Metabolic networks are almost nonfractal: a comprehensive evaluation.

PubMed

Takemoto, Kazuhiro

2014-08-01

Network self-similarity or fractality are widely accepted as an important topological property of metabolic networks; however, recent studies cast doubt on the reality of self-similarity in the networks. Therefore, we perform a comprehensive evaluation of metabolic network fractality using a box-covering method with an earlier version and the latest version of metabolic networks and demonstrate that the latest metabolic networks are almost self-dissimilar, while the earlier ones are fractal, as reported in a number of previous studies. This result may be because the networks were randomized because of an increase in network density due to database updates, suggesting that the previously observed network fractality was due to a lack of available data on metabolic reactions. This finding may not entirely discount the importance of self-similarity of metabolic networks. Rather, it highlights the need for a more suitable definition of network fractality and a more careful examination of self-similarity of metabolic networks.

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.

Modeling of frost crystal growth over a flat plate using artificial neural networks and fractal geometries

NASA Astrophysics Data System (ADS)

Tahavvor, Ali Reza

2017-03-01

In the present study artificial neural network and fractal geometry are used to predict frost thickness and density on a cold flat plate having constant surface temperature under forced convection for different ambient conditions. These methods are very applicable in this area because phase changes such as melting and solidification are simulated by conventional methods but frost formation is a most complicated phase change phenomenon consists of coupled heat and mass transfer. Therefore conventional mathematical techniques cannot capture the effects of all parameters on its growth and development because this process influenced by many factors and it is a time dependent process. Therefore, in this work soft computing method such as artificial neural network and fractal geometry are used to do this manner. The databases for modeling are generated from the experimental measurements. First, multilayer perceptron network is used and it is found that the back-propagation algorithm with Levenberg-Marquardt learning rule is the best choice to estimate frost growth properties due to accurate and faster training procedure. Second, fractal geometry based on the Von-Koch curve is used to model frost growth procedure especially in frost thickness and density. Comparison is performed between experimental measurements and soft computing methods. Results show that soft computing methods can be used more efficiently to determine frost properties over a flat plate. Based on the developed models, wide range of frost formation over flat plates can be determined for various conditions.

Dynamics of pulsatile flow in fractal models of vascular branching networks.

PubMed

Bui, Anh; Sutalo, Ilija D; Manasseh, Richard; Liffman, Kurt

2009-07-01

Efficient regulation of blood flow is critically important to the normal function of many organs, especially the brain. To investigate the circulation of blood in complex, multi-branching vascular networks, a computer model consisting of a virtual fractal model of the vasculature and a mathematical model describing the transport of blood has been developed. Although limited by some constraints, in particular, the use of simplistic, uniformly distributed model for cerebral vasculature and the omission of anastomosis, the proposed computer model was found to provide insights into blood circulation in the cerebral vascular branching network plus the physiological and pathological factors which may affect its functionality. The numerical study conducted on a model of the middle cerebral artery region signified the important effects of vessel compliance, blood viscosity variation as a function of the blood hematocrit, and flow velocity profile on the distributions of flow and pressure in the vascular network.

Fractal Viscous Fingering in Fracture Networks

NASA Astrophysics Data System (ADS)

Boyle, E.; Sams, W.; Ferer, M.; Smith, D. H.

2007-12-01

We have used two very different physical models and computer codes to study miscible injection of a low- viscosity fluid into a simple fracture network, where it displaces a much-more viscous "defending" fluid through "rock" that is otherwise impermeable. The one code (NETfLow) is a standard pore level model, originally intended to treat laboratory-scale experiments; it assumes negligible mixing of the two fluids. The other code (NFFLOW) was written to treat reservoir-scale engineering problems; It explicitly treats the flow through the fractures and allows for significant mixing of the fluids at the interface. Both codes treat the fractures as parallel plates, of different effective apertures. Results are presented for the composition profiles from both codes. Independent of the degree of fluid-mixing, the profiles from both models have a functional form identical to that for fractal viscous fingering (i.e., diffusion limited aggregation, DLA). The two codes that solve the equations for different models gave similar results; together they suggest that the injection of a low-viscosity fluid into large- scale fracture networks may be much more significantly affected by fractal fingering than previously illustrated.

A deterministic width function model

NASA Astrophysics Data System (ADS)

Puente, C. E.; Sivakumar, B.

Use of a deterministic fractal-multifractal (FM) geometric method to model width functions of natural river networks, as derived distributions of simple multifractal measures via fractal interpolating functions, is reported. It is first demonstrated that the FM procedure may be used to simulate natural width functions, preserving their most relevant features like their overall shape and texture and their observed power-law scaling on their power spectra. It is then shown, via two natural river networks (Racoon and Brushy creeks in the United States), that the FM approach may also be used to closely approximate existing width functions.

Estimation of soil saturated hydraulic conductivity by artificial neural networks ensemble in smectitic soils

NASA Astrophysics Data System (ADS)

Sedaghat, A.; Bayat, H.; Safari Sinegani, A. A.

2016-03-01

The saturated hydraulic conductivity ( K s ) of the soil is one of the main soil physical properties. Indirect estimation of this parameter using pedo-transfer functions (PTFs) has received considerable attention. The Purpose of this study was to improve the estimation of K s using fractal parameters of particle and micro-aggregate size distributions in smectitic soils. In this study 260 disturbed and undisturbed soil samples were collected from Guilan province, the north of Iran. The fractal model of Bird and Perrier was used to compute the fractal parameters of particle and micro-aggregate size distributions. The PTFs were developed by artificial neural networks (ANNs) ensemble to estimate K s by using available soil data and fractal parameters. There were found significant correlations between K s and fractal parameters of particles and microaggregates. Estimation of K s was improved significantly by using fractal parameters of soil micro-aggregates as predictors. But using geometric mean and geometric standard deviation of particles diameter did not improve K s estimations significantly. Using fractal parameters of particles and micro-aggregates simultaneously, had the most effect in the estimation of K s . Generally, fractal parameters can be successfully used as input parameters to improve the estimation of K s in the PTFs in smectitic soils. As a result, ANNs ensemble successfully correlated the fractal parameters of particles and micro-aggregates to K s .

Subnetworks of percolation backbones to model karst systems around Tulum, Mexico

NASA Astrophysics Data System (ADS)

Hendrick, Martin; Renard, Philippe

2016-11-01

Karstic caves, which play a key role in groundwater transport, are often organized as complex connected networks resulting from the dissolution of carbonate rocks. In this work, we propose a new model to describe and study the structures of the two largest submersed karst networks in the world. Both of these networks are located in the area of Tulum (Quintana Roo, Mexico). In a previous work te{hendrick2016fractal} we showed that these networks behave as self-similar structures exhibiting well-defined scaling behaviours. In this paper, we suggest that these networks can be modeled using substructures of percolation clusters (θ-subnetworks) having similar structural behaviour (in terms of fractal dimension and conductivity exponent) to those observed in Tulum's karst networks. We show in addition that these θ-subnetworks correspond to structures that minimise a global function, where this global function includes energy dissipation by the viscous forces when water flows through the network, and the cost of network formation itself.

Fractal ladder models and power law wave equations

PubMed Central

Kelly, James F.; McGough, Robert J.

2009-01-01

The ultrasonic attenuation coefficient in mammalian tissue is approximated by a frequency-dependent power law for frequencies less than 100 MHz. To describe this power law behavior in soft tissue, a hierarchical fractal network model is proposed. The viscoelastic and self-similar properties of tissue are captured by a constitutive equation based on a lumped parameter infinite-ladder topology involving alternating springs and dashpots. In the low-frequency limit, this ladder network yields a stress-strain constitutive equation with a time-fractional derivative. By combining this constitutive equation with linearized conservation principles and an adiabatic equation of state, a fractional partial differential equation that describes power law attenuation is derived. The resulting attenuation coefficient is a power law with exponent ranging between 1 and 2, while the phase velocity is in agreement with the Kramers–Kronig relations. The fractal ladder model is compared to published attenuation coefficient data, thus providing equivalent lumped parameters. PMID:19813816

Average weighted receiving time on the non-homogeneous double-weighted fractal networks

NASA Astrophysics Data System (ADS)

Ye, Dandan; Dai, Meifeng; Sun, Yu; Su, Weiyi

2017-05-01

In this paper, based on actual road networks, a model of the non-homogeneous double-weighted fractal networks is introduced depending on the number of copies s and two kinds of weight factors wi ,ri(i = 1 , 2 , … , s) . The double-weights represent the capacity-flowing weights and the cost-traveling weights, respectively. Denote by wijF the capacity-flowing weight connecting the nodes i and j, and denote by wijC the cost-traveling weight connecting the nodes i and j. Let wijF be related to the weight factors w1 ,w2 , … ,ws, and let wijC be related to the weight factors r1 ,r2 , … ,rs. Assuming that the walker, at each step, starting from its current node, moves to any of its neighbors with probability proportional to the capacity-flowing weight of edge linking them. The weighted time for two adjacency nodes is the cost-traveling weight connecting the two nodes. The average weighted receiving time (AWRT) is defined on the non-homogeneous double-weighted fractal networks. AWRT depends on the relationships of the number of copies s and two kinds of weight factors wi ,ri(i = 1 , 2 , … , s) . The obtained remarkable results display that in the large network, the AWRT grows as a power-law function of the network size Ng with the exponent, represented by θ =logs(w1r1 +w2r2 + ⋯ +wsrs) < 1 when w1r1 +w2r2 + ⋯ +wsrs ≠ 1, which means that the smaller the value of w1r1 +w2r2 + ⋯ +wsrs is, the more efficient the process of receiving information is. Especially when w1r1 +w2r2 + ⋯ +wsrs = 1, AWRT grows with increasing order Ng as logNg or (logNg) 2 . In the classic fractal networks, the average receiving time (ART) grows with linearly with the network size Ng. Thus, the non-homogeneous double-weighted fractal networks are more efficient than classic fractal networks in term of receiving information.

Understanding the complexity of human gait dynamics

NASA Astrophysics Data System (ADS)

Scafetta, Nicola; Marchi, Damiano; West, Bruce J.

2009-06-01

Time series of human gait stride intervals exhibit fractal and multifractal properties under several conditions. Records from subjects walking at normal, slow, and fast pace speed are analyzed to determine changes in the fractal scalings as a function of the stress condition of the system. Records from subjects with different age from children to elderly and patients suffering from neurodegenerative disease are analyzed to determine changes in the fractal scalings as a function of the physical maturation or degeneration of the system. A supercentral pattern generator model is presented to simulate the above two properties that are typically found in dynamical network performance: that is, how a dynamical network responds to stress and to evolution.

Integrated workflow for characterizing and modeling fracture network in unconventional reservoirs using microseismic data

NASA Astrophysics Data System (ADS)

Ayatollahy Tafti, Tayeb

We develop a new method for integrating information and data from different sources. We also construct a comprehensive workflow for characterizing and modeling a fracture network in unconventional reservoirs, using microseismic data. The methodology is based on combination of several mathematical and artificial intelligent techniques, including geostatistics, fractal analysis, fuzzy logic, and neural networks. The study contributes to scholarly knowledge base on the characterization and modeling fractured reservoirs in several ways; including a versatile workflow with a novel objective functions. Some the characteristics of the methods are listed below: 1. The new method is an effective fracture characterization procedure estimates different fracture properties. Unlike the existing methods, the new approach is not dependent on the location of events. It is able to integrate all multi-scaled and diverse fracture information from different methodologies. 2. It offers an improved procedure to create compressional and shear velocity models as a preamble for delineating anomalies and map structures of interest and to correlate velocity anomalies with fracture swarms and other reservoir properties of interest. 3. It offers an effective way to obtain the fractal dimension of microseismic events and identify the pattern complexity, connectivity, and mechanism of the created fracture network. 4. It offers an innovative method for monitoring the fracture movement in different stages of stimulation that can be used to optimize the process. 5. Our newly developed MDFN approach allows to create a discrete fracture network model using only microseismic data with potential cost reduction. It also imposes fractal dimension as a constraint on other fracture modeling approaches, which increases the visual similarity between the modeled networks and the real network over the simulated volume.

