we conclude that there is no fractal atomic-level structure associated with the packing of all atoms or solute-centered clusters. The results are in contradiction with conclusions derived from previous studies based on analyses of shifts in radial distribution function and structure factor peaks associated with volume changes induced by pressure and compositional variations. Here in this paper, the interpretation of such shifts is shownmore » to be challenged by the heterogeneous nature of MG structure and deformation at the atomic scale. Moreover, our analysis in the present work illustrates clearly the percolation theory applied to MGs, for example, the percolation threshold and characteristics of percolation clusters formed by subsets of atoms, which can have important consequences for structure–property relationships in these amorphous materials.« less

[Local fractal analysis of noise-like time series by all permutations method for 1-115 min periods].

PubMed

Panchelyuga, V A; Panchelyuga, M S

2015-01-01

Results of local fractal analysis of 329-per-day time series of 239Pu alpha-decay rate fluctuations by means of all permutations method (APM) are presented. The APM-analysis reveals in the time series some steady frequency set. The coincidence of the frequency set with the Earth natural oscillations was demonstrated. A short review of works by different authors who analyzed the time series of fluctuations in processes of different nature is given. We have shown that the periods observed in those works correspond to the periods revealed in our study. It points to a common mechanism of the phenomenon observed.

Diffusion-limited aggregation in two dimensions

NASA Astrophysics Data System (ADS)

Hurd, Alan J.; Schaefer, Dale W.

1985-03-01

We have studied the aggregation of silica microspheres confined to two dimensions at an air-water interface. Under microscopic observation, both monomers and clusters are seen to aggregate by a diffusion-limited process. The clusters' fractal dimension is 1.20+/-0.15, smaller than values obtained from current models of aggregation. We propose that anisotropic repulsive interactions account for the low dimensionality by more effectively repelling particles from the side of an existing dendrite than from the end.

A Stochastic Approach For Extending The Dimensionality Of Observed Datasets

NASA Technical Reports Server (NTRS)

Varnai, Tamas

2002-01-01

This paper addresses the problem that in many cases, observations cannot provide complete fields of the measured quantities, because they yield data only along a single cross-section through the examined fields. The paper describes a new Fourier-adjustment technique that allows existing fractal models to build realistic surroundings to the measured cross-sections. This new approach allows more representative calculations of cloud radiative processes and may be used in other areas as well.

Bound eigenstate dynamics under a sudden shift of the well's wall

NASA Astrophysics Data System (ADS)

Granot, Er'El; Marchewka, Avi

2010-03-01

We investigate the dynamics of the eigenstate of an infinite well under an abrupt shift of the well’s wall. It is shown that when the shift is small compared to the initial well’s dimensions, the short-time behavior changes from the well-known t3/2 behavior to t1/2. It is also shown that the complete dynamical picture converges to a universal function, which has fractal structure with dimensionality D=1.25.

Programming of the complex logarithm function in the solution of the cracked anisotropic plate loaded by a point force

NASA Astrophysics Data System (ADS)

Zaal, K. J. J. M.

1991-06-01

In programming solutions of complex function theory, the complex logarithm function is replaced by the complex logarithmic function, introducing a discontinuity along the branch cut into the programmed solution which was not present in the mathematical solution. Recently, Liaw and Kamel presented their solution of the infinite anisotropic centrally cracked plate loaded by an arbitrary point force, which they used as Green's function in a boundary element method intended to evaluate the stress intensity factor at the tip of a crack originating from an elliptical home. Their solution may be used as Green's function of many more numerical methods involving anisotropic elasticity. In programming applications of Liaw and Kamel's solution, the standard definition of the logarithmic function with the branch cut at the nonpositive real axis cannot provide a reliable computation of the displacement field for Liaw and Kamel's solution. Either the branch cut should be redefined outside the domain of the logarithmic function, after proving that the domain is limited to a part of the plane, or the logarithmic function should be defined on its Riemann surface. A two dimensional line fractal can provide the link between all mesh points on the plane essential to evaluate the logarithm function on its Riemann surface. As an example, a two dimensional line fractal is defined for a mesh once used by Erdogan and Arin.

Chaotic electron transport in semiconductor devices

NASA Astrophysics Data System (ADS)

Scannell, William Christian

The field of quantum chaos investigates the quantum mechanical behavior of classically chaotic systems. This dissertation begins by describing an experiment conducted on an apparatus constructed to represent a three dimensional analog of a classically chaotic system. Patterns of reflected light are shown to produce fractals, and the behavior of the fractal dimension D F is shown to depend on the light's ability to escape the apparatus. The classically chaotic system is then used to investigate the conductance properties of semiconductor heterostructures engineered to produce a conducting plane relatively free of impurities and defects. Introducing walls that inhibit conduction to partition off sections considerably smaller than the mean distance between impurities defines devices called 'billiards'. Cooling to low temperatures enables the electrons traveling through the billiard to maintain quantum mechanical phase. Exposure to a changing electric or magnetic field alters the electron's phase, leading to fluctuations in the conductance through the billiard. Magnetoconductance fluctuations in billiards have previously been shown to be fractal. This behavior has been charted using an empirical parameter, Q, that is a measure of the resolution of the energy levels within the billiard. The relationship with Q is shown to extend beyond the ballistic regime into the 'quasi-ballistic' and 'diffusive' regimes, characterized by having defects within the conduction plane. A model analogous to the classically chaotic system is proposed as the origin of the fractal conductance fluctuations. This model is shown to be consistent with experiment and to account for changes of fine scale features in MCF known to occur when a billiard is brought to room temperature between low temperature measurements. An experiment is conducted in which fractal conductance fluctuations (FCF) are produced by exposing a billiard to a changing electric field. Comparison of DF values of FCF produced by electric fields is made to FCF produced by magnetic fields. FCF with high DF values are shown to de-correlate at smaller increments of field than the FCF with lower DF values. This indicates that FCF may be used as a novel sensor of external fields, so the response of FCF to high bias voltages is investigated.

Nonlinear Dynamics Used to Classify Effects of Mild Traumatic Brain Injury

DTIC Science & Technology

2012-01-11

evaluate random fractal characteristics, and scale-dependent Lyapunov exponents (SDLE) to evaluate chaotic characteristics. Both Shannon and Renyi entropy...fluctuation analysis to evaluate random fractal characteristics, and scale-dependent Lyapunov exponents (SDLE) to evaluate chaotic characteristics. Both...often called the Hurst parameter [32]. When the scaling law described by Eq. (2) holds, the September 2011 I Volume 6 I Issue 9 I e24446 -Q.384

Fractal analysis of radiologists' visual scanning pattern in screening mammography

NASA Astrophysics Data System (ADS)

Alamudun, Folami T.; Yoon, Hong-Jun; Hudson, Kathy; Morin-Ducote, Garnetta; Tourassi, Georgia

2015-03-01

Several researchers have investigated radiologists' visual scanning patterns with respect to features such as total time examining a case, time to initially hit true lesions, number of hits, etc. The purpose of this study was to examine the complexity of the radiologists' visual scanning pattern when viewing 4-view mammographic cases, as they typically do in clinical practice. Gaze data were collected from 10 readers (3 breast imaging experts and 7 radiology residents) while reviewing 100 screening mammograms (24 normal, 26 benign, 50 malignant). The radiologists' scanpaths across the 4 mammographic views were mapped to a single 2-D image plane. Then, fractal analysis was applied on the composite 4- view scanpaths. For each case, the complexity of each radiologist's scanpath was measured using fractal dimension estimated with the box counting method. The association between the fractal dimension of the radiologists' visual scanpath, case pathology, case density, and radiologist experience was evaluated using fixed effects ANOVA. ANOVA showed that the complexity of the radiologists' visual search pattern in screening mammography is dependent on case specific attributes (breast parenchyma density and case pathology) as well as on reader attributes, namely experience level. Visual scanning patterns are significantly different for benign and malignant cases than for normal cases. There is also substantial inter-observer variability which cannot be explained only by experience level.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alamudun, Folami T.; Yoon, Hong-Jun; Hudson, Kathy

Purpose: The objective of this study was to assess the complexity of human visual search activity during mammographic screening using fractal analysis and to investigate its relationship with case and reader characteristics. Methods: The study was performed for the task of mammographic screening with simultaneous viewing of four coordinated breast views as typically done in clinical practice. Eye-tracking data and diagnostic decisions collected for 100 mammographic cases (25 normal, 25 benign, 50 malignant) and 10 readers (three board certified radiologists and seven radiology residents), formed the corpus data for this study. The fractal dimension of the readers’ visual scanning patternsmore » was computed with the Minkowski–Bouligand box-counting method and used as a measure of gaze complexity. Individual factor and group-based interaction ANOVA analysis was performed to study the association between fractal dimension, case pathology, breast density, and reader experience level. The consistency of the observed trends depending on gaze data representation was also examined. Results: Case pathology, breast density, reader experience level, and individual reader differences are all independent predictors of the visual scanning pattern complexity when screening for breast cancer. No higher order effects were found to be significant. Conclusions: Fractal characterization of visual search behavior during mammographic screening is dependent on case properties and image reader characteristics.« less

Can fractal methods applied to video tracking detect the effects of deltamethrin pesticide or mercury on the locomotion behavior of shrimps?

PubMed

Tenorio, Bruno Mendes; da Silva Filho, Eurípedes Alves; Neiva, Gentileza Santos Martins; da Silva, Valdemiro Amaro; Tenorio, Fernanda das Chagas Angelo Mendes; da Silva, Themis de Jesus; Silva, Emerson Carlos Soares E; Nogueira, Romildo de Albuquerque

2017-08-01

Shrimps can accumulate environmental toxicants and suffer behavioral changes. However, methods to quantitatively detect changes in the behavior of these shrimps are still needed. The present study aims to verify whether mathematical and fractal methods applied to video tracking can adequately describe changes in the locomotion behavior of shrimps exposed to low concentrations of toxic chemicals, such as 0.15µgL -1 deltamethrin pesticide or 10µgL -1 mercuric chloride. Results showed no change after 1min, 4, 24, and 48h of treatment. However, after 72 and 96h of treatment, both the linear methods describing the track length, mean speed, mean distance from the current to the previous track point, as well as the non-linear methods of fractal dimension (box counting or information entropy) and multifractal analysis were able to detect changes in the locomotion behavior of shrimps exposed to deltamethrin. Analysis of angular parameters of the track points vectors and lacunarity were not sensitive to those changes. None of the methods showed adverse effects to mercury exposure. These mathematical and fractal methods applicable to software represent low cost useful tools in the toxicological analyses of shrimps for quality of food, water and biomonitoring of ecosystems. Copyright © 2017 Elsevier Inc. All rights reserved.

Domain wall motion in ferroelectrics: Barkhausen noise

NASA Astrophysics Data System (ADS)

Shur, V.; Rumyantsev, E.; Kozhevnikov, V.; Nikolaeva, E.; Shishkin, E.

2002-03-01

The switching current noise has been recorded during polarization reversal in single-crystalline gadolinium molybdate (GMO) and lithium tantalate (LT). Analysis of Barkhausen noise (BN) data allows to classify the noise types by determination of the critical indexes and fractal dimensions. BN is manifested as the short pulses during the polarization reversal. We have analyzed the BN data recorded in GMO and LT with various types of controlled domain structure. The data treatment in terms of probability distribution of duration, area and energy of individual pulses reveals the critical behavior typical for the fractal records in time. We used the Fourier transform and Hurst's rescaled range analysis for obtaining the Hurst factor, fractal dimension and classifying the noise types. We investigated by computer simulation the mechanism of sideways motion of 180O domain wall by nucleation at the wall taking into account the nuclei-nuclei interaction. It was shown that the moving domain walls display the fractal shape and their motion is accompanied by Flicker noise, which is in accord with experimental data. The research was made possible in part by Programs "Basic Research in Russian Universities" and "Priority Research in High School. Electronics", by Grant No. 01-02-17443 of RFBR, by Award No.REC-005 of CRDF.

Characterization of microgravity effects on bone structure and strength using fractal analysis

NASA Technical Reports Server (NTRS)

Acharya, Raj S.; Shackelford, Linda

1995-01-01

The effect of micro-gravity on the musculoskeletal system has been well studied. Significant changes in bone and muscle have been shown after long term space flight. Similar changes have been demonstrated due to bed rest. Bone demineralization is particularly profound in weight bearing bones. Much of the current techniques to monitor bone condition use bone mass measurements. However, bone mass measurements are not reliable to distinguish Osteoporotic and Normal subjects. It has been shown that the overlap between normals and osteoporosis is found for all of the bone mass measurement technologies: single and dual photon absorptiometry, quantitative computed tomography and direct measurement of bone area/volume on biopsy as well as radiogrammetry. A similar discordance is noted in the fact that it has not been regularly possible to find the expected correlation between severity of osteoporosis and degree of bone loss. Structural parameters such as trabecular connectivity have been proposed as features for assessing bone conditions. In this report, we use fractal analysis to characterize bone structure. We show that the fractal dimension computed with MRI images and X-Ray images of the patella are the same. Preliminary experimental results show that the fractal dimension computed from MRI images of vertebrae of human subjects before bedrest is higher than during bedrest.