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.

Fractal Patterns of Neural Activity Exist within the Suprachiasmatic Nucleus and Require Extrinsic Network Interactions

PubMed Central

Hu, Kun; Meijer, Johanna H.; Shea, Steven A.; vanderLeest, Henk Tjebbe; Pittman-Polletta, Benjamin; Houben, Thijs; van Oosterhout, Floor; Deboer, Tom; Scheer, Frank A. J. L.

2012-01-01

The mammalian central circadian pacemaker (the suprachiasmatic nucleus, SCN) contains thousands of neurons that are coupled through a complex network of interactions. In addition to the established role of the SCN in generating rhythms of ∼24 hours in many physiological functions, the SCN was recently shown to be necessary for normal self-similar/fractal organization of motor activity and heart rate over a wide range of time scales—from minutes to 24 hours. To test whether the neural network within the SCN is sufficient to generate such fractal patterns, we studied multi-unit neural activity of in vivo and in vitro SCNs in rodents. In vivo SCN-neural activity exhibited fractal patterns that are virtually identical in mice and rats and are similar to those in motor activity at time scales from minutes up to 10 hours. In addition, these patterns remained unchanged when the main afferent signal to the SCN, namely light, was removed. However, the fractal patterns of SCN-neural activity are not autonomous within the SCN as these patterns completely broke down in the isolated in vitro SCN despite persistence of circadian rhythmicity. Thus, SCN-neural activity is fractal in the intact organism and these fractal patterns require network interactions between the SCN and extra-SCN nodes. Such a fractal control network could underlie the fractal regulation observed in many physiological functions that involve the SCN, including motor control and heart rate regulation. PMID:23185285

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.

Tracing the Attention of Moving Citizens

NASA Astrophysics Data System (ADS)

Wu, Lingfei; Wang, Cheng-Jun

2016-09-01

With the widespread use of mobile computing devices in contemporary society, our trajectories in the physical space and virtual world are increasingly closely connected. Using the anonymous smartphone data of 1 × 105 users in a major city of China, we study the interplay between online and offline human behaviors by constructing the mobility network (offline) and the attention network (online). Using the network renormalization technique, we find that they belong to two different classes: the mobility network is small-world, whereas the attention network is fractal. We then divide the city into different areas based on the features of the mobility network discovered under renormalization. Interestingly, this spatial division manifests the location-based online behaviors, for example shopping, dating, and taxi-requesting. Finally, we offer a geometric network model to help us understand the relationship between small-world and fractal networks.

CROSS-DISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY: The Fractal Dimensions of Complex Networks

NASA Astrophysics Data System (ADS)

Guo, Long; Cai, XU

2009-08-01

It is shown that many real complex networks share distinctive features, such as the small-world effect and the heterogeneous property of connectivity of vertices, which are different from random networks and regular lattices. Although these features capture the important characteristics of complex networks, their applicability depends on the style of networks. To unravel the universal characteristics many complex networks have in common, we study the fractal dimensions of complex networks using the method introduced by Shanker. We find that the average 'density' (ρ(r)) of complex networks follows a better power-law function as a function of distance r with the exponent df, which is defined as the fractal dimension, in some real complex networks. Furthermore, we study the relation between df and the shortcuts Nadd in small-world networks and the size N in regular lattices. Our present work provides a new perspective to understand the dependence of the fractal dimension df on the complex network structure.

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

Evaluating scaling models in biology using hierarchical Bayesian approaches

PubMed Central

Price, Charles A; Ogle, Kiona; White, Ethan P; Weitz, Joshua S

2009-01-01

Theoretical models for allometric relationships between organismal form and function are typically tested by comparing a single predicted relationship with empirical data. Several prominent models, however, predict more than one allometric relationship, and comparisons among alternative models have not taken this into account. Here we evaluate several different scaling models of plant morphology within a hierarchical Bayesian framework that simultaneously fits multiple scaling relationships to three large allometric datasets. The scaling models include: inflexible universal models derived from biophysical assumptions (e.g. elastic similarity or fractal networks), a flexible variation of a fractal network model, and a highly flexible model constrained only by basic algebraic relationships. We demonstrate that variation in intraspecific allometric scaling exponents is inconsistent with the universal models, and that more flexible approaches that allow for biological variability at the species level outperform universal models, even when accounting for relative increases in model complexity. PMID:19453621

Tracing the Attention of Moving Citizens

PubMed Central

Wu, Lingfei; Wang, Cheng-Jun

2016-01-01

With the widespread use of mobile computing devices in contemporary society, our trajectories in the physical space and virtual world are increasingly closely connected. Using the anonymous smartphone data of 1 × 105 users in a major city of China, we study the interplay between online and offline human behaviors by constructing the mobility network (offline) and the attention network (online). Using the network renormalization technique, we find that they belong to two different classes: the mobility network is small-world, whereas the attention network is fractal. We then divide the city into different areas based on the features of the mobility network discovered under renormalization. Interestingly, this spatial division manifests the location-based online behaviors, for example shopping, dating, and taxi-requesting. Finally, we offer a geometric network model to help us understand the relationship between small-world and fractal networks. PMID:27608929

Regional myocardial flow heterogeneity explained with fractal networks

PubMed Central

VAN BEEK, JOHANNES H. G. M.; ROGER, STEPHEN A.; BASSINGTHWAIGHTE, JAMES B.

2010-01-01

There is explain how the distribution of flow broadens with an increase in the spatial resolution of the measurement, we developed fractal models for vascular networks. A dichotomous branching network of vessels represents the arterial tree and connects to a similar venous network. A small difference in vessel lengths and radii between the two daughter vessels, with the same degree of asymmetry at each branch generation, predicts the dependence of the relative dispersion (mean ± SD) on spatial resolution of the perfusion measurement reasonably well. When the degree of asymmetry increases with successive branching, a better fit to data on sheep and baboons results. When the asymmetry is random, a satisfactory fit is found. These models show that a difference in flow of 20% between the daughter vessels at a branch point gives a relative dispersion of flow of ~30% when the heart is divided into 100–200 pieces. Although these simple models do not represent anatomic features accurately, they provide valuable insight on the heterogeneity of flow within the heart. PMID:2589520

Eigenvalues of normalized Laplacian matrices of fractal trees and dendrimers: Analytical results and applications

NASA Astrophysics Data System (ADS)

Julaiti, Alafate; Wu, Bin; Zhang, Zhongzhi

2013-05-01

The eigenvalues of the normalized Laplacian matrix of a network play an important role in its structural and dynamical aspects associated with the network. In this paper, we study the spectra and their applications of normalized Laplacian matrices of a family of fractal trees and dendrimers modeled by Cayley trees, both of which are built in an iterative way. For the fractal trees, we apply the spectral decimation approach to determine analytically all the eigenvalues and their corresponding multiplicities, with the eigenvalues provided by a recursive relation governing the eigenvalues of networks at two successive generations. For Cayley trees, we show that all their eigenvalues can be obtained by computing the roots of several small-degree polynomials defined recursively. By using the relation between normalized Laplacian spectra and eigentime identity, we derive the explicit solution to the eigentime identity for random walks on the two treelike networks, the leading scalings of which follow quite different behaviors. In addition, we corroborate the obtained eigenvalues and their degeneracies through the link between them and the number of spanning trees.

Estimating dynamic permeability in fractal pore network saturated by Maxwellian fluid

NASA Astrophysics Data System (ADS)

Sun, W.

2017-12-01

The frequency dependent flow of fluid in porous media is an important issue in geophysical prospecting. Oscillating flow in pipe leads to frequency dependent dynamic permeability and has been studied in pore network containing Newtonian fluid. But there is little work on oscillating complex fluid in pipe network, especially in irregular network. Here we formulated frequency dependent permeability for Maxwellian fluid and estimated the permeability in three-dimensional fractal network model. We consider an infinitely long cylindrical pipe with rigid solid wall. The pipe is filled with Maxwellian fluids. Based on the mass conservation equation, the equilibrium equation of force and Maxwell constitutive relationship, we formulated the flux by integration of axial velocity component over the pipe's cross section. Then we extend single pipe formulation to a 3D irregular network. Flux balance condition yields a set of linear equations whose unknowns are the fluid pressure at each node. By evaluating the total flow flux through the network, the dynamic permeability can be calculated.We investigated the dynamic permeability of brine and CPyCl/NaSal in a 3D porous sample with a cubic side length 1 cm. The pore network is created by a Voronoi cell filling method. The porosity, i.e., volume ratio between pore/pipe network and the overall cubic, is set as 0.1. The irregular pore network has a fractal structure. The dimension d of the pore network is defined by the relation between node number M within a sphere and the radius r of the sphere,M=rd.The results show that both brine and Maxwellian fluid's permeability maintain a stable value at low frequency, then decreases with fluctuating peaks. The dynamic permeability in pore networks saturated by Maxwellian fluid (CPyCl/NaSal (60 mM)) show larger peaks during the decline process at high frequency, which represents the typical resonance behavior. Dynamic permeability shows clear dependence on the dimension of the fractal network. Small-scale network has higher dimension than large-scale networks. The reason is that in larger networks pore and inter-pore connections are so dense that the probability P(r) to have a neighboring pore at distance r decays faster. The proposed model may be used to explain velocity dispersion in unconventional reservoir rocks observed in laboratory.

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.

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.

The fourth dimension of life: fractal geometry and allometric scaling of organisms.

PubMed

West, G B; Brown, J H; Enquist, B J

1999-06-04

Fractal-like networks effectively endow life with an additional fourth spatial dimension. This is the origin of quarter-power scaling that is so pervasive in biology. Organisms have evolved hierarchical branching networks that terminate in size-invariant units, such as capillaries, leaves, mitochondria, and oxidase molecules. Natural selection has tended to maximize both metabolic capacity, by maximizing the scaling of exchange surface areas, and internal efficiency, by minimizing the scaling of transport distances and times. These design principles are independent of detailed dynamics and explicit models and should apply to virtually all organisms.

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).

Application of Fractal Geometry in Evaluation of Effective Stimulated Reservoir Volume in Shale Gas Reservoirs

NASA Astrophysics Data System (ADS)

Sheng, Guanglong; Su, Yuliang; Wang, Wendong; Javadpour, Farzam; Tang, Meirong

According to hydraulic-fracturing practices conducted in shale reservoirs, effective stimulated reservoir volume (ESRV) significantly affects the production of hydraulic fractured well. Therefore, estimating ESRV is an important prerequisite for confirming the success of hydraulic fracturing and predicting the production of hydraulic fracturing wells in shale reservoirs. However, ESRV calculation remains a longstanding challenge in hydraulic-fracturing operation. In considering fractal characteristics of the fracture network in stimulated reservoir volume (SRV), this paper introduces a fractal random-fracture-network algorithm for converting the microseismic data into fractal geometry. Five key parameters, including bifurcation direction, generating length (d), deviation angle (α), iteration times (N) and generating rules, are proposed to quantitatively characterize fracture geometry. Furthermore, we introduce an orthogonal-fractures coupled dual-porosity-media representation elementary volume (REV) flow model to predict the volumetric flux of gas in shale reservoirs. On the basis of the migration of adsorbed gas in porous kerogen of REV with different fracture spaces, an ESRV criterion for shale reservoirs with SRV is proposed. Eventually, combining the ESRV criterion and fractal characteristic of a fracture network, we propose a new approach for evaluating ESRV in shale reservoirs. The approach has been used in the Eagle Ford shale gas reservoir, and results show that the fracture space has a measurable influence on migration of adsorbed gas. The fracture network can contribute to enhancement of the absorbed gas recovery ratio when the fracture space is less than 0.2 m. ESRV is evaluated in this paper, and results indicate that the ESRV accounts for 27.87% of the total SRV in shale gas reservoirs. This work is important and timely for evaluating fracturing effect and predicting production of hydraulic fracturing wells in shale reservoirs.