Fractal analysis of the ischemic transition region in chronic ischemic heart disease using magnetic resonance imaging.

PubMed

Michallek, Florian; Dewey, Marc

2017-04-01

To introduce a novel hypothesis and method to characterise pathomechanisms underlying myocardial ischemia in chronic ischemic heart disease by local fractal analysis (FA) of the ischemic myocardial transition region in perfusion imaging. Vascular mechanisms to compensate ischemia are regulated at various vascular scales with their superimposed perfusion pattern being hypothetically self-similar. Dedicated FA software ("FraktalWandler") has been developed. Fractal dimensions during first-pass (FD first-pass ) and recirculation (FD recirculation ) are hypothesised to indicate the predominating pathomechanism and ischemic severity, respectively. Twenty-six patients with evidence of myocardial ischemia in 108 ischemic myocardial segments on magnetic resonance imaging (MRI) were analysed. The 40th and 60th percentiles of FD first-pass were used for pathomechanical classification, assigning lesions with FD first-pass  ≤ 2.335 to predominating coronary microvascular dysfunction (CMD) and ≥2.387 to predominating coronary artery disease (CAD). Optimal classification point in ROC analysis was FD first-pass  = 2.358. FD recirculation correlated moderately with per cent diameter stenosis in invasive coronary angiography in lesions classified CAD (r = 0.472, p = 0.001) but not CMD (r = 0.082, p = 0.600). The ischemic transition region may provide information on pathomechanical composition and severity of myocardial ischemia. FA of this region is feasible and may improve diagnosis compared to traditional noninvasive myocardial perfusion analysis. • A novel hypothesis and method is introduced to pathophysiologically characterise myocardial ischemia. • The ischemic transition region appears a meaningful diagnostic target in perfusion imaging. • Fractal analysis may characterise pathomechanical composition and severity of myocardial ischemia.

The chaotic set and the cross section for chaotic scattering in three degrees of freedom

NASA Astrophysics Data System (ADS)

Jung, C.; Merlo, O.; Seligman, T. H.; Zapfe, W. P. K.

2010-10-01

This article treats chaotic scattering with three degrees of freedom, where one of them is open and the other two are closed, as a first step towards a more general understanding of chaotic scattering in higher dimensions. Despite the strong restrictions, it breaks the essential simplicity implicit in any two-dimensional time-independent scattering problem. Introducing the third degree of freedom by breaking a continuous symmetry, we first explore the topological structure of the homoclinic/heteroclinic tangle and the structures in the scattering functions. Then we work out the implications of these structures for the doubly differential cross section. The most prominent structures in the cross section are rainbow singularities. They form a fractal pattern that reflects the fractal structure of the chaotic invariant set. This allows us to determine structures in the cross section from the invariant set and, conversely, to obtain information about the topology of the invariant set from the cross section. The latter is a contribution to the inverse scattering problem for chaotic systems.

2010 Award for Outstanding Doctoral Thesis Research in Biological Physics Talk: How the Genome Folds

NASA Astrophysics Data System (ADS)

Lieberman-Aiden, Erez

2011-03-01

I describe Hi-C, a novel technology for probing the three-dimensional architecture of whole genomes by coupling proximity-based ligation with massively parallel sequencing. Working with collaborators at the Broad Institute and UMass Medical School, we used Hi-C to construct spatial proximity maps of the human genome at a resolution of 1Mb. These maps confirm the presence of chromosome territories and the spatial proximity of small, gene-rich chromosomes. We identified an additional level of genome organization that is characterized by the spatial segregation of open and closed chromatin to form two genome-wide compartments. At the megabase scale, the chromatin conformation is consistent with a fractal globule, a knot-free conformation that enables maximally dense packing while preserving the ability to easily fold and unfold any genomic locus. The fractal globule is distinct from the more commonly used globular equilibrium model. Our results demonstrate the power of Hi-C to map the dynamic conformations of whole genomes.

Plant light interception can be explained via computed tomography scanning: demonstration with pyramidal cedar (Thuja occidentalis, Fastigiata).

PubMed

Dutilleul, Pierre; Han, Liwen; Smith, Donald L

2008-01-01

Light interception by the leaf canopy is a key aspect of plant photosynthesis, which helps mitigate the greenhouse effect via atmospheric CO(2) recycling. The relationship between plant light interception and leaf area was traditionally modelled with the Beer-Lambert law, until the spatial distribution of leaves was incorporated through the fractal dimension of leafless plant structure photographed from the side allowing maximum appearance of branches and petioles. However, photographs of leafless plants are two-dimensional projections of three-dimensional structures, and sampled plants were cut at the stem base before leaf blades were detached manually, so canopy development could not be followed for individual plants. Therefore, a new measurement and modelling approach were developed to explain plant light interception more completely and precisely, based on appropriate processing of computed tomography (CT) scanning data collected for developing canopies. Three-dimensional images of canopies were constructed from CT scanning data. Leaf volumes (LV) were evaluated from complete canopy images, and fractal dimensions (FD) were estimated from skeletonized leafless images. The experimental plant species is pyramidal cedar (Thuja occidentalis, Fastigiata). The three-dimensional version of the Beer-Lambert law based on FD alone provided a much better explanation of plant light interception (R(2) = 0.858) than those using the product LV*FD (0.589) or LV alone (0.548). While values of all three regressors were found to increase over time, FD in the Beer-Lambert law followed the increase in light interception the most closely. The delayed increase of LV reflected the appearance of new leaves only after branches had lengthened and ramified. The very strong correlation obtained with FD demonstrates that CT scanning data contain fundamental information about the canopy architecture geometry. The model can be used to identify crops and plantation trees with improved light interception and productivity.

Plant Light Interception Can Be Explained via Computed Tomography Scanning: Demonstration with Pyramidal Cedar (Thuja occidentalis, Fastigiata)

PubMed Central

Dutilleul, Pierre; Han, Liwen; Smith, Donald L.

2008-01-01

Background and Aims Light interception by the leaf canopy is a key aspect of plant photosynthesis, which helps mitigate the greenhouse effect via atmospheric CO2 recycling. The relationship between plant light interception and leaf area was traditionally modelled with the Beer–Lambert law, until the spatial distribution of leaves was incorporated through the fractal dimension of leafless plant structure photographed from the side allowing maximum appearance of branches and petioles. However, photographs of leafless plants are two-dimensional projections of three-dimensional structures, and sampled plants were cut at the stem base before leaf blades were detached manually, so canopy development could not be followed for individual plants. Therefore, a new measurement and modelling approach were developed to explain plant light interception more completely and precisely, based on appropriate processing of computed tomography (CT) scanning data collected for developing canopies. Methods Three-dimensional images of canopies were constructed from CT scanning data. Leaf volumes (LV) were evaluated from complete canopy images, and fractal dimensions (FD) were estimated from skeletonized leafless images. The experimental plant species is pyramidal cedar (Thuja occidentalis, Fastigiata). Key Results The three-dimensional version of the Beer–Lambert law based on FD alone provided a much better explanation of plant light interception (R2 = 0·858) than those using the product LV*FD (0·589) or LV alone (0·548). While values of all three regressors were found to increase over time, FD in the Beer–Lambert law followed the increase in light interception the most closely. The delayed increase of LV reflected the appearance of new leaves only after branches had lengthened and ramified. Conclusions The very strong correlation obtained with FD demonstrates that CT scanning data contain fundamental information about the canopy architecture geometry. The model can be used to identify crops and plantation trees with improved light interception and productivity. PMID:17981879

Fractal Analysis of Permeability of Unsaturated Fractured Rocks

PubMed Central

Jiang, Guoping; Shi, Wei; Huang, Lili

2013-01-01

A physical conceptual model for water retention in fractured rocks is derived while taking into account the effect of pore size distribution and tortuosity of capillaries. The formula of calculating relative hydraulic conductivity of fractured rock is given based on fractal theory. It is an issue to choose an appropriate capillary pressure-saturation curve in the research of unsaturated fractured mass. The geometric pattern of the fracture bulk is described based on the fractal distribution of tortuosity. The resulting water content expression is then used to estimate the unsaturated hydraulic conductivity of the fractured medium based on the well-known model of Burdine. It is found that for large enough ranges of fracture apertures the new constitutive model converges to the empirical Brooks-Corey model. PMID:23690746

Fractal analysis of permeability of unsaturated fractured rocks.

PubMed

Jiang, Guoping; Shi, Wei; Huang, Lili

2013-01-01

A physical conceptual model for water retention in fractured rocks is derived while taking into account the effect of pore size distribution and tortuosity of capillaries. The formula of calculating relative hydraulic conductivity of fractured rock is given based on fractal theory. It is an issue to choose an appropriate capillary pressure-saturation curve in the research of unsaturated fractured mass. The geometric pattern of the fracture bulk is described based on the fractal distribution of tortuosity. The resulting water content expression is then used to estimate the unsaturated hydraulic conductivity of the fractured medium based on the well-known model of Burdine. It is found that for large enough ranges of fracture apertures the new constitutive model converges to the empirical Brooks-Corey model.

Fractal dimension of spatially extended systems

NASA Astrophysics Data System (ADS)

Torcini, A.; Politi, A.; Puccioni, G. P.; D'Alessandro, G.

1991-10-01

Properties of the invariant measure are numerically investigated in 1D chains of diffusively coupled maps. The coarse-grained fractal dimension is carefully computed in various embedding spaces, observing an extremely slow convergence towards the asymptotic value. This is in contrast with previous simulations, where the analysis of an insufficient number of points led the authors to underestimate the increase of fractal dimension with increasing the dimension of the embedding space. Orthogonal decomposition is also performed confirming that the slow convergence is intrinsically related to local nonlinear properties of the invariant measure. Finally, the Kaplan-Yorke conjecture is tested for short chains, showing that, despite the noninvertibility of the dynamical system, a good agreement is found between Lyapunov dimension and information dimension.

From kinetic-structure analysis to engineering crystalline fiber networks in soft materials.

PubMed

Wang, Rong-Yao; Wang, Peng; Li, Jing-Liang; Yuan, Bing; Liu, Yu; Li, Li; Liu, Xiang-Yang

2013-03-07

Understanding the role of kinetics in fiber network microstructure formation is of considerable importance in engineering gel materials to achieve their optimized performances/functionalities. In this work, we present a new approach for kinetic-structure analysis for fibrous gel materials. In this method, kinetic data is acquired using a rheology technique and is analyzed in terms of an extended Dickinson model in which the scaling behaviors of dynamic rheological properties in the gelation process are taken into account. It enables us to extract the structural parameter, i.e. the fractal dimension, of a fibrous gel from the dynamic rheological measurement of the gelation process, and to establish the kinetic-structure relationship suitable for both dilute and concentrated gelling systems. In comparison to the fractal analysis method reported in a previous study, our method is advantageous due to its general validity for a wide range of fractal structures of fibrous gels, from a highly compact network of the spherulitic domains to an open fibrous network structure. With such a kinetic-structure analysis, we can gain a quantitative understanding of the role of kinetic control in engineering the microstructure of the fiber network in gel materials.

Singularity analysis based on wavelet transform of fractal measures for identifying geochemical anomaly in mineral exploration

NASA Astrophysics Data System (ADS)

Chen, Guoxiong; Cheng, Qiuming

2016-02-01

Multi-resolution and scale-invariance have been increasingly recognized as two closely related intrinsic properties endowed in geofields such as geochemical and geophysical anomalies, and they are commonly investigated by using multiscale- and scaling-analysis methods. In this paper, the wavelet-based multiscale decomposition (WMD) method was proposed to investigate the multiscale natures of geochemical pattern from large scale to small scale. In the light of the wavelet transformation of fractal measures, we demonstrated that the wavelet approximation operator provides a generalization of box-counting method for scaling analysis of geochemical patterns. Specifically, the approximation coefficient acts as the generalized density-value in density-area fractal modeling of singular geochemical distributions. Accordingly, we presented a novel local singularity analysis (LSA) using the WMD algorithm which extends the conventional moving averaging to a kernel-based operator for implementing LSA. Finally, the novel LSA was validated using a case study dealing with geochemical data (Fe2O3) in stream sediments for mineral exploration in Inner Mongolia, China. In comparison with the LSA implemented using the moving averaging method the novel LSA using WMD identified improved weak geochemical anomalies associated with mineralization in covered area.

Classical evolution of fractal measures on the lattice

NASA Astrophysics Data System (ADS)

Antoniou, N. G.; Diakonos, F. K.; Saridakis, E. N.; Tsolias, G. A.