Seismic Hazard Analysis on a Complex, Interconnected Fault Network

NASA Astrophysics Data System (ADS)

Page, M. T.; Field, E. H.; Milner, K. R.

2017-12-01

In California, seismic hazard models have evolved from simple, segmented prescriptive models to much more complex representations of multi-fault and multi-segment earthquakes on an interconnected fault network. During the development of the 3rd Uniform California Earthquake Rupture Forecast (UCERF3), the prevalence of multi-fault ruptures in the modeling was controversial. Yet recent earthquakes, for example, the Kaikora earthquake - as well as new research on the potential of multi-fault ruptures (e.g., Nissen et al., 2016; Sahakian et al. 2017) - have validated this approach. For large crustal earthquakes, multi-fault ruptures may be the norm rather than the exception. As datasets improve and we can view the rupture process at a finer scale, the interconnected, fractal nature of faults is revealed even by individual earthquakes. What is the proper way to model earthquakes on a fractal fault network? We show multiple lines of evidence that connectivity even in modern models such as UCERF3 may be underestimated, although clustering in UCERF3 mitigates some modeling simplifications. We need a methodology that can be applied equally well where the fault network is well-mapped and where it is not - an extendable methodology that allows us to "fill in" gaps in the fault network and in our knowledge.

International trade network: fractal properties and globalization puzzle.

PubMed

Karpiarz, Mariusz; Fronczak, Piotr; Fronczak, Agata

2014-12-12

Globalization is one of the central concepts of our age. The common perception of the process is that, due to declining communication and transport costs, distance becomes less and less important. However, the distance coefficient in the gravity model of trade, which grows in time, indicates that the role of distance increases rather than decreases. This, in essence, captures the notion of the globalization puzzle. Here, we show that the fractality of the international trade system (ITS) provides a simple solution for the puzzle. We argue that the distance coefficient corresponds to the fractal dimension of ITS. We provide two independent methods, the box counting method and spatial choice model, which confirm this statement. Our results allow us to conclude that the previous approaches to solving the puzzle misinterpreted the meaning of the distance coefficient in the gravity model of trade.

International Trade Network: Fractal Properties and Globalization Puzzle

NASA Astrophysics Data System (ADS)

Karpiarz, Mariusz; Fronczak, Piotr; Fronczak, Agata

2014-12-01

Globalization is one of the central concepts of our age. The common perception of the process is that, due to declining communication and transport costs, distance becomes less and less important. However, the distance coefficient in the gravity model of trade, which grows in time, indicates that the role of distance increases rather than decreases. This, in essence, captures the notion of the globalization puzzle. Here, we show that the fractality of the international trade system (ITS) provides a simple solution for the puzzle. We argue that the distance coefficient corresponds to the fractal dimension of ITS. We provide two independent methods, the box counting method and spatial choice model, which confirm this statement. Our results allow us to conclude that the previous approaches to solving the puzzle misinterpreted the meaning of the distance coefficient in the gravity model of trade.

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.

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.

Optimal fractal tree-like microchannel networks with slip for laminar-flow-modified Murray's law.

PubMed

Jing, Dalei; Song, Shiyu; Pan, Yunlu; Wang, Xiaoming

2018-01-01

The fractal tree-like branched network is an effective channel design structure to reduce the hydraulic resistance as compared with the conventional parallel channel network. In order for a laminar flow to achieve minimum hydraulic resistance, it is believed that the optimal fractal tree-like channel network obeys the well-accepted Murray's law of β m = N -1/3 (β m is the optimal diameter ratio between the daughter channel and the parent channel and N is the branching number at every level), which is obtained under the assumption of no-slip conditions at the channel wall-liquid interface. However, at the microscale, the no-slip condition is not always reasonable; the slip condition should indeed be considered at some solid-liquid interfaces for the optimal design of the fractal tree-like channel network. The present work reinvestigates Murray's law for laminar flow in a fractal tree-like microchannel network considering slip condition. It is found that the slip increases the complexity of the optimal design of the fractal tree-like microchannel network to achieve the minimum hydraulic resistance. The optimal diameter ratio to achieve minimum hydraulic resistance is not only dependent on the branching number, as stated by Murray's law, but also dependent on the slip length, the level number, the length ratio between the daughter channel and the parent channel, and the diameter of the channel. The optimal diameter ratio decreases with the increasing slip length, the increasing level number and the increasing length ratio between the daughter channel and the parent channel, and decreases with decreasing channel diameter. These complicated relations were found to become relaxed and simplified to Murray's law when the ratio between the slip length and the diameter of the channel is small enough.

Two Simple Models for Fracking

NASA Astrophysics Data System (ADS)

Norris, Jaren Quinn

Recent developments in fracking have enable the recovery of oil and gas from tight shale reservoirs. These developments have also made fracking one of the most controversial environmental issues in the United States. Despite the growing controversy surrounding fracking, there is relatively little publicly available research. This dissertation introduces two simple models for fracking that were developed using techniques from non-linear and statistical physics. The first model assumes that the volume of induced fractures must be equal to the volume of injected fluid. For simplicity, these fractures are assumed to form a spherically symmetric damage region around the borehole. The predicted volumes of water necessary to create a damage region with a given radius are in good agreement with reported values. The second model is a modification of invasion percolation which was previously introduced to model water flooding. The reservoir rock is represented by a regular lattice of local traps that contain oil and/or gas separated by rock barriers. The barriers are assumed to be highly heterogeneous and are assigned random strengths. Fluid is injected from a central site and the weakest rock barrier breaks allowing fluid to flow into the adjacent site. The process repeats with the weakest barrier breaking and fluid flowing to an adjacent site each time step. Extensive numerical simulations were carried out to obtain statistical properties of the growing fracture network. The network was found to be fractal with fractal dimensions differing slightly from the accepted values for traditional percolation. Additionally, the network follows Horton-Strahler and Tokunaga branching statistics which have been used to characterize river networks. As with other percolation models, the growth of the network occurs in bursts. These bursts follow a power-law size distribution similar to observed microseismic events. Reservoir stress anisotropy is incorporated into the model by assigning horizontal bonds weaker strengths on average than vertical bonds. Numerical simulations show that increasing bond strength anisotropy tends to reduce the fractal dimension of the growing fracture network, and decrease the power-law slope of the burst size distribution. Although simple, these two models are useful for making informed decisions about fracking.

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).

Fracture Networks from a deterministic physical model as 'forerunners' of Maze Caves

NASA Astrophysics Data System (ADS)

Ferer, M. V.; Smith, D. H.; Lace, M. J.

2013-12-01

'Fractures are the chief forerunners of caves because they transmit water much more rapidly than intergranular pores.[1] Thus, the cave networks can follow the fracture networks from which the Karst caves formed by a variety of processes. Traditional models of continental Karst define water flow through subsurface geologic formations, slowly dissolving the rock along the pathways (e.g. water saturated with respect to carbon dioxide flowing through fractured carbonate formations). We have developed a deterministic, physical model of fracturing in a model geologic layer of a given thickness, when that layer is strained in one direction and subsequently in a perpendicular direction. It was observed that the connected fracture networks from our model visually resemble maps of maze caves. Since these detailed cave maps offer critical tools in modeling cave development patterns and conduit flow in Karst systems, we were able to test the qualitative resemblance by using statistical analyses to compare our model networks in geologic layers of four different thicknesses with the corresponding statistical analyses of four different maze caves, formed in a variety of geologic settings. The statistical studies performed are: i) standard box-counting to determine if either the caves or the model networks are fractal. We found that both are fractal with a fractal dimension Df ≈ 1.75 . ii) for each section inside a closed path, we determined the area and perimeter-length, enabling a study of the tortuosity of the networks. From the dependence of the section's area upon its perimeter-length, we have found a power-law behavior (for sufficiently large sections) characterized by a 'tortuosity' exponent. These exponents have similar values for both the model networks and the maze caves. The best agreement is between our thickest model layer and the maze-like part of Wind Cave in South Dakota where the data from the model and the cave overlie each other. For the present networks from the physical model, we assumed that the geologic layer was of uniform thickness and that the strain in both directions were the same. The latter may not be the case for the Brazilian, Toca de Boa Cave. These assumptions can be easily modified in our computer code to reflect different geologic histories. Even so the quantitative agreement suggests that our model networks are statistically realistic both for the 'forerunners' of caves and for general fracture networks in geologic layers, which should assist the study of underground fluid flow in many applications for which fracture patterns and fluid flow are difficult to determine (e.g., hydrology, watershed management, oil recovery, carbon dioxide sequestration, etc.). Keywords - Fracture Networks, Karst, Caves, Structurally Variable Pathways, hydrogeological modeling 1 Arthur N. Palmer, CAVE GEOLOGY, pub. Cave Books, Dayton OH, (2007).

The role of the circadian system in fractal neurophysiological control

PubMed Central

Pittman-Polletta, Benjamin R.; Scheer, Frank A.J.L.; Butler, Matthew P.; Shea, Steven A.; Hu, Kun

2013-01-01

Many neurophysiological variables such as heart rate, motor activity, and neural activity are known to exhibit intrinsic fractal fluctuations - similar temporal fluctuation patterns at different time scales. These fractal patterns contain information about health, as many pathological conditions are accompanied by their alteration or absence. In physical systems, such fluctuations are characteristic of critical states on the border between randomness and order, frequently arising from nonlinear feedback interactions between mechanisms operating on multiple scales. Thus, the existence of fractal fluctuations in physiology challenges traditional conceptions of health and disease, suggesting that high levels of integrity and adaptability are marked by complex variability, not constancy, and are properties of a neurophysiological network, not individual components. Despite the subject's theoretical and clinical interest, the neurophysiological mechanisms underlying fractal regulation remain largely unknown. The recent discovery that the circadian pacemaker (suprachiasmatic nucleus) plays a crucial role in generating fractal patterns in motor activity and heart rate sheds an entirely new light on both fractal control networks and the function of this master circadian clock, and builds a bridge between the fields of circadian biology and fractal physiology. In this review, we sketch the emerging picture of the developing interdisciplinary field of fractal neurophysiology by examining the circadian system’s role in fractal regulation. PMID:23573942

Dynamics of Fractal Cluster Gels with Embedded Active Colloids

NASA Astrophysics Data System (ADS)

Szakasits, Megan E.; Zhang, Wenxuan; Solomon, Michael J.

2017-08-01

We find that embedded active colloids increase the ensemble-averaged mean squared displacement of particles in otherwise passively fluctuating fractal cluster gels. The enhancement in dynamics occurs by a mechanism in which the active colloids contribute to the average dynamics both directly through their own active motion and indirectly through their excitation of neighboring passive colloids in the fractal network. Fractal cluster gels are synthesized by addition of magnesium chloride to an initially stable suspension of 1.0 μ m polystyrene colloids in which a dilute concentration of platinum coated Janus colloids has been dispersed. The Janus colloids are thereby incorporated into the fractal network. We measure the ensemble-averaged mean squared displacement of all colloids in the gel before and after the addition of hydrogen peroxide, a fuel that drives diffusiophoretic motion of the Janus particles. The gel mean squared displacement increases by up to a factor of 3 for an active to passive particle ratio of 1 ∶20 and inputted active energy—defined based on the hydrogen peroxide's effect on colloid swim speed and run length—that is up to 9.5 times thermal energy, on a per particle basis. We model the enhancement in gel particle dynamics as the sum of a direct contribution from the displacement of the Janus particles themselves and an indirect contribution from the strain field that the active colloids induce in the surrounding passive particles.

A simple model clarifies the complicated relationships of complex networks

PubMed Central

Zheng, Bojin; Wu, Hongrun; Kuang, Li; Qin, Jun; Du, Wenhua; Wang, Jianmin; Li, Deyi

2014-01-01

Real-world networks such as the Internet and WWW have many common traits. Until now, hundreds of models were proposed to characterize these traits for understanding the networks. Because different models used very different mechanisms, it is widely believed that these traits origin from different causes. However, we find that a simple model based on optimisation can produce many traits, including scale-free, small-world, ultra small-world, Delta-distribution, compact, fractal, regular and random networks. Moreover, by revising the proposed model, the community-structure networks are generated. By this model and the revised versions, the complicated relationships of complex networks are illustrated. The model brings a new universal perspective to the understanding of complex networks and provide a universal method to model complex networks from the viewpoint of optimisation. PMID:25160506

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.

Universal characteristics of fractal fluctuations in prime number distribution

NASA Astrophysics Data System (ADS)

Selvam, A. M.

2014-11-01

The frequency of occurrence of prime numbers at unit number spacing intervals exhibits self-similar fractal fluctuations concomitant with inverse power law form for power spectrum generic to dynamical systems in nature such as fluid flows, stock market fluctuations and population dynamics. The physics of long-range correlations exhibited by fractals is not yet identified. A recently developed general systems theory visualizes the eddy continuum underlying fractals to result from the growth of large eddies as the integrated mean of enclosed small scale eddies, thereby generating a hierarchy of eddy circulations or an inter-connected network with associated long-range correlations. The model predictions are as follows: (1) The probability distribution and power spectrum of fractals follow the same inverse power law which is a function of the golden mean. The predicted inverse power law distribution is very close to the statistical normal distribution for fluctuations within two standard deviations from the mean of the distribution. (2) Fractals signify quantum-like chaos since variance spectrum represents probability density distribution, a characteristic of quantum systems such as electron or photon. (3) Fractal fluctuations of frequency distribution of prime numbers signify spontaneous organization of underlying continuum number field into the ordered pattern of the quasiperiodic Penrose tiling pattern. The model predictions are in agreement with the probability distributions and power spectra for different sets of frequency of occurrence of prime numbers at unit number interval for successive 1000 numbers. Prime numbers in the first 10 million numbers were used for the study.

The Correlation Fractal Dimension of Complex Networks

NASA Astrophysics Data System (ADS)

Wang, Xingyuan; Liu, Zhenzhen; Wang, Mogei

2013-05-01

The fractality of complex networks is studied by estimating the correlation dimensions of the networks. Comparing with the previous algorithms of estimating the box dimension, our algorithm achieves a significant reduction in time complexity. For four benchmark cases tested, that is, the Escherichia coli (E. Coli) metabolic network, the Homo sapiens protein interaction network (H. Sapiens PIN), the Saccharomyces cerevisiae protein interaction network (S. Cerevisiae PIN) and the World Wide Web (WWW), experiments are provided to demonstrate the validity of our algorithm.

Improved visibility graph fractality with application for the diagnosis of Autism Spectrum Disorder

NASA Astrophysics Data System (ADS)

Ahmadlou, Mehran; Adeli, Hojjat; Adeli, Amir

2012-10-01

Recently, the visibility graph (VG) algorithm was proposed for mapping a time series to a graph to study complexity and fractality of the time series through investigation of the complexity of its graph. The visibility graph algorithm converts a fractal time series to a scale-free graph. VG has been used for the investigation of fractality in the dynamic behavior of both artificial and natural complex systems. However, robustness and performance of the power of scale-freeness of VG (PSVG) as an effective method for measuring fractality has not been investigated. Since noise is unavoidable in real life time series, the robustness of a fractality measure is of paramount importance. To improve the accuracy and robustness of PSVG to noise for measurement of fractality of time series in biological time-series, an improved PSVG is presented in this paper. The proposed method is evaluated using two examples: a synthetic benchmark time series and a complicated real life Electroencephalograms (EEG)-based diagnostic problem, that is distinguishing autistic children from non-autistic children. It is shown that the proposed improved PSVG is less sensitive to noise and therefore more robust compared with PSVG. Further, it is shown that using improved PSVG in the wavelet-chaos neural network model of Adeli and c-workers in place of the Katz fractality dimension results in a more accurate diagnosis of autism, a complicated neurological and psychiatric disorder.

On Allometry Relations

NASA Astrophysics Data System (ADS)

West, Damien; West, Bruce J.

2012-07-01

There are a substantial number of empirical relations that began with the identification of a pattern in data; were shown to have a terse power-law description; were interpreted using existing theory; reached the level of "law" and given a name; only to be subsequently fade away when it proved impossible to connect the "law" with a larger body of theory and/or data. Various forms of allometry relations (ARs) have followed this path. The ARs in biology are nearly two hundred years old and those in ecology, geophysics, physiology and other areas of investigation are not that much younger. In general if X is a measure of the size of a complex host network and Y is a property of a complex subnetwork embedded within the host network a theoretical AR exists between the two when Y = aXb. We emphasize that the reductionistic models of AR interpret X and Y as dynamic variables, albeit the ARs themselves are explicitly time independent even though in some cases the parameter values change over time. On the other hand, the phenomenological models of AR are based on the statistical analysis of data and interpret X and Y as averages to yield the empirical AR: = ab. Modern explanations of AR begin with the application of fractal geometry and fractal statistics to scaling phenomena. The detailed application of fractal geometry to the explanation of theoretical ARs in living networks is slightly more than a decade old and although well received it has not been universally accepted. An alternate perspective is given by the empirical AR that is derived using linear regression analysis of fluctuating data sets. We emphasize that the theoretical and empirical ARs are not the same and review theories "explaining" AR from both the reductionist and statistical fractal perspectives. The probability calculus is used to systematically incorporate both views into a single modeling strategy. We conclude that the empirical AR is entailed by the scaling behavior of the probability density, which is derived using the probability calculus.

Scaling Laws of Discrete-Fracture-Network Models

NASA Astrophysics Data System (ADS)

Philippe, D.; Olivier, B.; Caroline, D.; Jean-Raynald, D.

2006-12-01

The statistical description of fracture networks through scale still remains a concern for geologists, considering the complexity of fracture networks. A challenging task of the last 20-years studies has been to find a solid and rectifiable rationale to the trivial observation that fractures exist everywhere and at all sizes. The emergence of fractal models and power-law distributions quantifies this fact, and postulates in some ways that small-scale fractures are genetically linked to their larger-scale relatives. But the validation of these scaling concepts still remains an issue considering the unreachable amount of information that would be necessary with regards to the complexity of natural fracture networks. Beyond the theoretical interest, a scaling law is a basic and necessary ingredient of Discrete-Fracture-Network models (DFN) that are used for many environmental and industrial applications (groundwater resources, mining industry, assessment of the safety of deep waste disposal sites, ..). Indeed, such a function is necessary to assemble scattered data, taken at different scales, into a unified scaling model, and to interpolate fracture densities between observations. In this study, we discuss some important issues related to scaling laws of DFN: - We first describe a complete theoretical and mathematical framework that takes account of both the fracture- size distribution and the fracture clustering through scales (fractal dimension). - We review the scaling laws that have been obtained, and we discuss the ability of fracture datasets to really constrain the parameters of the DFN model. - And finally we discuss the limits of scaling models.

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.

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.

Introduction to the fractality principle of consciousness and the sentyon postulate

PubMed Central

Bieberich, Erhard

2013-01-01

Recently, consciousness research has gained much attention. Indeed, the question at stake is significant: why is the brain not just a computing device, but generates a perception from within? Ambitious endeavors trying to simulate the entire human brain assume that the algorithm will do the trick: as soon as we assemble the brain in a computer and increase the number of operations per time, consciousness will emerge by itself. I disagree with this simplistic representation. My argument emerges from the “atomism paradox”: the irreducible space of the consciously perceived world, the endospace is incompatible with the reducible and decomposable architecture of the brain or a computer. I will first discuss the fundamental challenges in current consciousness models and then propose a new model based on the fractality principle: “the whole is in each of its parts”. This new model copes with the atomism paradox by implementing an iterative mapping of information from higher order brain structures to smaller scales on the cellular and molecular level, which I will refer to as “fractalization”. This information fractalization gives rise to a new form of matter that is conscious (“bright matter”). Bright matter is composed of conscious particles or units named “sentyons”. The internal fractality of these sentyons will close a loop (the “psychic loop”) in a recurrent fractal neural network (RFNN) that allows for continuous and complete information transformation and sharing between higher order brain structures and the endpoint substrate of consciousness at the molecular level. PMID:23950765

Fractal dimension of the middle meningeal vessels: variation and evolution in Homo erectus, Neanderthals, and modern humans.

PubMed

Bruner, Emiliano; Mantini, Simone; Perna, Agostino; Maffei, Carlotta; Manzi, Giorgio

2005-01-01

The middle meningeal vascular network leaves its traces on the endocranial surface because of the tight relationship between neurocranial development and brain growth. Analysing the endocast of fossil specimens, it is therefore possible to describe the morphology of these structures, leading inferences on the cerebral physiology and metabolism in extinct human groups. In this paper, general features of the meningeal vascular traces are described for specimens included in the Homo erectus, Homo neanderthalensis, and Homo sapiens hypodigms. The complexity of the arterial network is quantified by its fractal dimension, calculated through the box-counting method. Modern humans show significant differences from the other two taxa because of the anterior vascular dominance and the larger fractal dimension. Neither the fractal dimension nor the anterior development are merely associated with cranial size increase. Considering the differences between Neanderthals and modern humans, these results may be interpreted in terms of phylogeny, cerebral functions, or cranial structural network.

Evaluation of Elevation, Slope and Stream Network Quality of SPOT Dems

NASA Astrophysics Data System (ADS)

El Hage, M.; Simonetto, E.; Faour, G.; Polidori, L.

2012-07-01

Digital elevation models are considered the most useful data for dealing with geomorphology. The quality of these models is an important issue for users. This quality concerns position and shape. Vertical accuracy is the most assessed in many studies and shape quality is often neglected. However, both of them have an impact on the quality of the final results for a particular application. For instance, the elevation accuracy is required for orthorectification and the shape quality for geomorphology and hydrology. In this study, we deal with photogrammetric DEMs and show the importance of the quality assessment of both elevation and shape. For this purpose, we produce several SPOT HRV DEMs with the same dataset but with different template size, that is one of the production parameters from optical images. Then, we evaluate both elevation and shape quality. The shape quality is assessed with in situ measurements and analysis of slopes as an elementary shape and stream networks as a complex shape. We use the fractal dimension and sinuosity to evaluate the stream network shape. The results show that the elevation accuracy as well as the slope accuracy are affected by the template size. Indeed, an improvement of 1 m in the elevation accuracy and of 5 degrees in the slope accuracy has been obtained while changing this parameter. The elevation RMSE ranges from 7.6 to 8.6 m, which is smaller than the pixel size (10 m). For slope, the RMSE depends on the sampling distance. With a distance of 10 m, the minimum slope RMSE is 11.4 degrees. The stream networks extracted from these DEMs present a higher fractal dimension than the reference river. Moreover, the fractal dimension of the extracted networks has a negligible change according to the template size. Finally, the sinuosity of the stream networks is slightly affected by the change of the template size.