2007-04-01

We consider the classical evolution of a lattice of nonlinear coupled oscillators for a special case of initial conditions resembling the equilibrium state of a macroscopic thermal system at the critical point. The displacements of the oscillators define initially a fractal measure on the lattice associated with the scaling properties of the order parameter fluctuations in the corresponding critical system. Assuming a sudden symmetry breaking (quench), leading to a change in the equilibrium position of each oscillator, we investigate in some detail the deformation of the initial fractal geometry as time evolves. In particular, we show that traces of the critical fractal measure can be sustained for large times, and we extract the properties of the chain that determine the associated time scales. Our analysis applies generally to critical systems for which, after a slow developing phase where equilibrium conditions are justified, a rapid evolution, induced by a sudden symmetry breaking, emerges on time scales much shorter than the corresponding relaxation or observation time. In particular, it can be used in the fireball evolution in a heavy-ion collision experiment, where the QCD critical point emerges, or in the study of evolving fractals of astrophysical and cosmological scales, and may lead to determination of the initial critical properties of the Universe through observations in the symmetry-broken phase.

Fractal nematic colloids

NASA Astrophysics Data System (ADS)

Hashemi, S. M.; Jagodič, U.; Mozaffari, M. R.; Ejtehadi, M. R.; Muševič, I.; Ravnik, M.

2017-01-01

Fractals are remarkable examples of self-similarity where a structure or dynamic pattern is repeated over multiple spatial or time scales. However, little is known about how fractal stimuli such as fractal surfaces interact with their local environment if it exhibits order. Here we show geometry-induced formation of fractal defect states in Koch nematic colloids, exhibiting fractal self-similarity better than 90% over three orders of magnitude in the length scales, from micrometers to nanometres. We produce polymer Koch-shaped hollow colloidal prisms of three successive fractal iterations by direct laser writing, and characterize their coupling with the nematic by polarization microscopy and numerical modelling. Explicit generation of topological defect pairs is found, with the number of defects following exponential-law dependence and reaching few 100 already at fractal iteration four. This work demonstrates a route for generation of fractal topological defect states in responsive soft matter.

Complexity-Entropy Causality Plane as a Complexity Measure for Two-Dimensional Patterns

PubMed Central

Ribeiro, Haroldo V.; Zunino, Luciano; Lenzi, Ervin K.; Santoro, Perseu A.; Mendes, Renio S.

2012-01-01

Complexity measures are essential to understand complex systems and there are numerous definitions to analyze one-dimensional data. However, extensions of these approaches to two or higher-dimensional data, such as images, are much less common. Here, we reduce this gap by applying the ideas of the permutation entropy combined with a relative entropic index. We build up a numerical procedure that can be easily implemented to evaluate the complexity of two or higher-dimensional patterns. We work out this method in different scenarios where numerical experiments and empirical data were taken into account. Specifically, we have applied the method to fractal landscapes generated numerically where we compare our measures with the Hurst exponent; liquid crystal textures where nematic-isotropic-nematic phase transitions were properly identified; 12 characteristic textures of liquid crystals where the different values show that the method can distinguish different phases; and Ising surfaces where our method identified the critical temperature and also proved to be stable. PMID:22916097

Fractal-Based Oscillation of Macular Arteriogenesis and Dropout During Progressive Diabetic Retinopathy

NASA Technical Reports Server (NTRS)

Radharkrishnan, Krishnan; Kaiser, Peter K.

2011-01-01

By both fractal (D1) and branching (Lv) analysis, macular arterial density oscillated with progression from mild NPDR to PDR. Results are consistent with out study reported recently for the entire arterial and venous branching trees within 50 degree FAs by VESGEN generational branching analysis. Current and previous results are important for advances in early-stage regenerative DR therapies, for which reversal of DR progression to a normal vessel density may be possible. For example, potential use of regenerative angiogenesis stimulators to reverse vascular dropout during mild and severe NPDR is not indicated for treatment of moderate NPDR.

Fractal Dimension of Cohesive Sediment Flocs at Steady State under Seven Shear Flow Conditions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhu, Zhongfan; Yu, Jingshan; Wang, Hongrui

2015-08-01

The morphological properties of kaolin flocs were investigated in a Couetteflow experiment at the steady state under seven shear flow conditions (shear rates of 5.36, 9.17, 14, 24, 31, 41 and 53 s-1). These properties include a one-dimensional (1-D) fractal dimension (D1), a two-dimensional (2-D) fractal dimension (D2), a perimeter-based fractal dimension (Dpf) and an aspect ratio (AR). They were calculated based on the projected area (A), equivalent size, perimeter (P) and length (L) of the major axis of the floc determined through sample observation and an image analysis system. The parameter D2, which characterizes the relationship between the projectedmore » area and the length of the major axis using a power function, , increased from 1.73 ± 0.03, 1.72 ± 0.03, and 1.75 ± 0.04 in the low shear rate group (G = 5.36, 9.17, and 14 s-1) to 1.92 ± 0.03, 1.82 ± 0.02, 1.85 ± 0.02, and 1.81 ± 0.02 in the high shear rate group (24, 31, 41 and 53 s-1), respectively. The parameter D1 characterizes the relationship between the perimeter and length of the major axis by the function and decreased from 1.52 ± 0.02, 1.48 ± 0.02, 1.55 ± 0.02, and 1.63 ± 0.02 in the low shear group (5.36, 9.17, 14 and 24 s-1) to 1.45 ± 0.02, 1.39 ± 0.02, and 1.39 ± 0.02 in the high shear group (31, 41 and 53 s-1), respectively. The results indicate that with increasing shear rates, the flocs become less elongated and that their boundary lines become tighter and more regular, caused by more breakages and possible restructurings of the flocs. The parameter Dpf, which is related to the perimeter and the projected area through the function , decreased as the shear rate increased approximately linearly. The parameter AR, which is the ratio of the length of the major axis and equivalent diameter, decreased from 1.56, 1.59, 1.53 and 1.51 in the low shear rate group to 1.43, 1.47 and 1.48 in the high shear rate group. These changes in Dpf and AR show that the flocs become less convoluted and more symmetrical and that their boundaries become smoother and more regular in the high shear rate group than in the low shear rate group due to breakage and possible restructuring processes. To assess the effects of electrolyte and sediment concentration, 0.1 mol/litre calcium chloride (CaCl2) and initial sediment concentration from 7.87 × 10-5 to 1.57 × 10-5 were used in this preliminary study. The addition of electrolyte and increasing sediment concentration could produce more symmetrical flocs with less convoluted and simpler boundaries. In addition, some new information on the temporal variation of the median size of the flocs during the flocculation process is presented.« less

Fractal dimension analysis for robust ultrasonic non-destructive evaluation (NDE) of coarse grained materials

NASA Astrophysics Data System (ADS)

Li, Minghui; Hayward, Gordon

2018-04-01

Over the recent decades, there has been a growing demand on reliable and robust non-destructive evaluation (NDE) of structures and components made from coarse grained materials such as alloys, stainless steels, carbon-reinforced composites and concrete; however, when inspected using ultrasound, the flaw echoes are usually contaminated by high-level, time-invariant, and correlated grain noise originating from the microstructure and grain boundaries, leading to pretty low signal-to-noise ratio (SNR) and the flaw information being obscured or completely hidden by the grain noise. In this paper, the fractal dimension analysis of the A-scan echoes is investigated as a measure of complexity of the time series to distinguish the echoes originating from the real defects and the grain noise, and then the normalized fractal dimension coefficients are applied to the amplitudes as the weighting factor to enhance the SNR and defect detection. Experiments on industrial samples of the mild steel and the stainless steel are conducted and the results confirm the great benefits of the method.

Multiscale multifractal detrended-fluctuation analysis of two-dimensional surfaces

NASA Astrophysics Data System (ADS)

Wang, Fang; Fan, Qingju; Stanley, H. Eugene

2016-04-01

Two-dimensional (2D) multifractal detrended fluctuation analysis (MF-DFA) has been used to study monofractality and multifractality on 2D surfaces, but when it is used to calculate the generalized Hurst exponent in a fixed time scale, the presence of crossovers can bias the outcome. To solve this problem, multiscale multifractal analysis (MMA) was recent employed in a one-dimensional case. MMA produces a Hurst surface h (q ,s ) that provides a spectrum of local scaling exponents at different scale ranges such that the positions of the crossovers can be located. We apply this MMA method to a 2D surface and identify factors that influence the results. We generate several synthesized surfaces and find that crossovers are consistently present, which means that their fractal properties differ at different scales. We apply MMA to the surfaces, and the results allow us to observe these differences and accurately estimate the generalized Hurst exponents. We then study eight natural texture images and two real-world images and find (i) that the moving window length (WL) and the slide length (SL) are the key parameters in the MMA method, that the WL more strongly influences the Hurst surface than the SL, and that the combination of WL =4 and SL =4 is optimal for a 2D image; (ii) that the robustness of h (2 ,s ) to four common noises is high at large scales but variable at small scales; and (iii) that the long-term correlations in the images weaken as the intensity of Gaussian noise and salt and pepper noise is increased. Our findings greatly improve the performance of the MMA method on 2D surfaces.

Fractal nematic colloids

PubMed Central

Hashemi, S. M.; Jagodič, U.; Mozaffari, M. R.; Ejtehadi, M. R.; Muševič, I.; Ravnik, M.

2017-01-01

Fractals are remarkable examples of self-similarity where a structure or dynamic pattern is repeated over multiple spatial or time scales. However, little is known about how fractal stimuli such as fractal surfaces interact with their local environment if it exhibits order. Here we show geometry-induced formation of fractal defect states in Koch nematic colloids, exhibiting fractal self-similarity better than 90% over three orders of magnitude in the length scales, from micrometers to nanometres. We produce polymer Koch-shaped hollow colloidal prisms of three successive fractal iterations by direct laser writing, and characterize their coupling with the nematic by polarization microscopy and numerical modelling. Explicit generation of topological defect pairs is found, with the number of defects following exponential-law dependence and reaching few 100 already at fractal iteration four. This work demonstrates a route for generation of fractal topological defect states in responsive soft matter. PMID:28117325

Hierarchical socioeconomic fractality: The rich, the poor, and the middle-class

NASA Astrophysics Data System (ADS)

Eliazar, Iddo; Cohen, Morrel H.

2014-05-01

Since the seminal work of the Italian economist Vilfredo Pareto, the study of wealth and income has been a topic of active scientific exploration engaging researches ranging from economics and political science to econophysics and complex systems. This paper investigates the intrinsic fractality of wealth and income. To that end we introduce and characterize three forms of socioeconomic scale-invariance-poor fractality, rich fractality, and middle-class fractality-and construct hierarchical fractal approximations of general wealth and income distributions, based on the stitching of these three forms of fractality. Intertwining the theoretical results with real-world empirical data we then establish that the three forms of socioeconomic fractality-amalgamated into a composite hierarchical structure-underlie the distributions of wealth and income in human societies. We further establish that the hierarchical socioeconomic fractality of wealth and income is also displayed by empirical rank distributions observed across the sciences.

Fractal symmetry of protein interior: what have we learned?

PubMed

Banerji, Anirban; Ghosh, Indira

2011-08-01

The application of fractal dimension-based constructs to probe the protein interior dates back to the development of the concept of fractal dimension itself. Numerous approaches have been tried and tested over a course of (almost) 30 years with the aim of elucidating the various facets of symmetry of self-similarity prevalent in the protein interior. In the last 5 years especially, there has been a startling upsurge of research that innovatively stretches the limits of fractal-based studies to present an array of unexpected results on the biophysical properties of protein interior. In this article, we introduce readers to the fundamentals of fractals, reviewing the commonality (and the lack of it) between these approaches before exploring the patterns in the results that they produced. Clustering the approaches in major schools of protein self-similarity studies, we describe the evolution of fractal dimension-based methodologies. The genealogy of approaches (and results) presented here portrays a clear picture of the contemporary state of fractal-based studies in the context of the protein interior. To underline the utility of fractal dimension-based measures further, we have performed a correlation dimension analysis on all of the available non-redundant protein structures, both at the level of an individual protein and at the level of structural domains. In this investigation, we were able to separately quantify the self-similar symmetries in spatial correlation patterns amongst peptide-dipole units, charged amino acids, residues with the π-electron cloud and hydrophobic amino acids. The results revealed that electrostatic environments in the interiors of proteins belonging to 'α/α toroid' (all-α class) and 'PLP-dependent transferase-like' domains (α/β class) are highly conducive. In contrast, the interiors of 'zinc finger design' ('designed proteins') and 'knottins' ('small proteins') were identified as folds with the least conducive electrostatic environments. The fold 'conotoxins' (peptides) could be unambiguously identified as one type with the least stability. The same analyses revealed that peptide-dipoles in the α/β class of proteins, in general, are more correlated to each other than are the peptide-dipoles in proteins belonging to the all-α class. Highly favorable electrostatic milieu in the interiors of TIM-barrel, α/β-hydrolase structures could explain their remarkably conserved (evolutionary) stability from a new light. Finally, we point out certain inherent limitations of fractal constructs before attempting to identify the areas and problems where the implementation of fractal dimension-based constructs can be of paramount help to unearth latent information on protein structural properties.