Scaling relationships of channel networks at large scales: Examples from two large-magnitude watersheds in Brittany, France

NASA Astrophysics Data System (ADS)

Crave, A.; Davy, P.

1997-01-01

We present a statistical analysis on two watersheds in French Brittany whose drainage areas are about 10,000 and 2000 km2. The channel system was analysed from the digitised blue lines of the 1:100,000 map and from a 250-m DEM. Link lengths follow an exponential distribution, consistent with the Markovian model of channel branching proposed by Smart (1968). The departure from the exponential distribution for small lengths, that has been extensively discussed before, results from a statistical effect due to the finite number of channels and junctions. The Strahler topology applied on channels defines a self-similar organisation whose similarity dimension is about 1.7, that is clearly smaller than the value of 2 expected for a random organisation. The similarity dimension is consistent with an independent measurement of the Horton ratios of stream numbers and lengths. The variables defined by an upstream integral (drainage area, mainstream length, upstream length) follow power-law distributions limited at large scales by a finite size effect, due to the finite area of the watersheds. A special emphasis is given to the exponent of the drainage area, aA, that has been previously discussed in the context of different aggregation models relevant to channel network growth. We show that aA is consistent with 4/3, a value that was obtained and analytically demonstrated from directed random walk aggregating models, inspired by the model of Scheidegger (1967). The drainage density and mainstream length present no simple scaling with area, except at large areas where they tend to trivial values: constant density and square root of drainage area, respectively. These asymptotic limits necessarily imply that the space dimension of channel networks is 2, equal to the embedding space. The limits are reached for drainage areas larger than 100 km2. For smaller areas, the asymptotic limit represents either a lower bound (drainage density) or an upper bound (mainstream length) of the distributions. Because the fluctuations of the drainage density slowly converge to a finite limit, the system could be adequately described as a fat fractal, where the average drainage density is the sum of a constant plus a fluctuation decreasing as a power law with integrating area. A fat fractal hypothesis could explain why the similarity dimension is not equal to the fractal capacity dimension, as it is for thin fractals. The physical consequences are not yet really understood, but we draw an analogy with a directed aggregating system where the growth process involves both stochastic and deterministic growth. These models are known to be fat fractals, and the deterministic growth, which constitutes a fundamental ingredient of these models, could be attributed in river systems to the role of terrestrial gravity.

Fractal Hypothesis of the Pelagic Microbial Ecosystem-Can Simple Ecological Principles Lead to Self-Similar Complexity in the Pelagic Microbial Food Web?

PubMed

Våge, Selina; Thingstad, T Frede

2015-01-01

Trophic interactions are highly complex and modern sequencing techniques reveal enormous biodiversity across multiple scales in marine microbial communities. Within the chemically and physically relatively homogeneous pelagic environment, this calls for an explanation beyond spatial and temporal heterogeneity. Based on observations of simple parasite-host and predator-prey interactions occurring at different trophic levels and levels of phylogenetic resolution, we present a theoretical perspective on this enormous biodiversity, discussing in particular self-similar aspects of pelagic microbial food web organization. Fractal methods have been used to describe a variety of natural phenomena, with studies of habitat structures being an application in ecology. In contrast to mathematical fractals where pattern generating rules are readily known, however, identifying mechanisms that lead to natural fractals is not straight-forward. Here we put forward the hypothesis that trophic interactions between pelagic microbes may be organized in a fractal-like manner, with the emergent network resembling the structure of the Sierpinski triangle. We discuss a mechanism that could be underlying the formation of repeated patterns at different trophic levels and discuss how this may help understand characteristic biomass size-spectra that hint at scale-invariant properties of the pelagic environment. If the idea of simple underlying principles leading to a fractal-like organization of the pelagic food web could be formalized, this would extend an ecologists mindset on how biological complexity could be accounted for. It may furthermore benefit ecosystem modeling by facilitating adequate model resolution across multiple scales.

Fractal Hypothesis of the Pelagic Microbial Ecosystem—Can Simple Ecological Principles Lead to Self-Similar Complexity in the Pelagic Microbial Food Web?

PubMed Central

Våge, Selina; Thingstad, T. Frede

2015-01-01

Trophic interactions are highly complex and modern sequencing techniques reveal enormous biodiversity across multiple scales in marine microbial communities. Within the chemically and physically relatively homogeneous pelagic environment, this calls for an explanation beyond spatial and temporal heterogeneity. Based on observations of simple parasite-host and predator-prey interactions occurring at different trophic levels and levels of phylogenetic resolution, we present a theoretical perspective on this enormous biodiversity, discussing in particular self-similar aspects of pelagic microbial food web organization. Fractal methods have been used to describe a variety of natural phenomena, with studies of habitat structures being an application in ecology. In contrast to mathematical fractals where pattern generating rules are readily known, however, identifying mechanisms that lead to natural fractals is not straight-forward. Here we put forward the hypothesis that trophic interactions between pelagic microbes may be organized in a fractal-like manner, with the emergent network resembling the structure of the Sierpinski triangle. We discuss a mechanism that could be underlying the formation of repeated patterns at different trophic levels and discuss how this may help understand characteristic biomass size-spectra that hint at scale-invariant properties of the pelagic environment. If the idea of simple underlying principles leading to a fractal-like organization of the pelagic food web could be formalized, this would extend an ecologists mindset on how biological complexity could be accounted for. It may furthermore benefit ecosystem modeling by facilitating adequate model resolution across multiple scales. PMID:26648929

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.

[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.

Reengineering through natural structures: the fractal factory

NASA Astrophysics Data System (ADS)

Sihn, Wilfried

1995-08-01

Many branches of European industry have had to recognize that their lead in the world market has been caught up with, particularly through Asian competition. In many cases a deficit of up to 30% in costs and productivity already exists. The reasons are rigid, Tayloristic company structures. The companies are not in a position to react flexibly to constantly changing environmental conditions. This article illustrates the methods of the `fractal company' which are necessary to solve the structure crisis. The fractal company distinguishes itself through its dynamics and its vitality, as well as its independent reaction to the changing circumstances. The developed methods, procedures, and framework conditions such as company structuring, human networking, hierarchy formation, and models for renumeration and working time are explained. They are based on practical examples from IPA's work with the automobile industry, their suppliers, and the engineering industry.

Deterministic chaos and fractal complexity in the dynamics of cardiovascular behavior: perspectives on a new frontier.

PubMed

Sharma, Vijay

2009-09-10

Physiological systems such as the cardiovascular system are capable of five kinds of behavior: equilibrium, periodicity, quasi-periodicity, deterministic chaos and random behavior. Systems adopt one or more these behaviors depending on the function they have evolved to perform. The emerging mathematical concepts of fractal mathematics and chaos theory are extending our ability to study physiological behavior. Fractal geometry is observed in the physical structure of pathways, networks and macroscopic structures such the vasculature and the His-Purkinje network of the heart. Fractal structure is also observed in processes in time, such as heart rate variability. Chaos theory describes the underlying dynamics of the system, and chaotic behavior is also observed at many levels, from effector molecules in the cell to heart function and blood pressure. This review discusses the role of fractal structure and chaos in the cardiovascular system at the level of the heart and blood vessels, and at the cellular level. Key functional consequences of these phenomena are highlighted, and a perspective provided on the possible evolutionary origins of chaotic behavior and fractal structure. The discussion is non-mathematical with an emphasis on the key underlying concepts.

Deterministic Chaos and Fractal Complexity in the Dynamics of Cardiovascular Behavior: Perspectives on a New Frontier

PubMed Central

Sharma, Vijay

2009-01-01

Physiological systems such as the cardiovascular system are capable of five kinds of behavior: equilibrium, periodicity, quasi-periodicity, deterministic chaos and random behavior. Systems adopt one or more these behaviors depending on the function they have evolved to perform. The emerging mathematical concepts of fractal mathematics and chaos theory are extending our ability to study physiological behavior. Fractal geometry is observed in the physical structure of pathways, networks and macroscopic structures such the vasculature and the His-Purkinje network of the heart. Fractal structure is also observed in processes in time, such as heart rate variability. Chaos theory describes the underlying dynamics of the system, and chaotic behavior is also observed at many levels, from effector molecules in the cell to heart function and blood pressure. This review discusses the role of fractal structure and chaos in the cardiovascular system at the level of the heart and blood vessels, and at the cellular level. Key functional consequences of these phenomena are highlighted, and a perspective provided on the possible evolutionary origins of chaotic behavior and fractal structure. The discussion is non-mathematical with an emphasis on the key underlying concepts. PMID:19812706

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

Communities and classes in symmetric fractals

NASA Astrophysics Data System (ADS)

Krawczyk, Małgorzata J.

2015-07-01

Two aspects of fractal networks are considered: the community structure and the class structure, where classes of nodes appear as a consequence of a local symmetry of nodes. The analyzed systems are the networks constructed for two selected symmetric fractals: the Sierpinski triangle and the Koch curve. Communities are searched for by means of a set of differential equations. Overlapping nodes which belong to two different communities are identified by adding some noise to the initial connectivity matrix. Then, a node can be characterized by a spectrum of probabilities of belonging to different communities. Our main goal is that the overlapping nodes with the same spectra belong to the same class.

Flat electronic bands in fractal-kagomé network and the effect of perturbation

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

Nandy, Atanu, E-mail: atanunandy1989@gmail.com; Chakrabarti, Arunava, E-mail: arunava-chakrabarti@yahoo.co.in

2016-05-06

We demonstrate an analytical prescription of demonstrating the flat band [FB] states in a fractal incorporated kagomé type network that can give rise to a countable infinity of flat non-dispersive eigenstates with a multitude of localization area. The onset of localization can, in principle, be delayed in space by an appropriate choice of energy regime. The length scale, at which the onset of localization for each mode occurs, can be tuned at will following the formalism developed within the framework of real space renormalization group. This scheme leads to an exact determination of energy eigenvalue for which one can havemore » dispersionless flat electronic bands. Furthermore, we have shown the effect ofuniform magnetic field for the same non-translationally invariant network model that has ultimately led to an‘apparent invisibility’ of such staggered localized states and to generate absolutely continuous sub-bands in the energy spectrum and again an interesting re-entrant behavior of those FB states.« less

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.

In situ recording of particle network formation in liquids by ion conductivity measurements.

PubMed

Pfaffenhuber, Christian; Sörgel, Seniz; Weichert, Katja; Bele, Marjan; Mundinger, Tabea; Göbel, Marcus; Maier, Joachim

2011-09-21

The formation of fractal silica networks from a colloidal initial state was followed in situ by ion conductivity measurements. The underlying effect is a high interfacial lithium ion conductivity arising when silica particles are brought into contact with Li salt-containing liquid electrolytes. The experimental results were modeled using Monte Carlo simulations and tested using confocal fluorescence laser microscopy and ζ-potential measurements.

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.

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.