Branching Patterns and Stepped Leaders in an Electric-Circuit Model for Creeping Discharge

NASA Astrophysics Data System (ADS)

Hidetsugu Sakaguchi,; Sahim M. Kourkouss,

2010-06-01

We construct a two-dimensional electric circuit model for creeping discharge. Two types of discharge, surface corona and surface leader, are modeled by a two-step function of conductance. Branched patterns of surface leaders surrounded by the surface corona appear in numerical simulation. The fractal dimension of branched discharge patterns is calculated by changing voltage and capacitance. We find that surface leaders often grow stepwise in time, as is observed in lightning leaders of thunder.

Heart rate dynamics in patients with stable angina pectoris and utility of fractal and complexity measures

NASA Technical Reports Server (NTRS)

Makikallio, T. H.; Ristimae, T.; Airaksinen, K. E.; Peng, C. K.; Goldberger, A. L.; Huikuri, H. V.

1998-01-01

Dynamic analysis techniques may uncover abnormalities in heart rate (HR) behavior that are not easily detectable with conventional statistical measures. However, the applicability of these new methods for detecting possible abnormalities in HR behavior in various cardiovascular disorders is not well established. Conventional measures of HR variability were compared with short-term (< or = 11 beats, alpha1) and long-term (> 11 beats, alpha2) fractal correlation properties and with approximate entropy of RR interval data in 38 patients with stable angina pectoris without previous myocardial infarction or cardiac medication at the time of the study and 38 age-matched healthy controls. The short- and long-term fractal scaling exponents (alpha1, alpha2) were significantly higher in the coronary patients than in the healthy controls (1.34 +/- 0.15 vs 1.11 +/- 0.12 [p <0.001] and 1.10 +/- 0.08 vs 1.04 +/- 0.06 [p <0.01], respectively), and they also had lower approximate entropy (p <0.05), standard deviation of all RR intervals (p <0.01), and high-frequency spectral component of HR variability (p <0.05). The short-term fractal scaling exponent performed better than other heart rate variability parameters in differentiating patients with coronary artery disease from healthy subjects, but it was not related to the clinical or angiographic severity of coronary artery disease or any single nonspectral or spectral measure of HR variability in this retrospective study. Patients with stable angina pectoris have altered fractal properties and reduced complexity in their RR interval dynamics relative to age-matched healthy subjects. Dynamic analysis may complement traditional analyses in detecting altered HR behavior in patients with stable angina pectoris.

Probing the fractal pattern and organization of Bacillus thuringiensis bacteria colonies growing under different conditions using quantitative spectral light scattering polarimetry

NASA Astrophysics Data System (ADS)

Banerjee, Paromita; Soni, Jalpa; Purwar, Harsh; Ghosh, Nirmalya; Sengupta, Tapas K.

2013-03-01

Development of methods for quantification of cellular association and patterns in growing bacterial colony is of considerable current interest, not only to help understand multicellular behavior of a bacterial species but also to facilitate detection and identification of a bacterial species in a given space and under a given set of condition(s). We have explored quantitative spectral light scattering polarimetry for probing the morphological and structural changes taking place during colony formations of growing Bacillus thuringiensis bacteria under different conditions (in normal nutrient agar representing favorable growth environment, in the presence of 1% glucose as an additional nutrient, and 3 mM sodium arsenate as toxic material). The method is based on the measurement of spectral 3×3 Mueller matrices (which involves linear polarization measurements alone) and its subsequent analysis via polar decomposition to extract the intrinsic polarization parameters. Moreover, the fractal micro-optical parameter, namely, the Hurst exponent H, is determined via fractal-Born approximation-based inverse analysis of the polarization-preserving component of the light scattering spectra. Interesting differences are noted in the derived values for the H parameter and the intrinsic polarization parameters (linear diattenuation d, linear retardance δ, and linear depolarization Δ coefficients) of the growing bacterial colonies under different conditions. The bacterial colony growing in presence of 1% glucose exhibit the strongest fractality (lowest value of H), whereas that growing in presence of 3 mM sodium arsenate showed the weakest fractality. Moreover, the values for δ and d parameters are found to be considerably higher for the colony growing in presence of glucose, indicating more structured growth pattern. These findings are corroborated further with optical microscopic studies conducted on the same samples.

Quantitative Assessment of Heart Rate Dynamics during Meditation: An ECG Based Study with Multi-Fractality and Visibility Graph

PubMed Central

Bhaduri, Anirban; Ghosh, Dipak

2016-01-01

The cardiac dynamics during meditation is explored quantitatively with two chaos-based non-linear techniques viz. multi-fractal detrended fluctuation analysis and visibility network analysis techniques. The data used are the instantaneous heart rate (in beats/minute) of subjects performing Kundalini Yoga and Chi meditation from PhysioNet. The results show consistent differences between the quantitative parameters obtained by both the analysis techniques. This indicates an interesting phenomenon of change in the complexity of the cardiac dynamics during meditation supported with quantitative parameters. The results also produce a preliminary evidence that these techniques can be used as a measure of physiological impact on subjects performing meditation. PMID:26909045

Quantitative Assessment of Heart Rate Dynamics during Meditation: An ECG Based Study with Multi-Fractality and Visibility Graph.

PubMed

Bhaduri, Anirban; Ghosh, Dipak

2016-01-01

The cardiac dynamics during meditation is explored quantitatively with two chaos-based non-linear techniques viz. multi-fractal detrended fluctuation analysis and visibility network analysis techniques. The data used are the instantaneous heart rate (in beats/minute) of subjects performing Kundalini Yoga and Chi meditation from PhysioNet. The results show consistent differences between the quantitative parameters obtained by both the analysis techniques. This indicates an interesting phenomenon of change in the complexity of the cardiac dynamics during meditation supported with quantitative parameters. The results also produce a preliminary evidence that these techniques can be used as a measure of physiological impact on subjects performing meditation.

Fractal-like hierarchical organization of bone begins at the nanoscale

NASA Astrophysics Data System (ADS)

Reznikov, Natalie; Bilton, Matthew; Lari, Leonardo; Stevens, Molly M.; Kröger, Roland

2018-05-01

The components of bone assemble hierarchically to provide stiffness and toughness. However, the organization and relationship between bone’s principal components—mineral and collagen—has not been clearly elucidated. Using three-dimensional electron tomography imaging and high-resolution two-dimensional electron microscopy, we demonstrate that bone mineral is hierarchically assembled beginning at the nanoscale: Needle-shaped mineral units merge laterally to form platelets, and these are further organized into stacks of roughly parallel platelets. These stacks coalesce into aggregates that exceed the lateral dimensions of the collagen fibrils and span adjacent fibrils as continuous, cross-fibrillar mineralization. On the basis of these observations, we present a structural model of hierarchy and continuity for the mineral phase, which contributes to the structural integrity of bone.

Domain wall roughness and creep in nanoscale crystalline ferroelectric polymers

NASA Astrophysics Data System (ADS)

Xiao, Z.; Poddar, Shashi; Ducharme, Stephen; Hong, X.

2013-09-01

We report piezo-response force microscopy studies of the static and dynamic properties of domain walls (DWs) in 11 to 36 nm thick films of crystalline ferroelectric poly(vinylidene-fluoride-trifluorethylene). The DW roughness exponent ζ ranges from 0.39 to 0.48 and the DW creep exponent μ varies from 0.20 to 0.28, revealing an unexpected effective dimensionality of ˜1.5 that is independent of film thickness. Our results suggest predominantly 2D ferroelectricity in the layered polymer and we attribute the fractal dimensionality to DW deroughening due to the correlations between the in-plane and out-of-plane polarization, an effect that can be exploited to achieve high lateral domain density for developing nanoscale ferroelectrics-based applications.

Predicting chaos for infinite dimensional dynamical systems: The Kuramoto-Sivashinsky equation, a case study

NASA Technical Reports Server (NTRS)

Smyrlis, Yiorgos S.; Papageorgiou, Demetrios T.

1991-01-01

The results of extensive computations are presented in order to accurately characterize transitions to chaos for the Kuramoto-Sivashinsky equation. In particular, the oscillatory dynamics in a window that supports a complete sequence of period doubling bifurcations preceding chaos is followed. As many as thirteen period doublings are followed and used to compute the Feigenbaum number for the cascade and so enable, for the first time, an accurate numerical evaluation of the theory of universal behavior of nonlinear systems, for an infinite dimensional dynamical system. Furthermore, the dynamics at the threshold of chaos exhibit a fractal behavior which is demonstrated and used to compute a universal scaling factor that enables the self-similar continuation of the solution into a chaotic regime.

Cardiac interbeat interval dynamics from childhood to senescence : comparison of conventional and new measures based on fractals and chaos theory

NASA Technical Reports Server (NTRS)

Pikkujamsa, S. M.; Makikallio, T. H.; Sourander, L. B.; Raiha, I. J.; Puukka, P.; Skytta, J.; Peng, C. K.; Goldberger, A. L.; Huikuri, H. V.

1999-01-01

BACKGROUND: New methods of R-R interval variability based on fractal scaling and nonlinear dynamics ("chaos theory") may give new insights into heart rate dynamics. The aims of this study were to (1) systematically characterize and quantify the effects of aging from early childhood to advanced age on 24-hour heart rate dynamics in healthy subjects; (2) compare age-related changes in conventional time- and frequency-domain measures with changes in newly derived measures based on fractal scaling and complexity (chaos) theory; and (3) further test the hypothesis that there is loss of complexity and altered fractal scaling of heart rate dynamics with advanced age. METHODS AND RESULTS: The relationship between age and cardiac interbeat (R-R) interval dynamics from childhood to senescence was studied in 114 healthy subjects (age range, 1 to 82 years) by measurement of the slope, beta, of the power-law regression line (log power-log frequency) of R-R interval variability (10(-4) to 10(-2) Hz), approximate entropy (ApEn), short-term (alpha(1)) and intermediate-term (alpha(2)) fractal scaling exponents obtained by detrended fluctuation analysis, and traditional time- and frequency-domain measures from 24-hour ECG recordings. Compared with young adults (<40 years old, n=29), children (<15 years old, n=27) showed similar complexity (ApEn) and fractal correlation properties (alpha(1), alpha(2), beta) of R-R interval dynamics despite lower spectral and time-domain measures. Progressive loss of complexity (decreased ApEn, r=-0.69, P<0.001) and alterations of long-term fractal-like heart rate behavior (increased alpha(2), r=0.63, decreased beta, r=-0.60, P<0.001 for both) were observed thereafter from middle age (40 to 60 years, n=29) to old age (>60 years, n=29). CONCLUSIONS: Cardiac interbeat interval dynamics change markedly from childhood to old age in healthy subjects. Children show complexity and fractal correlation properties of R-R interval time series comparable to those of young adults, despite lower overall heart rate variability. Healthy aging is associated with R-R interval dynamics showing higher regularity and altered fractal scaling consistent with a loss of complex variability.

Thin film growth by 3D multi-particle diffusion limited aggregation model: Anomalous roughening and fractal analysis

NASA Astrophysics Data System (ADS)

Nasehnejad, Maryam; Nabiyouni, G.; Gholipour Shahraki, Mehran

2018-03-01

In this study a 3D multi-particle diffusion limited aggregation method is employed to simulate growth of rough surfaces with fractal behavior in electrodeposition process. A deposition model is used in which the radial motion of the particles with probability P, competes with random motions with probability 1 - P. Thin films growth is simulated for different values of probability P (related to the electric field) and thickness of the layer(related to the number of deposited particles). The influence of these parameters on morphology, kinetic of roughening and the fractal dimension of the simulated surfaces has been investigated. The results show that the surface roughness increases with increasing the deposition time and scaling exponents exhibit a complex behavior which is called as anomalous scaling. It seems that in electrodeposition process, radial motion of the particles toward the growing seeds may be an important mechanism leading to anomalous scaling. The results also indicate that the larger values of probability P, results in smoother topography with more densely packed structure. We have suggested a dynamic scaling ansatz for interface width has a function of deposition time, scan length and probability. Two different methods are employed to evaluate the fractal dimension of the simulated surfaces which are "cube counting" and "roughness" methods. The results of both methods show that by increasing the probability P or decreasing the deposition time, the fractal dimension of the simulated surfaces is increased. All gained values for fractal dimensions are close to 2.5 in the diffusion limited aggregation model.

The fractal forest: fractal geometry and applications in forest science.

Treesearch

Nancy D. Lorimer; Robert G. Haight; Rolfe A. Leary

1994-01-01

Fractal geometry is a tool for describing and analyzing irregularity. Because most of what we measure in the forest is discontinuous, jagged, and fragmented, fractal geometry has potential for improving the precision of measurement and description. This study reviews the literature on fractal geometry and its applications to forest measurements.

Reply to "Comment on 'Hydrodynamics of fractal continuum flow' and 'Map of fluid flow in fractal porous medium into fractal continuum flow'".

PubMed

Balankin, Alexander S; Elizarraraz, Benjamin Espinoza

2013-11-01

The aim of this Reply is to elucidate the difference between the fractal continuum models used in the preceding Comment and the models of fractal continuum flow which were put forward in our previous articles [Phys. Rev. E 85, 025302(R) (2012); 85, 056314 (2012)]. In this way, some drawbacks of the former models are highlighted. Specifically, inconsistencies in the definitions of the fractal derivative, the Jacobian of transformation, the displacement vector, and angular momentum are revealed. The proper forms of the Reynolds' transport theorem and angular momentum principle for the fractal continuum are reaffirmed in a more illustrative manner. Consequently, we emphasize that in the absence of any internal angular momentum, body couples, and couple stresses, the Cauchy stress tensor in the fractal continuum should be symmetric. Furthermore, we stress that the approach based on the Cartesian product measured and used in the preceding Comment cannot be employed to study the path-connected fractals, such as a flow in a fractally permeable medium. Thus, all statements of our previous works remain unchallenged.

Fractal lacunarity of trabecular bone and magnetic resonance imaging: New perspectives for osteoporotic fracture risk assessment

PubMed Central

Zaia, Annamaria

2015-01-01

Osteoporosis represents one major health condition for our growing elderly population. It accounts for severe morbidity and increased mortality in postmenopausal women and it is becoming an emerging health concern even in aging men. Screening of the population at risk for bone degeneration and treatment assessment of osteoporotic patients to prevent bone fragility fractures represent useful tools to improve quality of life in the elderly and to lighten the related socio-economic impact. Bone mineral density (BMD) estimate by means of dual-energy X-ray absorptiometry is normally used in clinical practice for osteoporosis diagnosis. Nevertheless, BMD alone does not represent a good predictor of fracture risk. From a clinical point of view, bone microarchitecture seems to be an intriguing aspect to characterize bone alteration patterns in aging and pathology. The widening into clinical practice of medical imaging techniques and the impressive advances in information technologies together with enhanced capacity of power calculation have promoted proliferation of new methods to assess changes of trabecular bone architecture (TBA) during aging and osteoporosis. Magnetic resonance imaging (MRI) has recently arisen as a useful tool to measure bone structure in vivo. In particular, high-resolution MRI techniques have introduced new perspectives for TBA characterization by non-invasive non-ionizing methods. However, texture analysis methods have not found favor with clinicians as they produce quite a few parameters whose interpretation is difficult. The introduction in biomedical field of paradigms, such as theory of complexity, chaos, and fractals, suggests new approaches and provides innovative tools to develop computerized methods that, by producing a limited number of parameters sensitive to pathology onset and progression, would speed up their application into clinical practice. Complexity of living beings and fractality of several physio-anatomic structures suggest fractal analysis as a promising approach to quantify morpho-functional changes in both aging and pathology. In this particular context, fractal lacunarity seems to be the proper tool to characterize TBA texture as it is able to describe both discontinuity of bone network and sizes of bone marrow spaces, whose changes are an index of bone fracture risk. In this paper, an original method of MRI texture analysis, based on TBA fractal lacunarity is described and discussed in the light of new perspectives for early diagnosis of osteoporotic fractures. PMID:25793162

When Human Walking is a Random Walk

NASA Astrophysics Data System (ADS)

Hausdorff, J. M.

1998-03-01

The complex, hierarchical locomotor system normally does a remarkable job of controlling an inherently unstable, multi-joint system. Nevertheless, the stride interval --- the duration of a gait cycle --- fluctuates from one stride to the next, even under stationary conditions. We used random walk analysis to study the dynamical properties of these fluctuations under normal conditions and how they change with disease and aging. Random walk analysis of the stride-to-stride fluctuations of healthy, young adult men surprisingly reveals a self-similar pattern: fluctuations at one time scale are statistically similar to those at multiple other time scales (Hausdorff et al, J Appl Phsyiol, 1995). To study the stability of this fractal property, we analyzed data obtained from healthy subjects who walked for 1 hour at their usual pace, as well as at slower and faster speeds. The stride interval fluctuations exhibited long-range correlations with power-law decay for up to a thousand strides at all three walking rates. In contrast, during metronomically-paced walking, these long-range correlations disappeared; variations in the stride interval were uncorrelated and non-fractal (Hausdorff et al, J Appl Phsyiol, 1996). To gain insight into the mechanism(s) responsible for this fractal property, we examined the effects of aging and neurological impairment. Using detrended fluctuation analysis (DFA), we computed α, a measure of the degree to which one stride interval is correlated with previous and subsequent intervals over different time scales. α was significantly lower in healthy elderly subjects compared to young adults (p < .003) and in subjects with Huntington's disease, a neuro-degenerative disorder of the central nervous system, compared to disease-free controls (p < 0.005) (Hausdorff et al, J Appl Phsyiol, 1997). α was also significantly related to degree of functional impairment in subjects with Huntington's disease (r=0.78). Recently, we have observed that just as there are changes with α during aging, there also changes with development. Apparently, the fractal scaling of walking does not become mature until children are eleven years old. Conclusions: The fractal dynamics of spontaneous stride interval fluctuations are normally quite robust and are apparently intrinsic to the healthy adult locomotor system. However, alterations in this fractal scaling property are associated with impairment in central nervous system control, aging and neural development.

Multifractality and Network Analysis of Phase Transition

PubMed Central

Li, Wei; Yang, Chunbin; Han, Jihui; Su, Zhu; Zou, Yijiang

2017-01-01

Many models and real complex systems possess critical thresholds at which the systems shift dramatically from one sate to another. The discovery of early-warnings in the vicinity of critical points are of great importance to estimate how far the systems are away from the critical states. Multifractal Detrended Fluctuation analysis (MF-DFA) and visibility graph method have been employed to investigate the multifractal and geometrical properties of the magnetization time series of the two-dimensional Ising model. Multifractality of the time series near the critical point has been uncovered from the generalized Hurst exponents and singularity spectrum. Both long-term correlation and broad probability density function are identified to be the sources of multifractality. Heterogeneous nature of the networks constructed from magnetization time series have validated the fractal properties. Evolution of the topological quantities of the visibility graph, along with the variation of multifractality, serve as new early-warnings of phase transition. Those methods and results may provide new insights about the analysis of phase transition problems and can be used as early-warnings for a variety of complex systems. PMID:28107414

Describing soil surface microrelief by crossover length and fractal dimension

NASA Astrophysics Data System (ADS)

Vidal Vázquez, E.; Miranda, J. G. V.; Paz González, A.

2007-05-01

Accurate description of soil surface topography is essential because different tillage tools produce different soil surface roughness conditions, which in turn affects many processes across the soil surface boundary. Advantages of fractal analysis in soil microrelief assessment have been recognised but the use of fractal indices in practice remains challenging. There is also little information on how soil surface roughness decays under natural rainfall conditions. The objectives of this work were to investigate the decay of initial surface roughness induced by natural rainfall under different soil tillage systems and to compare the performances of a classical statistical index and fractal microrelief indices. Field experiments were performed on an Oxisol at Campinas, São Paulo State (Brazil). Six tillage treatments, namely, disc harrow, disc plow, chisel plow, disc harrow + disc level, disc plow + disc level and chisel plow + disc level were tested. Measurements were made four times, firstly just after tillage and subsequently with increasing amounts of natural rainfall. Duplicated measurements were taken per treatment and date, yielding a total of 48 experimental surfaces. The sampling scheme was a square grid with 25×25 mm point spacing and the plot size was 1350×1350 mm, so that each data set consisted of 3025 individual elevation points. Statistical and fractal indices were calculated both for oriented and random roughness conditions, i.e. after height reading have been corrected for slope and for slope and tillage tool marks. The main drawback of the standard statistical index random roughness, RR, lies in its no spatial nature. The fractal approach requires two indices, fractal dimension, D, which describes how roughness changes with scale, and crossover length, l, specifying the variance of surface microrelief at a reference scale. Fractal parameters D and l, were estimated by two independent self-affine models, semivariogram (SMV) and local root mean square (RMS). Both algorithms, SMV and RMS, gave equivalent results for D and l indices, irrespective of trend removal procedure, even if some bias was present which is in accordance with previous work. Treatments with two tillage operations had the greatest D values, irrespective of evolution stage under rainfall and trend removal procedure. Primary tillage had the greatest initial values of RR and l. Differences in D values between treatments with primary tillage and those with two successive tillage operations were significant for oriented but not for random conditions. The statistical index RR and the fractal indices l and D decreased with increasing cumulative rainfall following different patterns. The l and D decay from initial value was very sharp after the first 24.4 mm cumulative rainfall. For five out of six tillage treatments a significant relationship between D and l was found for the random microrelief conditions allowing a covariance analysis. It was concluded that using RR or l together with D best allow joint description of vertical and horizontal soil roughness variations.

Integrated Central-Autonomic Multifractal Complexity in the Heart Rate Variability of Healthy Humans

PubMed Central

Lin, D. C.; Sharif, A.

2012-01-01

Purpose of Study: The aim of this study was to characterize the central-autonomic interaction underlying the multifractality in heart rate variability (HRV) of healthy humans. Materials and Methods: Eleven young healthy subjects participated in two separate ~40 min experimental sessions, one in supine (SUP) and one in, head-up-tilt (HUT), upright (UPR) body positions. Surface scalp electroencephalography (EEG) and electrocardiogram (ECG) were collected and fractal correlation of brain and heart rate data was analyzed based on the idea of relative multifractality. The fractal correlation was further examined with the EEG, HRV spectral measures using linear regression of two variables and principal component analysis (PCA) to find clues for the physiological processing underlying the central influence in fractal HRV. Results: We report evidence of a central-autonomic fractal correlation (CAFC) where the HRV multifractal complexity varies significantly with the fractal correlation between the heart rate and brain data (P = 0.003). The linear regression shows significant correlation between CAFC measure and EEG Beta band spectral component (P = 0.01 for SUP and P = 0.002 for UPR positions). There is significant correlation between CAFC measure and HRV LF component in the SUP position (P = 0.04), whereas the correlation with the HRV HF component approaches significance (P = 0.07). The correlation between CAFC measure and HRV spectral measures in the UPR position is weak. The PCA results confirm these findings and further imply multiple physiological processes underlying CAFC, highlighting the importance of the EEG Alpha, Beta band, and the HRV LF, HF spectral measures in the supine position. Discussion and Conclusion: The findings of this work can be summarized into three points: (i) Similar fractal characteristics exist in the brain and heart rate fluctuation and the change toward stronger fractal correlation implies the change toward more complex HRV multifractality. (ii) CAFC is likely contributed by multiple physiological mechanisms, with its central elements mainly derived from the EEG Alpha, Beta band dynamics. (iii) The CAFC in SUP and UPR positions is qualitatively different, with a more predominant central influence in the fractal HRV of the UPR position. PMID:22403548

Organization of complex networks

NASA Astrophysics Data System (ADS)

Kitsak, Maksim

Many large complex systems can be successfully analyzed using the language of graphs and networks. Interactions between the objects in a network are treated as links connecting nodes. This approach to understanding the structure of networks is an important step toward understanding the way corresponding complex systems function. Using the tools of statistical physics, we analyze the structure of networks as they are found in complex systems such as the Internet, the World Wide Web, and numerous industrial and social networks. In the first chapter we apply the concept of self-similarity to the study of transport properties in complex networks. Self-similar or fractal networks, unlike non-fractal networks, exhibit similarity on a range of scales. We find that these fractal networks have transport properties that differ from those of non-fractal networks. In non-fractal networks, transport flows primarily through the hubs. In fractal networks, the self-similar structure requires any transport to also flow through nodes that have only a few connections. We also study, in models and in real networks, the crossover from fractal to non-fractal networks that occurs when a small number of random interactions are added by means of scaling techniques. In the second chapter we use k-core techniques to study dynamic processes in networks. The k-core of a network is the network's largest component that, within itself, exhibits all nodes with at least k connections. We use this k-core analysis to estimate the relative leadership positions of firms in the Life Science (LS) and Information and Communication Technology (ICT) sectors of industry. We study the differences in the k-core structure between the LS and the ICT sectors. We find that the lead segment (highest k-core) of the LS sector, unlike that of the ICT sector, is remarkably stable over time: once a particular firm enters the lead segment, it is likely to remain there for many years. In the third chapter we study how epidemics spread though networks. Our results indicate that a virus is more likely to infect a large area of a network if it originates at a node contained within k-core of high index k.

Fractal Bread.

ERIC Educational Resources Information Center

Esbenshade, Donald H., Jr.