Supply-demand balance in outward-directed networks and Kleiber's law

PubMed Central

Painter, Page R

2005-01-01

Background Recent theories have attempted to derive the value of the exponent α in the allometric formula for scaling of basal metabolic rate from the properties of distribution network models for arteries and capillaries. It has recently been stated that a basic theorem relating the sum of nutrient currents to the specific nutrient uptake rate, together with a relationship claimed to be required in order to match nutrient supply to nutrient demand in 3-dimensional outward-directed networks, leads to Kleiber's law (b = 3/4). Methods The validity of the supply-demand matching principle and the assumptions required to prove the basic theorem are assessed. The supply-demand principle is evaluated by examining the supply term and the demand term in outward-directed lattice models of nutrient and water distribution systems and by applying the principle to fractal-like models of mammalian arterial systems. Results Application of the supply-demand principle to bifurcating fractal-like networks that are outward-directed does not predict 3/4-power scaling, and evaluation of water distribution system models shows that the matching principle does not match supply to demand in such systems. Furthermore, proof of the basic theorem is shown to require that the covariance of nutrient uptake and current path length is 0, an assumption unlikely to be true in mammalian arterial systems. Conclusion The supply-demand matching principle does not lead to a satisfactory explanation for the approximately 3/4-power scaling of mammalian basal metabolic rate. PMID:16283939

Supply-demand balance in outward-directed networks and Kleiber's law.

PubMed

Painter, Page R

2005-11-10

Recent theories have attempted to derive the value of the exponent alpha in the allometric formula for scaling of basal metabolic rate from the properties of distribution network models for arteries and capillaries. It has recently been stated that a basic theorem relating the sum of nutrient currents to the specific nutrient uptake rate, together with a relationship claimed to be required in order to match nutrient supply to nutrient demand in 3-dimensional outward-directed networks, leads to Kleiber's law (b = 3/4). The validity of the supply-demand matching principle and the assumptions required to prove the basic theorem are assessed. The supply-demand principle is evaluated by examining the supply term and the demand term in outward-directed lattice models of nutrient and water distribution systems and by applying the principle to fractal-like models of mammalian arterial systems. Application of the supply-demand principle to bifurcating fractal-like networks that are outward-directed does not predict 3/4-power scaling, and evaluation of water distribution system models shows that the matching principle does not match supply to demand in such systems. Furthermore, proof of the basic theorem is shown to require that the covariance of nutrient uptake and current path length is 0, an assumption unlikely to be true in mammalian arterial systems. The supply-demand matching principle does not lead to a satisfactory explanation for the approximately 3/4-power scaling of mammalian basal metabolic rate.

P-adic model of transport in porous disordered media

NASA Astrophysics Data System (ADS)

Khrennikov, Adrei Yu.; Oleschko, Klaudia

2014-05-01

The soil porosity and permeability are the most important quantitative indicators of soil dynamics under the land-use change. The main problema in the modeling of this dynamic is still poor correlation between the real measuring data and the mathematical and computer simulation models. In order to overpassed this deep divorce we have designed a new technique, able to compare the data arised from the multiscale image analices and time series of the basic physical properties dynamics in porous media studied in time and space. We present a model of the diffusion reaction type describing transport in disordered porous media, e.g., water or oil flow in a complex network of pores. Our model is based on p-adic representation of such networks. This is a kind of fractal representation. We explore advantages of p- adic representation, namely, the possibility to endow p-adic trees with an algebraic structure and ultrametric topology and, hence, to apply analysis which have (at least some) similarities with ordinary real analysis on the straight line. We present the system of two diffusion reaction equations describing propagation of particles in networks of pores in disordered media. As an application, one can consider water transport through the soil pore Networks, or oil flow through capillaries nets. Under some restrictions on potentials and rate coefficients we found the stationary regime corresponding to water content or concentration of oil in a cluster of capillaries. Usage of p-adic analysis (in particular, p-adic wavelets) gives a possibility to find the stationary solution in the analytic form which makes possible to present a clear pedological or geological picture of the process. The mathematical model elaborated in this paper (Khrennikov, 2013) can be applied to variety of problems from water concentration in aquifers to the problem of formation of oil reservoirs in disordered media with porous structures. Another possible application may have real practical output. In fact, our system of diffusion-reaction equations can be used to model the process of extraction of water or oil from an extended network of capillaries (Khrennikov et al., 2013). The accomplished analyses show that the time series of water content/pressure dynamics in saturated/unsaturated conditions reflect the fractal structure of pores separated by familias base don the seven geometric descriptors which we used for the soils multiscale images (Oleschko et al., 2012). The similar models were applied to the porous media behind the oil flow from wells. These results motivate usage of the fractal and, in particular, p-adic methods of modeling.

Fractal analysis of phasic laser images of the myocardium for the purpose of diagnostics of acute coronary insufficiency

NASA Astrophysics Data System (ADS)

Wanchuliak, O. Y.; Bachinskyi, V. T.

2011-09-01

In this work on the base of Mueller-matrix description of optical anisotropy, the possibility of monitoring of time changes of myocardium tissue birefringence, has been considered. The optical model of polycrystalline networks of myocardium is suggested. The results of investigating the interrelation between the values correlation (correlation area, asymmetry coefficient and autocorrelation function excess) and fractal (dispersion of logarithmic dependencies of power spectra) parameters are presented. They characterize the distributions of Mueller matrix elements in the points of laser images of myocardium histological sections. The criteria of differentiation of death coming reasons are determined.

Mapping Transient Hyperventilation Induced Alterations with Estimates of the Multi-Scale Dynamics of BOLD Signal.

PubMed

Kiviniemi, Vesa; Remes, Jukka; Starck, Tuomo; Nikkinen, Juha; Haapea, Marianne; Silven, Olli; Tervonen, Osmo

2009-01-01

Temporal blood oxygen level dependent (BOLD) contrast signals in functional MRI during rest may be characterized by power spectral distribution (PSD) trends of the form 1/f(alpha). Trends with 1/f characteristics comprise fractal properties with repeating oscillation patterns in multiple time scales. Estimates of the fractal properties enable the quantification of phenomena that may otherwise be difficult to measure, such as transient, non-linear changes. In this study it was hypothesized that the fractal metrics of 1/f BOLD signal trends can map changes related to dynamic, multi-scale alterations in cerebral blood flow (CBF) after a transient hyperventilation challenge. Twenty-three normal adults were imaged in a resting-state before and after hyperventilation. Different variables (1/f trend constant alpha, fractal dimension D(f), and, Hurst exponent H) characterizing the trends were measured from BOLD signals. The results show that fractal metrics of the BOLD signal follow the fractional Gaussian noise model, even during the dynamic CBF change that follows hyperventilation. The most dominant effect on the fractal metrics was detected in grey matter, in line with previous hyperventilation vaso-reactivity studies. The alpha was able to differentiate also blood vessels from grey matter changes. D(f) was most sensitive to grey matter. H correlated with default mode network areas before hyperventilation but this pattern vanished after hyperventilation due to a global increase in H. In the future, resting-state fMRI combined with fractal metrics of the BOLD signal may be used for analyzing multi-scale alterations of cerebral blood flow.

A key heterogeneous structure of fractal networks based on inverse renormalization scheme

NASA Astrophysics Data System (ADS)

Bai, Yanan; Huang, Ning; Sun, Lina

2018-06-01

Self-similarity property of complex networks was found by the application of renormalization group theory. Based on this theory, network topologies can be classified into universality classes in the space of configurations. In return, through inverse renormalization scheme, a given primitive structure can grow into a pure fractal network, then adding different types of shortcuts, it exhibits different characteristics of complex networks. However, the effect of primitive structure on networks structural property has received less attention. In this paper, we introduce a degree variance index to measure the dispersion of nodes degree in the primitive structure, and investigate the effect of the primitive structure on network structural property quantified by network efficiency. Numerical simulations and theoretical analysis show a primitive structure is a key heterogeneous structure of generated networks based on inverse renormalization scheme, whether or not adding shortcuts, and the network efficiency is positively correlated with degree variance of the primitive structure.

Kinetic signature of fractal-like filament networks formed by orientational linear epitaxy.

PubMed

Hwang, Wonmuk; Eryilmaz, Esma

2014-07-11

We study a broad class of epitaxial assembly of filament networks on lattice surfaces. Over time, a scale-free behavior emerges with a 2.5-3 power-law exponent in filament length distribution. Partitioning between the power-law and exponential behaviors in a network can be used to find the stage and kinetic parameters of the assembly process. To analyze real-world networks, we develop a computer program that measures the network architecture in experimental images. Application to triaxial networks of collagen fibrils shows quantitative agreement with our model. Our unifying approach can be used for characterizing and controlling the network formation that is observed across biological and nonbiological systems.

Elasticity of fractal materials using the continuum model with non-integer dimensional space

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2015-01-01

Using a generalization of vector calculus for space with non-integer dimension, we consider elastic properties of fractal materials. Fractal materials are described by continuum models with non-integer dimensional space. A generalization of elasticity equations for non-integer dimensional space, and its solutions for the equilibrium case of fractal materials are suggested. Elasticity problems for fractal hollow ball and cylindrical fractal elastic pipe with inside and outside pressures, for rotating cylindrical fractal pipe, for gradient elasticity and thermoelasticity of fractal materials are solved.

Formation and rupture of Ca(2+) induced pectin biopolymer gels.

PubMed

Basak, Rajib; Bandyopadhyay, Ranjini

2014-10-07

When calcium salts are added to an aqueous solution of polysaccharide pectin, ionic cross-links form between pectin chains, giving rise to a gel network in dilute solution. In this work, dynamic light scattering (DLS) is employed to study the microscopic dynamics of the fractal aggregates (flocs) that constitute the gels, while rheological measurements are carried out to study the process of gel rupture. As the calcium salt concentration is increased, DLS experiments reveal that the polydispersity of the flocs increase simultaneously with the characteristic relaxation times of the gel network. Above a critical salt concentration, the flocs become interlinked to form a reaction-limited fractal gel network. Rheological studies demonstrate that the limits of the linear rheological response and the critical stresses required to rupture these networks both decrease with the increase in salt concentration. These features indicate that the ion-mediated pectin gels studied here lie in a 'strong link' regime that is characterised by inter-floc links that are stronger than intra-floc links. A scaling analysis of the experimental data presented here demonstrates that the elasticities of the individual fractal flocs exhibit power-law dependences on the added salt concentration. We conclude that when both pectin and salt concentrations are increased, the number of fractal flocs of pectin increases simultaneously with the density of crosslinks, giving rise to very large values of the bulk elastic modulus.

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.

Comparison of caprock pore networks which potentially will be impacted by carbon sequestration projects.

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

McCray, John; Navarre-Sitchler, Alexis; Mouzakis, Katherine

Injection of CO2 into underground rock formations can reduce atmospheric CO2 emissions. Caprocks present above potential storage formations are the main structural trap inhibiting CO2 from leaking into overlying aquifers or back to the Earth's surface. Dissolution and precipitation of caprock minerals resulting from reaction with CO2 may alter the pore network where many pores are of the micrometer to nanometer scale, thus altering the structural trapping potential of the caprock. However, the distribution, geometry and volume of pores at these scales are poorly characterized. In order to evaluate the overall risk of leakage of CO2 from storage formations, amore » first critical step is understanding the distribution and shape of pores in a variety of different caprocks. As the caprock is often comprised of mudstones, we analyzed samples from several mudstone formations with small angle neutron scattering (SANS) and high-resolution transmission electron microscopy (TEM) imaging to compare the pore networks. Mudstones were chosen from current or potential sites for carbon sequestration projects including the Marine Tuscaloosa Group, the Lower Tuscaloosa Group, the upper and lower shale members of the Kirtland Formation, and the Pennsylvanian Gothic shale. Expandable clay contents ranged from 10% to approximately 40% in the Gothic shale and Kirtland Formation, respectively. During SANS, neutrons effectively scatter from interfaces between materials with differing scattering length density (i.e., minerals and pores). The intensity of scattered neutrons, I(Q), where Q is the scattering vector, gives information about the volume and arrangement of pores in the sample. The slope of the scattering data when plotted as log I(Q) vs. log Q provides information about the fractality or geometry of the pore network. On such plots slopes from -2 to -3 represent mass fractals while slopes from -3 to -4 represent surface fractals. Scattering data showed surface fractal dimensions for the Kirtland formation and one sample from the Tuscaloosa formation close to 3, indicating very rough surfaces. In contrast, scattering data for the Gothic shale formation exhibited mass fractal behavior. In one sample of the Tuscaloosa formation the data are described by a surface fractal at low Q (larger pores) and a mass fractal at high Q (smaller pores), indicating two pore populations contributing to the scattering behavior. These small angle neutron scattering results, combined with high-resolution TEM imaging, provided a means for both qualitative and quantitative analysis of the differences in pore networks between these various mudstones.« less

Complex Networks, Fractals and Topology Trends for Oxidative Activity of DNA in Cells for Populations of Fluorescing Neutrophils in Medical Diagnostics

NASA Astrophysics Data System (ADS)

Galich, N. E.