1991-01-01

Develops the idea of fractals through a laboratory activity that calculates the fractal dimension of ordinary white bread. Extends use of the fractal dimension to compare other complex structures as other breads and sponges. (MDH)

Dual Fractal Dimension and Long-Range Correlation of Chinese Stock Prices

NASA Astrophysics Data System (ADS)

Chen, Chaoshi; Wang, Lei

2012-03-01

The recently developed modified inverse random midpoint displacement (mIRMD) and conventional detrended fluctuation analysis (DFA) algorithms are used to analyze the tick-by-tick high-frequency time series of Chinese A-share stock prices and indexes. A dual-fractal structure with a crossover at about 10 min is observed. The majority of the selected time series show visible persistence within this time threshold, but approach a random walk on a longer time scale. The phenomenon is found to be industry-dependent, i.e., the crossover is much more prominent for stocks belonging to cyclical industries than for those belonging to noncyclical (defensive) industries. We have also shown that the sign series show a similar dual-fractal structure, while like generally found, the magnitude series show a much longer time persistence.

Effect of angle of deposition on the Fractal properties of ZnO thin film surface

NASA Astrophysics Data System (ADS)

Yadav, R. P.; Agarwal, D. C.; Kumar, Manvendra; Rajput, Parasmani; Tomar, D. S.; Pandey, S. N.; Priya, P. K.; Mittal, A. K.

2017-09-01

Zinc oxide (ZnO) thin films were prepared by atom beam sputtering at various deposition angles in the range of 20-75°. The deposited thin films were examined by glancing angle X-ray diffraction and atomic force microscopy (AFM). Scaling law analysis was performed on AFM images to show that the thin film surfaces are self-affine. Fractal dimension of each of the 256 vertical sections along the fast scan direction of a discretized surface, obtained from the AFM height data, was estimated using the Higuchi's algorithm. Hurst exponent was computed from the fractal dimension. The grain sizes, as determined by applying self-correlation function on AFM micrographs, varied with the deposition angle in the same manner as the Hurst exponent.

Research on the fractal structure in the Chinese stock market

NASA Astrophysics Data System (ADS)

Zhuang, Xin-tian; Huang, Xiao-yuan; Sha, Yan-li

2004-02-01

Applying fractal theory, this paper probes and discusses self-similarity and scale invariance of the Chinese stock market. It analyses three kinds of scale indexes, i.e., autocorrelation index, Hurst index and the scale index on the basis of detrended fluctuation analysis (DFA) algorithm and promotes DFA into a recursive algorithm. Using the three kinds of scale indexes, we conduct empirical research on the Chinese Shanghai and Shenzhen stock markets. The results indicate that the rate of returns of the two stock markets does not obey the normal distribution. A correlation exists between the stock price indexes over time scales. The stock price indexes exhibit fractal time series. It indicates that the policy guide hidden at the back influences the characteristic of the Chinese stock market.

Spectral analysis for weighted tree-like fractals

NASA Astrophysics Data System (ADS)

Dai, Meifeng; Chen, Yufei; Wang, Xiaoqian; Sun, Yu; Su, Weiyi

2018-02-01

Much information about the structural properties and dynamical aspects of a network is measured by the eigenvalues of its normalized Laplacian matrix. In this paper, we aim to present a study on the spectra of the normalized Laplacian of weighted tree-like fractals. We analytically obtain the relationship between the eigenvalues and their multiplicities for two successive generations. As an example of application of these results, we then derive closed-form expressions for their multiplicative Kirchhoff index and Kemeny's constant.

Study on the Adsorption Phenomenon in Shale with the Combination of Molecular Dynamic Simulation and Fractal Analysis

NASA Astrophysics Data System (ADS)

Zhang, Liehui; Li, Jianchao; Jia, Du; Zhao, Yulong; Xie, Chunyu; Tao, Zhengwu

As one of the key status of gas in shale reservoir, adsorption gas accounts for considerable percentage of total gas amount. Due to the complexity and nanostructure of shale gas reservoir, it is very challenging to represent adsorption gas through traditional methods. However, the integration of the fractal theory and molecular dynamics (MD) simulation may provide a new perspective of understanding such nanostructure and the micro-phenomenon happening in it. The key purpose of this paper is to investigate the adsorption phenomenon in shale kerogen. By using MD simulation and grand canonical Monte Carlo (GCMC) algorithm, the adsorption of methane in 2, 5 and 10nm slit-like pores is simulated for different temperature and pressure status. According to the results, the average gas density in smaller pores is higher than that in bigger pores, and multilayer adsorption presents on some areas of pore surfaces. Then, the simulation results are analyzed using the multilayer fractal adsorption model. The analysis indicates that the number of adsorption layer increases with pressure increase: four-layer adsorption presents in 10nm pores while three-layer adsorption shows up in 2nm and 5nm pores due to pore volume limit. Fractal dimension of pore wall surface generated in this study is in the range of 2.31-2.63. Moreover, high temperature could decrease the adsorption behavior in reservoir condition.

Pore surface fractal analysis of palladium-alumina ceramic membrane using Frenkel-Halsey-Hill (FHH) model.

PubMed

Ahmad, A L; Mustafa, N N N

2006-09-15

The alumina ceramic membrane has been modified by the addition of palladium in order to improve the H(2) permeability and selectivity. Palladium-alumina ceramic membrane was prepared via a sol-gel method and subjected to thermal treatment in the temperature range 500-1100 degrees C. Fractal analysis from nitrogen adsorption isotherm is used to study the pore surface roughness of palladium-alumina ceramic membrane with different chemical composition (nitric acid, PVA and palladium) and calcinations process in terms of surface fractal dimension, D. Frenkel-Halsey-Hill (FHH) model was used to determine the D value of palladium-alumina membrane. Following FHH model, the D value of palladium-alumina membrane increased as the calcinations temperature increased from 500 to 700 degrees C but decreased after calcined at 900 and 1100 degrees C. With increasing palladium concentration from 0.5 g Pd/100 ml H(2)O to 2 g Pd/100 ml H(2)O, D value of membrane decreased, indicating to the smoother surface. Addition of higher amount of PVA and palladium reduced the surface fractal of the membrane due to the heterogeneous distribution of pores. However, the D value increased when nitric acid concentration was increased from 1 to 15 M. The effect of calcinations temperature, PVA ratio, palladium and acid concentration on membrane surface area, pore size and pore distribution also studied.

Long-range correlations and fractal dynamics in C. elegans: Changes with aging and stress

NASA Astrophysics Data System (ADS)

Alves, Luiz G. A.; Winter, Peter B.; Ferreira, Leonardo N.; Brielmann, Renée M.; Morimoto, Richard I.; Amaral, Luís A. N.

2017-08-01

Reduced motor control is one of the most frequent features associated with aging and disease. Nonlinear and fractal analyses have proved to be useful in investigating human physiological alterations with age and disease. Similar findings have not been established for any of the model organisms typically studied by biologists, though. If the physiology of a simpler model organism displays the same characteristics, this fact would open a new research window on the control mechanisms that organisms use to regulate physiological processes during aging and stress. Here, we use a recently introduced animal-tracking technology to simultaneously follow tens of Caenorhabdits elegans for several hours and use tools from fractal physiology to quantitatively evaluate the effects of aging and temperature stress on nematode motility. Similar to human physiological signals, scaling analysis reveals long-range correlations in numerous motility variables, fractal properties in behavioral shifts, and fluctuation dynamics over a wide range of timescales. These properties change as a result of a superposition of age and stress-related adaptive mechanisms that regulate motility.

Fractal dimension values of cerebral and cerebellar activity in rats loaded with aluminium.

PubMed

Kekovic, Goran; Culic, Milka; Martac, Ljiljana; Stojadinovic, Gordana; Capo, Ivan; Lalosevic, Dusan; Sekulic, Slobodan

2010-07-01

Aluminium interferes with a variety of cellular metabolic processes in the mammalian nervous system and its intake might increase a risk of developing Alzheimer's disease (AD). While cerebral involvement even at the early stages of intoxication is well known, the role of cerebellum is underestimated. Our aim was to investigate cerebral and cerebellar electrocortical activity in adult male rats exposed to chronic aluminium treatment by nonlinear analytic tools. The adult rats in an aluminium-treated group were injected by AlCl(3), intraperitoneally (2 mg Al/kg, daily for 4 weeks). Fractal analysis of brain activity was performed off-line using Higuchi's algorithm. The average fractal dimension of electrocortical activity in aluminium-treated animals was lower than the average fractal dimension of electrocortical activity in the control rats, at cerebral but not at cerebellar level. The changes in the stationary and nonlinear properties of time series were more expressed in cerebral electrocortical activity than in cerebellar activity. This can be useful for developing effective diagnostic and therapeutic strategies in neurodegenerative diseases.

Evaluation of Dewatering Performance and Fractal Characteristics of Alum Sludge

PubMed Central

Sun, Yongjun; Fan, Wei; Zheng, Huaili; Zhang, Yuxin; Li, Fengting; Chen, Wei

2015-01-01

The dewatering performance and fractal characteristics of alum sludge from a drinking-water treatment plant were investigated in this study. Variations in residual turbidity of supernatant, dry solid content (DS), specific resistance to filtration (SRF), floc size, fractal dimension, and zeta potential were analyzed. Sludge dewatering efficiency was evaluated by measuring both DS and SRF. Results showed that the optimum sludge dewatering efficiency was achieved at 16 mg∙L-1 flocculant dosage and pH 7. Under these conditions, the maximum DS was 54.6%, and the minimum SRF was 0.61 × 1010 m∙kg-1. Floc-size measurements demonstrated that high flocculant dosage significantly improved floc size. Correlation analysis further revealed a strong correlation between fractal dimension and floc size after flocculation. A strong correlation also existed between floc size and zeta potential, and flocculants with a higher cationic degree had a larger correlation coefficient between floc size and zeta potential. In the flocculation process, the main flocculation mechanisms involved adsorption bridging under an acidic condition, and a combination between charge neutralization and adsorption-bridging interaction under neutral and alkaline conditions. PMID:26121132

BOOK REVIEW: The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine and Finance

NASA Astrophysics Data System (ADS)

Ng, J.; Kingsbury, N. G.

2004-02-01

This book provides an overview of the theory and practice of continuous and discrete wavelet transforms. Divided into seven chapters, the first three chapters of the book are introductory, describing the various forms of the wavelet transform and their computation, while the remaining chapters are devoted to applications in fluids, engineering, medicine and miscellaneous areas. Each chapter is well introduced, with suitable examples to demonstrate key concepts. Illustrations are included where appropriate, thus adding a visual dimension to the text. A noteworthy feature is the inclusion, at the end of each chapter, of a list of further resources from the academic literature which the interested reader can consult. The first chapter is purely an introduction to the text. The treatment of wavelet transforms begins in the second chapter, with the definition of what a wavelet is. The chapter continues by defining the continuous wavelet transform and its inverse and a description of how it may be used to interrogate signals. The continuous wavelet transform is then compared to the short-time Fourier transform. Energy and power spectra with respect to scale are also discussed and linked to their frequency counterparts. Towards the end of the chapter, the two-dimensional continuous wavelet transform is introduced. Examples of how the continuous wavelet transform is computed using the Mexican hat and Morlet wavelets are provided throughout. The third chapter introduces the discrete wavelet transform, with its distinction from the discretized continuous wavelet transform having been made clear at the end of the second chapter. In the first half of the chapter, the logarithmic discretization of the wavelet function is described, leading to a discussion of dyadic grid scaling, frames, orthogonal and orthonormal bases, scaling functions and multiresolution representation. The fast wavelet transform is introduced and its computation is illustrated with an example using the Haar wavelet. The second half of the chapter groups together miscellaneous points about the discrete wavelet transform, including coefficient manipulation for signal denoising and smoothing, a description of Daubechies’ wavelets, the properties of translation invariance and biorthogonality, the two-dimensional discrete wavelet transforms and wavelet packets. The fourth chapter is dedicated to wavelet transform methods in the author’s own specialty, fluid mechanics. Beginning with a definition of wavelet-based statistical measures for turbulence, the text proceeds to describe wavelet thresholding in the analysis of fluid flows. The remainder of the chapter describes wavelet analysis of engineering flows, in particular jets, wakes, turbulence and coherent structures, and geophysical flows, including atmospheric and oceanic processes. The fifth chapter describes the application of wavelet methods in various branches of engineering, including machining, materials, dynamics and information engineering. Unlike previous chapters, this (and subsequent) chapters are styled more as literature reviews that describe the findings of other authors. The areas addressed in this chapter include: the monitoring of machining processes, the monitoring of rotating machinery, dynamical systems, chaotic systems, non-destructive testing, surface characterization and data compression. The sixth chapter continues in this vein with the attention now turned to wavelets in the analysis of medical signals. Most of the chapter is devoted to the analysis of one-dimensional signals (electrocardiogram, neural waveforms, acoustic signals etc.), although there is a small section on the analysis of two-dimensional medical images. The seventh and final chapter of the book focuses on the application of wavelets in three seemingly unrelated application areas: fractals, finance and geophysics. The treatment on wavelet methods in fractals focuses on stochastic fractals with a short section on multifractals. The treatment on finance touches on the use of wavelets by other authors in studying stock prices, commodity behaviour, market dynamics and foreign exchange rates. The treatment on geophysics covers what was omitted from the fourth chapter, namely, seismology, well logging, topographic feature analysis and the analysis of climatic data. The text concludes with an assortment of other application areas which could only be mentioned in passing. Unlike most other publications in the subject, this book does not treat wavelet transforms in a mathematically rigorous manner but rather aims to explain the mechanics of the wavelet transform in a way that is easy to understand. Consequently, it serves as an excellent overview of the subject rather than as a reference text. Keeping the mathematics to a minimum and omitting cumbersome and detailed proofs from the text, the book is best-suited to those who are new to wavelets or who want an intuitive understanding of the subject. Such an audience may include graduate students in engineering and professionals and researchers in engineering and the applied sciences.

Statistical analysis of Geopotential Height (GH) timeseries based on Tsallis non-extensive statistical mechanics

NASA Astrophysics Data System (ADS)

Karakatsanis, L. P.; Iliopoulos, A. C.; Pavlos, E. G.; Pavlos, G. P.

2018-02-01

In this paper, we perform statistical analysis of time series deriving from Earth's climate. The time series are concerned with Geopotential Height (GH) and correspond to temporal and spatial components of the global distribution of month average values, during the period (1948-2012). The analysis is based on Tsallis non-extensive statistical mechanics and in particular on the estimation of Tsallis' q-triplet, namely {qstat, qsens, qrel}, the reconstructed phase space and the estimation of correlation dimension and the Hurst exponent of rescaled range analysis (R/S). The deviation of Tsallis q-triplet from unity indicates non-Gaussian (Tsallis q-Gaussian) non-extensive character with heavy tails probability density functions (PDFs), multifractal behavior and long range dependences for all timeseries considered. Also noticeable differences of the q-triplet estimation found in the timeseries at distinct local or temporal regions. Moreover, in the reconstructive phase space revealed a lower-dimensional fractal set in the GH dynamical phase space (strong self-organization) and the estimation of Hurst exponent indicated multifractality, non-Gaussianity and persistence. The analysis is giving significant information identifying and characterizing the dynamical characteristics of the earth's climate.

Influence of Turbulent Flow and Fractal Scaling on Effective Permeability of Fracture Network

NASA Astrophysics Data System (ADS)

Zhu, J.

2017-12-01

A new approach is developed to calculate hydraulic gradient dependent effective permeability of a fractal fracture network where both laminar and turbulent flows may occur in individual fractures. A critical fracture length is used to distinguish flow characteristics in individual fractures. The developed new solutions can be used for the case of a general scaling relationship, an extension to the linear scaling. We examine the impact on the effective permeability of the network of fractal fracture network characteristics, which include the fractal scaling coefficient and exponent, fractal dimension, ratio of minimum over maximum fracture lengths. Results demonstrate that the developed solution can explain more variations of the effective permeability in relation to the fractal dimensions estimated from the field observations. At high hydraulic gradient the effective permeability decreases with the fractal scaling exponent, but increases with the fractal scaling exponent at low gradient. The effective permeability increases with the scaling coefficient, fractal dimension, fracture length ratio and maximum fracture length.

Detrended Fluctuation Analysis and Adaptive Fractal Analysis of Stride Time Data in Parkinson's Disease: Stitching Together Short Gait Trials

PubMed Central

Liebherr, Magnus; Haas, Christian T.

2014-01-01

Variability indicates motor control disturbances and is suitable to identify gait pathologies. It can be quantified by linear parameters (amplitude estimators) and more sophisticated nonlinear methods (structural information). Detrended Fluctuation Analysis (DFA) is one method to measure structural information, e.g., from stride time series. Recently, an improved method, Adaptive Fractal Analysis (AFA), has been proposed. This method has not been applied to gait data before. Fractal scaling methods (FS) require long stride-to-stride data to obtain valid results. However, in clinical studies, it is not usual to measure a large number of strides (e.g., strides). Amongst others, clinical gait analysis is limited due to short walkways, thus, FS seem to be inapplicable. The purpose of the present study was to evaluate FS under clinical conditions. Stride time data of five self-paced walking trials ( strides each) of subjects with PD and a healthy control group (CG) was measured. To generate longer time series, stride time sequences were stitched together. The coefficient of variation (CV), fractal scaling exponents (DFA) and (AFA) were calculated. Two surrogate tests were performed: A) the whole time series was randomly shuffled; B) the single trials were randomly shuffled separately and afterwards stitched together. CV did not discriminate between PD and CG. However, significant differences between PD and CG were found concerning and . Surrogate version B yielded a higher mean squared error and empirical quantiles than version A. Hence, we conclude that the stitching procedure creates an artificial structure resulting in an overestimation of true . The method of stitching together sections of gait seems to be appropriate in order to distinguish between PD and CG with FS. It provides an approach to integrate FS as standard in clinical gait analysis and to overcome limitations such as short walkways. PMID:24465708

A Complex Story: Universal Preference vs. Individual Differences Shaping Aesthetic Response to Fractals Patterns.

PubMed

Street, Nichola; Forsythe, Alexandra M; Reilly, Ronan; Taylor, Richard; Helmy, Mai S

2016-01-01

Fractal patterns offer one way to represent the rough complexity of the natural world. Whilst they dominate many of our visual experiences in nature, little large-scale perceptual research has been done to explore how we respond aesthetically to these patterns. Previous research (Taylor et al., 2011) suggests that the fractal patterns with mid-range fractal dimensions (FDs) have universal aesthetic appeal. Perceptual and aesthetic responses to visual complexity have been more varied with findings suggesting both linear (Forsythe et al., 2011) and curvilinear (Berlyne, 1970) relationships. Individual differences have been found to account for many of the differences we see in aesthetic responses but some, such as culture, have received little attention within the fractal and complexity research fields. This two-study article aims to test preference responses to FD and visual complexity, using a large cohort (N = 443) of participants from around the world to allow universality claims to be tested. It explores the extent to which age, culture and gender can predict our preferences for fractally complex patterns. Following exploratory analysis that found strong correlations between FD and visual complexity, a series of linear mixed-effect models were implemented to explore if each of the individual variables could predict preference. The first tested a linear complexity model (likelihood of selecting the more complex image from the pair of images) and the second a mid-range FD model (likelihood of selecting an image within mid-range). Results show that individual differences can reliably predict preferences for complexity across culture, gender and age. However, in fitting with current findings the mid-range models show greater consistency in preference not mediated by gender, age or culture. This article supports the established theory that the mid-range fractal patterns appear to be a universal construct underlying preference but also highlights the fragility of universal claims by demonstrating individual differences in preference for the interrelated concept of visual complexity. This highlights a current stalemate in the field of empirical aesthetics.

Emergence of fractal scaling in complex networks

NASA Astrophysics Data System (ADS)

Wei, Zong-Wen; Wang, Bing-Hong

2016-09-01

Some real-world networks are shown to be fractal or self-similar. It is widespread that such a phenomenon originates from the repulsion between hubs or disassortativity. Here we show that this common belief fails to capture the causality. Our key insight to address it is to pinpoint links critical to fractality. Those links with small edge betweenness centrality (BC) constitute a special architecture called fractal reference system, which gives birth to the fractal structure of those reported networks. In contrast, a small amount of links with high BC enable small-world effects, hiding the intrinsic fractality. With enough of such links removed, fractal scaling spontaneously arises from nonfractal networks. Our results provide a multiple-scale view on the structure and dynamics and place fractality as a generic organizing principle of complex networks on a firmer ground.

Formation of fivefold axes in the FCC-metal nanoclusters

NASA Astrophysics Data System (ADS)

Myasnichenko, Vladimir S.; Starostenkov, Mikhail D.

2012-11-01

Formation of atomistic structures of metallic Cu, Au, Ag clusters and bimetallic Cu-Au clusters was studied with the help of molecular dynamics using the many-body tight-binding interatomic potential. The simulation of the crystallization process of clusters with the number of atoms ranging from 300 to 1092 was carried out. The most stable configurations of atoms in the system, corresponding to the minimum of potential energy, was found during super-fast cooling from 1000 K. Atoms corresponding to fcc, hcp, and Ih phases were identified by the method of common neighbor analysis. Incomplete icosahedral core can be discovered at the intersection of one of the Ih axes with the surface of monometallic cluster. The decahedron-shaped structure of bimetallic Cu-Au cluster with seven completed icosahedral cores was obtained. The principles of the construction of small bimetallic clusters with icosahedral symmetry and increased fractal dimensionality were offered.

Similarity principles for the biology of pelagic animals

PubMed Central

Barenblatt, G. I.; Monin, A. S.

1983-01-01

A similarity principle is formulated according to which the statistical pattern of the pelagic population is identical in all scales sufficiently large in comparison with the molecular one. From this principle, a power law is obtained analytically for the pelagic animal biomass distribution over the animal sizes. A hypothesis is presented according to which, under fixed external conditions, the oxygen exchange intensity of an animal is governed only by its mass and density and by the specific absorbing capacity of the animal's respiratory organ. From this hypothesis a power law is obtained by the method of dimensional analysis for the exchange intensity mass dependence. The known empirical values of the exponent of this power law are interpreted as an indication that the oxygen-absorbing organs of the animals can be represented as so-called fractal surfaces. In conclusion the biological principle of the decrease in specific exchange intensity with increase in animal mass is discussed. PMID:16593327

Scaling of size distributions of C60 and C70 fullerene surface islands

NASA Astrophysics Data System (ADS)

Dubrovskii, V. G.; Berdnikov, Y.; Olyanich, D. A.; Mararov, V. V.; Utas, T. V.; Zotov, A. V.; Saranin, A. A.

2017-06-01

We present experimental data and a theoretical analysis for the size distributions of C60 and C70 surface islands deposited onto In-modified Si(111)√3 × √3-Au surface under different conditions. We show that both fullerene islands feature an analytic Vicsek-Family scaling shape where the scaled size distributions are given by a power law times an incomplete beta-function with the required normalization. The power exponent in this distribution corresponds to the fractal shape of two-dimensional islands, confirmed by the experimentally observed morphologies. Quite interestingly, we do not see any significant difference between C60 and C70 fullerenes in terms of either scaling parameters or temperature dependence of the diffusion constants. In particular, we deduce the activation energy for surface diffusion of ED = 140 ± 10 meV for both types of fullerenes.

Advances in fractal germanium micro/nanoclusters induced by gold: microstructures and properties.

PubMed

Chen, Zhiwen; Shek, Chan-Hung; Wu, C M Lawrence; Lai, Joseph K L

2014-02-01

Germanium materials are a class of unique semiconductor materials with widespread technological applications because of their valuable semiconducting, electrical, optical, and thermoelectric power properties in the fields of macro/mesoscopic materials and micro/nanodevices. In this review, we describe the efforts toward understanding the microstructures and various properties of the fractal germanium micro/nanoclusters induced by gold prepared by high vacuum thermal evaporation techniques, highlighting contributions from our laboratory. First, we present the integer and non-integer dimensional germanium micro/nanoclusters such as nanoparticles, nanorings, and nanofractals induced by gold and annealing. In particular, the nonlinear electrical behavior of a gold/germanium bilayer film with the interesting nanofractal is discussed in detail. In addition, the third-order optical nonlinearities of the fractal germanium nanocrystals embedded in gold matrix will be summarized by using the sensitive and reliable Z-scan techniques aimed to determine the nonlinear absorption coefficient and nonlinear refractive index. Finally, we emphasize the thermoelectric power properties of the gold/germanium bilayer films. The thermoelectric power measurement is considered to be a more effective method than the conductivity for investigating superlocalization in a percolating system. This research may provide a novel insight to modulate their competent performance and promote rational design of micro/nanodevices. Once mastered, germanium thin films with a variety of fascinating micro/nanoclusters will offer vast and unforeseen opportunities in the semiconductor industry as well as in other fields of science and technology.

Species survival and scaling laws in hostile and disordered environments

NASA Astrophysics Data System (ADS)

Rocha, Rodrigo P.; Figueiredo, Wagner; Suweis, Samir; Maritan, Amos

2016-10-01

In this work we study the likelihood of survival of single-species in the context of hostile and disordered environments. Population dynamics in this environment, as modeled by the Fisher equation, is characterized by negative average growth rate, except in some random spatially distributed patches that may support life. In particular, we are interested in the phase diagram of the survival probability and in the critical size problem, i.e., the minimum patch size required for surviving in the long-time dynamics. We propose a measure for the critical patch size as being proportional to the participation ratio of the eigenvector corresponding to the largest eigenvalue of the linearized Fisher dynamics. We obtain the (extinction-survival) phase diagram and the probability distribution function (PDF) of the critical patch sizes for two topologies, namely, the one-dimensional system and the fractal Peano basin. We show that both topologies share the same qualitative features, but the fractal topology requires higher spatial fluctuations to guarantee species survival. We perform a finite-size scaling and we obtain the associated scaling exponents. In addition, we show that the PDF of the critical patch sizes has an universal shape for the 1D case in terms of the model parameters (diffusion, growth rate, etc.). In contrast, the diffusion coefficient has a drastic effect on the PDF of the critical patch sizes of the fractal Peano basin, and it does not obey the same scaling law of the 1D case.