A novel nonlinear statistical method of immunofluorescence data analysis is presented. The data of DNA fluorescence due to oxidative activity in neutrophils nuclei of peripheral blood is analyzed. Histograms of photon counts statistics are generated using flow cytometry method. The histograms represent the distributions of fluorescence flash frequency as functions of intensity for large populations∼104-105 of fluorescing cells. We have shown that these experiments present 3D-correlations of oxidative activity of DNA for full chromosomes set in cells with spatial resolution of measurements is about few nanometers in the flow direction the jet of blood. Detailed analysis showed that large-scale correlations in oxidative activity of DNA in cells are described as networks of small- worlds (complex systems with logarithmic scaling) with self own small-world networks for given donor at given time for all states of health. We observed changes in fractal networks of oxidative activity of DNA in neutrophils in vivo and during medical treatments for classification and diagnostics of pathologies for wide spectra of diseases. Our approach based on analysis of changes topology of networks (fractal dimension) at variation the scales of networks. We produce the general estimation of health status of a given donor in a form of yes/no of answers (healthy/sick) in the dependence on the sign of plus/minus in the trends change of fractal dimensions due to decreasing the scale of nets. We had noted the increasing biodiversity of neutrophils and stochastic (Brownian) character of intercellular correlations of different neutrophils in the blood of healthy donor. In the blood of sick people we observed the deterministic cell-cell correlations of neutrophils and decreasing their biodiversity.

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.

Influence of trap location on the efficiency of trapping in dendrimers and regular hyperbranched polymers.

PubMed

Lin, Yuan; Zhang, Zhongzhi

2013-03-07

The trapping process in polymer systems constitutes a fundamental mechanism for various other dynamical processes taking place in these systems. In this paper, we study the trapping problem in two representative polymer networks, Cayley trees and Vicsek fractals, which separately model dendrimers and regular hyperbranched polymers. Our goal is to explore the impact of trap location on the efficiency of trapping in these two important polymer systems, with the efficiency being measured by the average trapping time (ATT) that is the average of source-to-trap mean first-passage time over every staring point in the whole networks. For Cayley trees, we derive an exact analytic formula for the ATT to an arbitrary trap node, based on which we further obtain the explicit expression of ATT for the case that the trap is uniformly distributed. For Vicsek fractals, we provide the closed-form solution for ATT to a peripheral node farthest from the central node, as well as the numerical solutions for the case when the trap is placed on other nodes. Moreover, we derive the exact formula for the ATT corresponding to the trapping problem when the trap has a uniform distribution over all nodes. Our results show that the influence of trap location on the trapping efficiency is completely different for the two polymer networks. In Cayley trees, the leading scaling of ATT increases with the shortest distance between the trap and the central node, implying that trap's position has an essential impact on the trapping efficiency; while in Vicsek fractals, the effect of location of the trap is negligible, since the dominant behavior of ATT is identical, respective of the location where the trap is placed. We also present that for all cases of trapping problems being studied, the trapping process is more efficient in Cayley trees than in Vicsek fractals. We demonstrate that all differences related to trapping in the two polymer systems are rooted in their underlying topological structures.

Surrogate-based optimization of hydraulic fracturing in pre-existing fracture networks

NASA Astrophysics Data System (ADS)

Chen, Mingjie; Sun, Yunwei; Fu, Pengcheng; Carrigan, Charles R.; Lu, Zhiming; Tong, Charles H.; Buscheck, Thomas A.

2013-08-01

Hydraulic fracturing has been used widely to stimulate production of oil, natural gas, and geothermal energy in formations with low natural permeability. Numerical optimization of fracture stimulation often requires a large number of evaluations of objective functions and constraints from forward hydraulic fracturing models, which are computationally expensive and even prohibitive in some situations. Moreover, there are a variety of uncertainties associated with the pre-existing fracture distributions and rock mechanical properties, which affect the optimized decisions for hydraulic fracturing. In this study, a surrogate-based approach is developed for efficient optimization of hydraulic fracturing well design in the presence of natural-system uncertainties. The fractal dimension is derived from the simulated fracturing network as the objective for maximizing energy recovery sweep efficiency. The surrogate model, which is constructed using training data from high-fidelity fracturing models for mapping the relationship between uncertain input parameters and the fractal dimension, provides fast approximation of the objective functions and constraints. A suite of surrogate models constructed using different fitting methods is evaluated and validated for fast predictions. Global sensitivity analysis is conducted to gain insights into the impact of the input variables on the output of interest, and further used for parameter screening. The high efficiency of the surrogate-based approach is demonstrated for three optimization scenarios with different and uncertain ambient conditions. Our results suggest the critical importance of considering uncertain pre-existing fracture networks in optimization studies of hydraulic fracturing.

Percolation properties of 3-D multiscale pore networks: how connectivity controls soil filtration processes

NASA Astrophysics Data System (ADS)

Perrier, E. M. A.; Bird, N. R. A.; Rieutord, T. B.

2010-04-01

Quantifying the connectivity of pore networks is a key issue not only for modelling fluid flow and solute transport in porous media but also for assessing the ability of soil ecosystems to filter bacteria, viruses and any type of living microorganisms as well inert particles which pose a contamination risk. Straining is the main mechanical component of filtration processes: it is due to size effects, when a given soil retains a conveyed entity larger than the pores through which it is attempting to pass. We postulate that the range of sizes of entities which can be trapped inside soils has to be associated with the large range of scales involved in natural soil structures and that information on the pore size distribution has to be complemented by information on a Critical Filtration Size (CFS) delimiting the transition between percolating and non percolating regimes in multiscale pore networks. We show that the mass fractal dimensions which are classically used in soil science to quantify scaling laws in observed pore size distributions can also be used to build 3-D multiscale models of pore networks exhibiting such a critical transition. We extend to the 3-D case a new theoretical approach recently developed to address the connectivity of 2-D fractal networks (Bird and Perrier, 2009). Theoretical arguments based on renormalisation functions provide insight into multi-scale connectivity and a first estimation of CFS. Numerical experiments on 3-D prefractal media confirm the qualitative theory. These results open the way towards a new methodology to estimate soil filtration efficiency from the construction of soil structural models to be calibrated on available multiscale data.

Percolation properties of 3-D multiscale pore networks: how connectivity controls soil filtration processes

NASA Astrophysics Data System (ADS)

Perrier, E. M. A.; Bird, N. R. A.; Rieutord, T. B.

2010-10-01

Quantifying the connectivity of pore networks is a key issue not only for modelling fluid flow and solute transport in porous media but also for assessing the ability of soil ecosystems to filter bacteria, viruses and any type of living microorganisms as well inert particles which pose a contamination risk. Straining is the main mechanical component of filtration processes: it is due to size effects, when a given soil retains a conveyed entity larger than the pores through which it is attempting to pass. We postulate that the range of sizes of entities which can be trapped inside soils has to be associated with the large range of scales involved in natural soil structures and that information on the pore size distribution has to be complemented by information on a critical filtration size (CFS) delimiting the transition between percolating and non percolating regimes in multiscale pore networks. We show that the mass fractal dimensions which are classically used in soil science to quantify scaling laws in observed pore size distributions can also be used to build 3-D multiscale models of pore networks exhibiting such a critical transition. We extend to the 3-D case a new theoretical approach recently developed to address the connectivity of 2-D fractal networks (Bird and Perrier, 2009). Theoretical arguments based on renormalisation functions provide insight into multi-scale connectivity and a first estimation of CFS. Numerical experiments on 3-D prefractal media confirm the qualitative theory. These results open the way towards a new methodology to estimate soil filtration efficiency from the construction of soil structural models to be calibrated on available multiscale data.

Fractal electrodynamics via non-integer dimensional space approach

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2015-09-01

Using the recently suggested vector calculus for non-integer dimensional space, we consider electrodynamics problems in isotropic case. This calculus allows us to describe fractal media in the framework of continuum models with non-integer dimensional space. We consider electric and magnetic fields of fractal media with charges and currents in the framework of continuum models with non-integer dimensional spaces. An application of the fractal Gauss's law, the fractal Ampere's circuital law, the fractal Poisson equation for electric potential, and equation for fractal stream of charges are suggested. Lorentz invariance and speed of light in fractal electrodynamics are discussed. An expression for effective refractive index of non-integer dimensional space is suggested.

Resting-state EEG delta power is associated with psychological pain in adults with a history of depression.

PubMed

Meerwijk, Esther L; Ford, Judith M; Weiss, Sandra J

2015-02-01

Psychological pain is a prominent symptom of clinical depression. We asked if frontal alpha asymmetry, frontal EEG power, and frontal fractal dimension asymmetry predicted psychological pain in adults with a history of depression. Resting-state frontal EEG (F3/F4) was recorded while participants (N=35) sat upright with their eyes closed. Frontal delta power predicted psychological pain while controlling for depressive symptoms, with participants who exhibited less power experiencing greater psychological pain. Frontal fractal dimension asymmetry, a nonlinear measure of complexity, also predicted psychological pain, such that greater left than right complexity was associated with greater psychological pain. Frontal alpha asymmetry did not contribute unique variance to any regression model of psychological pain. As resting-state delta power is associated with the brain's default mode network, results suggest that the default mode network was less activated during high psychological pain. Findings are consistent with a state of arousal associated with psychological pain. Copyright © 2015 Elsevier B.V. All rights reserved.

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.

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.

Fractality à la carte: a general particle aggregation model.

PubMed

Nicolás-Carlock, J R; Carrillo-Estrada, J L; Dossetti, V

2016-01-19

In nature, fractal structures emerge in a wide variety of systems as a local optimization of entropic and energetic distributions. The fractality of these systems determines many of their physical, chemical and/or biological properties. Thus, to comprehend the mechanisms that originate and control the fractality is highly relevant in many areas of science and technology. In studying clusters grown by aggregation phenomena, simple models have contributed to unveil some of the basic elements that give origin to fractality, however, the specific contribution from each of these elements to fractality has remained hidden in the complex dynamics. Here, we propose a simple and versatile model of particle aggregation that is, on the one hand, able to reveal the specific entropic and energetic contributions to the clusters' fractality and morphology, and, on the other, capable to generate an ample assortment of rich natural-looking aggregates with any prescribed fractal dimension.

Disassortativity of random critical branching trees

NASA Astrophysics Data System (ADS)

Kim, J. S.; Kahng, B.; Kim, D.

2009-06-01

Random critical branching trees (CBTs) are generated by the multiplicative branching process, where the branching number is determined stochastically, independent of the degree of their ancestor. Here we show analytically that despite this stochastic independence, there exists the degree-degree correlation (DDC) in the CBT and it is disassortative. Moreover, the skeletons of fractal networks, the maximum spanning trees formed by the edge betweenness centrality, behave similarly to the CBT in the DDC. This analytic solution and observation support the argument that the fractal scaling in complex networks originates from the disassortativity in the DDC.