Band structures in fractal grading porous phononic crystals

NASA Astrophysics Data System (ADS)

Wang, Kai; Liu, Ying; Liang, Tianshu; Wang, Bin

2018-05-01

In this paper, a new grading porous structure is introduced based on a Sierpinski triangle routine, and wave propagation in this fractal grading porous phononic crystal is investigated. The influences of fractal hierarchy and porosity on the band structures in fractal graidng porous phononic crystals are clarified. Vibration modes of unit cell at absolute band gap edges are given to manifest formation mechanism of absolute band gaps. The results show that absolute band gaps are easy to form in fractal structures comparatively to the normal ones with the same porosity. Structures with higher fractal hierarchies benefit multiple wider absolute band gaps. This work provides useful guidance in design of fractal porous phononic crystals.

Fractals in geology and geophysics

NASA Technical Reports Server (NTRS)

Turcotte, Donald L.

1989-01-01

The definition of a fractal distribution is that the number of objects N with a characteristic size greater than r scales with the relation N of about r exp -D. The frequency-size distributions for islands, earthquakes, fragments, ore deposits, and oil fields often satisfy this relation. This application illustrates a fundamental aspect of fractal distributions, scale invariance. The requirement of an object to define a scale in photograhs of many geological features is one indication of the wide applicability of scale invariance to geological problems; scale invariance can lead to fractal clustering. Geophysical spectra can also be related to fractals; these are self-affine fractals rather than self-similar fractals. Examples include the earth's topography and geoid.

Changes of soil particle size distribution in tidal flats in the Yellow River Delta.

PubMed

Lyu, Xiaofei; Yu, Junbao; Zhou, Mo; Ma, Bin; Wang, Guangmei; Zhan, Chao; Han, Guangxuan; Guan, Bo; Wu, Huifeng; Li, Yunzhao; Wang, De

2015-01-01

The tidal flat is one of the important components of coastal wetland systems in the Yellow River Delta (YRD). It can stabilize shorelines and protect coastal biodiversity. The erosion risk in tidal flats in coastal wetlands was seldom been studied. Characterizing changes of soil particle size distribution (PSD) is an important way to quantity soil erosion in tidal flats. Based on the fractal scale theory and network analysis, we determined the fractal characterizations (singular fractal dimension and multifractal dimension) soil PSD in a successional series of tidal flats in a coastal wetland in the YRD in eastern China. The results showed that the major soil texture was from silt loam to sandy loam. The values of fractal dimensions, ranging from 2.35 to 2.55, decreased from the low tidal flat to the high tidal flat. We also found that the percent of particles with size ranging between 0.4 and 126 μm was related with fractal dimensions. Tide played a great effort on soil PSD than vegetation by increasing soil organic matter (SOM) content and salinity in the coastal wetland in the YRD. Tidal flats in coastal wetlands in the YRD, especially low tidal flats, are facing the risk of soil erosion. This study will be essential to provide a firm basis for the coast erosion control and assessment, as well as wetland ecosystem restoration.

Estimation of Fractal Dimension in Differential Diagnosis of Pigmented Skin Lesions

NASA Astrophysics Data System (ADS)

Aralica, Gorana; Milošević, Danko; Konjevoda, Paško; Seiwerth, Sven; Štambuk, Nikola

Medical differential diagnosis is a method of identifying the presence of a particular entity (disease) within a set of multiple possible alternatives. The significant problem in dermatology and pathology is the differential diagnosis of malignant melanoma and other pigmented skin lesions, especially of dysplastic nevi. Malignant melanoma is the most malignant skin neoplasma, with increasing incidence in various parts of the world. It is hoped that the methods of quantitative pathology, i.e. morphometry, can help objectification of the diagnostic process, since early discovery of melanoma results in 10-year survival rate of 90%. The aim of the study was to use fractal dimension calculated from the perimeter-area relation of the cell nuclei as a tool for the differential diagnosis of pigmented skin lesions. We analyzed hemalaun-eosin stained pathohistological slides of pigmented skin lesions: intradermal naevi (n = 45), dysplastic naevi (n = 47), and malignant melanoma (n = 50). It was found that fractal dimension of malignant melanoma cell nuclei differs significantly from the intradermal and dysplastic naevi (p ≤ 0. 001, Steel-Dwass Multiple Comparison Test). Additionaly, ROC analysis confirmed the value of fractal dimension based evaluation. It is suggested that the estimation of fractal dimension from the perimeter-area relation of the cell nuclei may be a potentially useful morphometric parameter in the medical differential diagnosis of pigmented skin lesions.

Determination of Irreducible Water Saturation from nuclear magnetic resonance based on fractal theory — a case study of sandstone with complex pore structure

NASA Astrophysics Data System (ADS)

Peng, L.; Pan, H.; Ma, H.; Zhao, P.; Qin, R.; Deng, C.

2017-12-01

The irreducible water saturation (Swir) is a vital parameter for permeability prediction and original oil and gas estimation. However, the complex pore structure of the rocks makes the parameter difficult to be calculated from both laboratory and conventional well logging methods. In this study, an effective statistical method to predict Swir is derived directly from nuclear magnetic resonance (NMR) data based on fractal theory. The spectrum of transversal relaxation time (T2) is normally considered as an indicator of pore size distribution, and the micro- and meso-pore's fractal dimension in two specific range of T2 spectrum distribution are calculated. Based on the analysis of the fractal characteristics of 22 core samples, which were drilled from four boreholes of tight lithologic oil reservoirs of Ordos Basin in China, the positive correlation between Swir and porosity is derived. Afterwards a predicting model for Swir based on linear regressions of fractal dimensions is proposed. It reveals that the Swir is controlled by the pore size and the roughness of the pore. The reliability of this model is tested and an ideal consistency between predicted results and experimental data is found. This model is a reliable supplementary to predict the irreducible water saturation in the case that T2 cutoff value cannot be accurately determined.

Functional slit lamp biomicroscopy for imaging bulbar conjunctival microvasculature in contact lens wearers

PubMed Central

Jiang, Hong; Zhong, Jianguang; DeBuc, Delia Cabrera; Tao, Aizhu; Xu, Zhe; Lam, Byron L.; Liu, Che; Wang, Jianhua

2014-01-01

Purpose To develop, test and validate functional slit lamp biomicroscopy (FSLB) for generating non-invasive bulbar conjunctival microvascular perfusion maps (nMPMs) and assessing morphometry and hemodyanmics. Methods FSLB was adapted from a traditional slit-lamp microscope by attaching a digital camera to image the bulbar conjunctiva to create nMPMs and measure venular blood flow hemodyanmics. High definition images with a large field of view were obtained on the temporal bulbar conjunctiva for creating nMPMs. A high imaging rate of 60 frame per second and a ~210× high magnification were achieved using the camera inherited high speed setting and movie crop function, for imaging hemodyanmics. Custom software was developed to segment bulbar conjunctival nMPMs for further fractal analysis and quantitatively measure blood vessel diameter, blood flow velocity and flow rate. Six human subjects were imaged before and after 6 hours of wearing contact lenses. Monofractal and multifractal analyses were performed to quantify fractality of the nMPMs. Results The mean bulbar conjunctival vessel diameter was 18.8 ± 2.7 μm at baseline and increased to 19.6 ± 2.4 μm after 6 hours of lens wear (P = 0.020). The blood flow velocity was increased from 0.60 ± 0.12 mm/s to 0.88 ± 0.21 mm/s (P = 0.001). The blood flow rate was also increased from 129.8 ± 59.9 pl/s to 207.2 ± 81.3 pl/s (P = 0.001). Bulbar conjunctival nMPMs showed the intricate details of the bulbar conjunctival microvascular network. At baseline, fractal dimension was 1.63 ± 0.05 and 1.71 ± 0.03 analyzed by monofractal and multifractal analysis, respectively. Significant increases in fractal dimensions were found after 6 hours of lens wear (P < 0.05). Conclusions Microvascular network’s fractality, morphometry and hemodyanmics of the human bulbar conjunctiva can be measured easily and reliably using FSLB. The alternations of the fractal dimensions, morphometry and hemodyanmics during contact lens wear may indicate ocular microvascular responses to contact lens wear. PMID:24444784

Simulating Titan's aerosols in a three dimensional general circulation model

NASA Astrophysics Data System (ADS)

Larson, Erik J. L.; Toon, Owen B.; Friedson, Andrew J.

2014-11-01

We present results from a new three dimensional GCM with a complete microphysics treatment of the aerosols. We used the Titan Community Atmospheres Model (CAM), to which we have coupled the Community Aerosol and Radiation Model for Atmospheres (CARMA). This model was unable to reproduce superrotating winds without an ad hoc forcing of the zonal winds. Our model was validated by comparing the extinction, optical depth, phase functions, and number densities with data from Cassini and Huygens, as well as other space based and ground based observations. These comparisons allowed us to constrain the microphysical properties of Titan's haze in the tropics at the time of the Huygens descent. Our best fit of the free aerosol parameters include a haze production rate of 1 × 10-14 g cm-2 s-1 and a charge to radius ratio on the particles of 7.5 e-/μm. Despite recent evidence of equatorial precipitation on Titan, we find the aerosols are only slowly removed by rainfall, less than once in 50 Earth years. One way to fit the wavelength dependence of the optical depth is to model the haze as fractal particles with a changing fractal dimension of 2 above 80 km that increases to 2.8 below 30 km. We investigate the spatial and seasonal variability of Titan's haze in our model. We find that the haze particle size and number density responds to the dynamics and creates a seasonal cycle in Titan's albedo.

Aerosol Particle Shape and Radiative Coupling in a Three Dimensional Titan GCM

NASA Astrophysics Data System (ADS)

Larson, Erik J.; Toon, O. B.; Friedson, A. J.; West, R. A.

2010-10-01

Understanding the aerosols on Titan is imperative for understanding the atmosphere as a whole. The aerosols affect the albedo, optical depth, as well as heating and cooling rates which in turn affect the circulation on Titan leading to feedback with the aerosol distribution. Correctly representing the aerosols in atmospheric models is crucial to understanding this atmosphere. Friedson et al. (2009, A global climate model of Titan's atmosphere and surface. Planet. SpaceSci. 57, 1931-1949.) produced a three-dimensional model for Titan using the NCAR CAM3 model, to which we coupled the aerosol microphysics model CARMA. We have also made the aerosols produced by CARMA interactive with the radiation code in CAM. We compare simulations with radiatively interactive aerosols with those using a prescribed aerosol radiative effect. Preliminary results show that this model is capable of reproducing the seasonal changes in aerosols on Titan and many of the associated phenomena. For instance, the radiatively interactive aerosols are lofted by winds more in the summer hemisphere than the non-radiatively interactive aerosols, which is necessary to reproduce the observed seasonal cycle of the albedo. We compare simulations using spherical particles to simulations using fractal aggregate particles, which are expected from laboratory and observational data. Fractal particles have higher absorption in the UV, slower fall velocities and faster coagulation rates than equivalent mass spherical particles. We compare model simulations with observational data from the Cassini and Huygens missions.

Order-fractal transitions in abstract paintings

DOE Office of Scientific and Technical Information (OSTI.GOV)

Calleja, E.M. de la, E-mail: elsama79@gmail.com; Cervantes, F.; Calleja, J. de la

2016-08-15

In this study, we determined the degree of order for 22 Jackson Pollock paintings using the Hausdorff–Besicovitch fractal dimension. Based on the maximum value of each multi-fractal spectrum, the artworks were classified according to the year in which they were painted. It has been reported that Pollock’s paintings are fractal and that this feature was more evident in his later works. However, our results show that the fractal dimension of these paintings ranges among values close to two. We characterize this behavior as a fractal-order transition. Based on the study of disorder-order transition in physical systems, we interpreted the fractal-ordermore » transition via the dark paint strokes in Pollock’s paintings as structured lines that follow a power law measured by the fractal dimension. We determined self-similarity in specific paintings, thereby demonstrating an important dependence on the scale of observations. We also characterized the fractal spectrum for the painting entitled Teri’s Find. We obtained similar spectra for Teri’s Find and Number 5, thereby suggesting that the fractal dimension cannot be rejected completely as a quantitative parameter for authenticating these artworks. -- Highlights: •We determined the degree of order in Jackson Pollock paintings using the Hausdorff–Besicovitch dimension. •We detected a fractal-order transition from Pollock’s paintings between 1947 and 1951. •We suggest that Jackson Pollock could have painted Teri’s Find.« less