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

Multifractal cross-correlation effects in two-variable time series of complex network vertex observables

NASA Astrophysics Data System (ADS)

OświÈ©cimka, Paweł; Livi, Lorenzo; DroŻdŻ, Stanisław

2016-10-01

We investigate the scaling of the cross-correlations calculated for two-variable time series containing vertex properties in the context of complex networks. Time series of such observables are obtained by means of stationary, unbiased random walks. We consider three vertex properties that provide, respectively, short-, medium-, and long-range information regarding the topological role of vertices in a given network. In order to reveal the relation between these quantities, we applied the multifractal cross-correlation analysis technique, which provides information about the nonlinear effects in coupling of time series. We show that the considered network models are characterized by unique multifractal properties of the cross-correlation. In particular, it is possible to distinguish between Erdös-Rényi, Barabási-Albert, and Watts-Strogatz networks on the basis of fractal cross-correlation. Moreover, the analysis of protein contact networks reveals characteristics shared with both scale-free and small-world models.

Fractal Analysis of Drainage Basins on Mars

NASA Technical Reports Server (NTRS)

Stepinski, T. F.; Marinova, M. M.; McGovern, P. J.; Clifford, S. M.

2002-01-01

We used statistical properties of drainage networks on Mars as a measure of martian landscape morphology and an indicator of landscape evolution processes. We utilize the Mars Orbiter Laser Altimeter (MOLA) data to construct digital elevation maps (DEMs) of several, mostly ancient, martian terrains. Drainage basins and channel networks are computationally extracted from DEMs and their structures are analyzed and compared to drainage networks extracted from terrestrial and lunar DEMs. We show that martian networks are self-affine statistical fractals with planar properties similar to terrestrial networks, but vertical properties similar to lunar networks. The uniformity of martian drainage density is between those for terrestrial and lunar landscapes. Our results are consistent with the roughening of ancient martian terrains by combination of rainfall-fed erosion and impacts, although roughening by other fluvial processes cannot be excluded. The notion of sustained rainfall in recent Mars history is inconsistent with our findings.

Chimera states in brain networks: Empirical neural vs. modular fractal connectivity

NASA Astrophysics Data System (ADS)

Chouzouris, Teresa; Omelchenko, Iryna; Zakharova, Anna; Hlinka, Jaroslav; Jiruska, Premysl; Schöll, Eckehard

2018-04-01

Complex spatiotemporal patterns, called chimera states, consist of coexisting coherent and incoherent domains and can be observed in networks of coupled oscillators. The interplay of synchrony and asynchrony in complex brain networks is an important aspect in studies of both the brain function and disease. We analyse the collective dynamics of FitzHugh-Nagumo neurons in complex networks motivated by its potential application to epileptology and epilepsy surgery. We compare two topologies: an empirical structural neural connectivity derived from diffusion-weighted magnetic resonance imaging and a mathematically constructed network with modular fractal connectivity. We analyse the properties of chimeras and partially synchronized states and obtain regions of their stability in the parameter planes. Furthermore, we qualitatively simulate the dynamics of epileptic seizures and study the influence of the removal of nodes on the network synchronizability, which can be useful for applications to epileptic surgery.

Probing the water distribution in porous model sands with two immiscible fluids: A nuclear magnetic resonance micro-imaging study

NASA Astrophysics Data System (ADS)

Lee, Bum Han; Lee, Sung Keun

2017-10-01

The effect of the structural heterogeneity of porous networks on the water distribution in porous media, initially saturated with immiscible fluid followed by increasing durations of water injection, remains one of the important problems in hydrology. The relationship among convergence rates (i.e., the rate of fluid saturation with varying injection time) and the macroscopic properties and structural parameters of porous media have been anticipated. Here, we used nuclear magnetic resonance (NMR) micro-imaging to obtain images (down to ∼50 μm resolution) of the distribution of water injected for varying durations into porous networks that were initially saturated with silicone oil. We then established the relationships among the convergence rates, structural parameters, and transport properties of porous networks. The volume fraction of the water phase increases as the water injection duration increases. The 3D images of the water distributions for silica gel samples are similar to those of the glass bead samples. The changes in water saturation (and the accompanying removal of silicone oil) and the variations in the volume fraction, specific surface area, and cube-counting fractal dimension of the water phase fit well with the single-exponential recovery function { f (t) = a [ 1 -exp (- λt) ] } . The asymptotic values (a, i.e., saturated value) of the properties of the volume fraction, specific surface area, and cube-counting fractal dimension of the glass bead samples were greater than those for the silica gel samples primarily because of the intrinsic differences in the porous networks and local distribution of the pore size and connectivity. The convergence rates of all of the properties are inversely proportional to the entropy length and permeability. Despite limitations of the current study, such as insufficient resolution and uncertainty for the estimated parameters due to sparsely selected short injection times, the observed trends highlight the first analyses of the cube-counting fractal dimension (and other structural properties) and convergence rates in porous networks consisting of two fluid components. These results indicate that the convergence rates correlate with the geometric factor that characterizes the porous networks and transport property of the porous networks.

The fractal dimension of cell membrane correlates with its capacitance: A new fractal single-shell model

PubMed Central

Wang, Xujing; Becker, Frederick F.; Gascoyne, Peter R. C.

2010-01-01

The scale-invariant property of the cytoplasmic membrane of biological cells is examined by applying the Minkowski–Bouligand method to digitized scanning electron microscopy images of the cell surface. The membrane is found to exhibit fractal behavior, and the derived fractal dimension gives a good description of its morphological complexity. Furthermore, we found that this fractal dimension correlates well with the specific membrane dielectric capacitance derived from the electrorotation measurements. Based on these findings, we propose a new fractal single-shell model to describe the dielectrics of mammalian cells, and compare it with the conventional single-shell model (SSM). We found that while both models fit with experimental data well, the new model is able to eliminate the discrepancy between the measured dielectric property of cells and that predicted by the SSM. PMID:21198103

A preliminary study on the effects of acute ethanol ingestion on default mode network and temporal fractal properties of the brain.

PubMed

Weber, Alexander M; Soreni, Noam; Noseworthy, Michael D

2014-08-01

To study the effect of acute alcohol intoxication on the functional connectivity of the default mode network (DMN) and temporal fractal properties of the healthy adult brain. Eleven healthy male volunteers were asked to drink 0.59 g/kg of ethanol. Resting state blood oxygen level dependent (rsBOLD) MRI scans were obtained before consumption, 60 min post-consumption and 90 min post-consumption. Before each rsBOLD scan, pointed-resolved spectroscopy (PRESS) (1)H-MRS (magnetic resonance spectroscopy) scans were acquired to measure ethanol levels in the right basal ganglia. Significant changes in DMN connectivity were found following alcohol consumption (p < 0.01). Both increased and decreased regional connectivity were found after 60 min, whereas mostly decreased connectivity was found after 90 min. The fractal behaviour of the rsBOLD signal, which is believed to help reveal complexity of small-scale neuronal circuitry, became more ordered after both 60 and 90 min of alcohol consumption (p < 0.01). The DMN has been linked to personal identity and social behavior. As such, our preliminary findings may provide insight into the neuro-functional underpinnings of the cognitive and behavioral changes observed during acute alcohol intoxication. The reduced fractal dimension implies a change in function of small-scale neural networks towards less complex signaling.

Enhanced dewaterability of sludge during anaerobic digestion with thermal hydrolysis pretreatment: New insights through structure evolution.

PubMed

Zhang, Jingsi; Li, Ning; Dai, Xiaohu; Tao, Wenquan; Jenkinson, Ian R; Li, Zhuo

2017-12-19

Comprehensive insights into the sludge digestate dewaterability were gained through porous network structure of sludge. We measured the evolution of digestate dewaterability, represented by the solid content of centrifugally dewatered cake, in high-solids sequencing batch digesters with and without thermal hydrolysis pretreatment (THP). The results show that the dewaterability of the sludge after digestion was improved by 3.5% (±0.5%) for unpretreated sludge and 5.1% (±0.4%) for thermally hydrolyzed sludge. Compared to the unpretreated sludge digestate, thermal hydrolysis pretreatment eventually resulted in an improvement of dewaterability by 4.6% (±0.5%). Smaller particle size and larger surface area of sludge were induced by thermal hydrolysis and anaerobic digestion treatments. The structure strength and compactness of sludge, represented by elastic modulus and fractal dimension respectively, decreased with increase of digestion time. The porous network structure was broken up by thermal hydrolysis pretreatment and was further weakened during anaerobic digestion, which correspondingly improved the dewaterability of digestates. The logarithm of elastic modulus increased linearly with fractal dimension regardless of the pretreatment. Both fractal dimension and elastic modulus showed linear relationship with dewaterability. The rheological characterization combined with the analysis of fractal dimension of sewage sludge porous network structure was found applicable in quantitative evaluation of sludge dewaterability, which depended positively on both thermal hydrolysis and anaerobic digestion. Copyright © 2017 Elsevier Ltd. All rights reserved.

Effect of Amphiphiles on the Rheology of Triglyceride Networks

NASA Astrophysics Data System (ADS)

Seth, Jyoti

2014-11-01

Networks of aggregated crystallites form the structural backbone of many products from the food, cosmetic and pharmaceutical industries. Such materials are generally formulated by cooling a saturated solution to yield the desired solid fraction. Crystal nucleation and growth followed by aggregation leads to formation of a space percolating fractal-network. It is understood that microstructural hierarchy and particle-particle interactions determine material behavior during processing, storage and use. In this talk, rheology of suspensions of triglycerides (TAG, like tristearin) will be explored. TAGs exhibit a rich assortment of polymorphs and form suspensions that are evidently sensitive to surface modifying additives like surfactants and polymers. Here, a theoretical framework will be presented for suspensions containing TAG crystals interacting via pairwise potentials. The work builds on existing models of fractal aggregates to understand microstructure and its correlation with material rheology. Effect of amphiphilic additives is derived through variation of particle-particle interactions. Theoretical predictions for storage modulus will be compared against experimental observations and data from the literature and micro structural predictions against microscopy. Such a theory may serve as a step towards predicting short and long-term behavior of aggregated suspensions formulated via crystallization.

Fractal analysis of urban environment: land use and sewer system

NASA Astrophysics Data System (ADS)

Gires, A.; Ochoa Rodriguez, S.; Van Assel, J.; Bruni, G.; Murla Tulys, D.; Wang, L.; Pina, R.; Richard, J.; Ichiba, A.; Willems, P.; Tchiguirinskaia, I.; ten Veldhuis, M. C.; Schertzer, D. J. M.

2014-12-01

Land use distribution are usually obtained by automatic processing of satellite and airborne pictures. The complexity of the obtained patterns which are furthermore scale dependent is enhanced in urban environment. This scale dependency is even more visible in a rasterized representation where only a unique class is affected to each pixel. A parameter commonly analysed in urban hydrology is the coefficient of imperviousness, which reflects the proportion of rainfall that will be immediately active in the catchment response. This coefficient is strongly scale dependent with a rasterized representation. This complex behaviour is well grasped with the help of the scale invariant notion of fractal dimension which enables to quantify the space occupied by a geometrical set (here the impervious areas) not only at a single scale but across all scales. This fractal dimension is also compared to the ones computed on the representation of the catchments with the help of operational semi-distributed models. Fractal dimensions of the corresponding sewer systems are also computed and compared with values found in the literature for natural river networks. This methodology is tested on 7 pilot sites of the European NWE Interreg IV RainGain project located in France, Belgium, Netherlands, United-Kingdom and Portugal. Results are compared between all the case study which exhibit different physical features (slope, level of urbanisation, population density...).

Evidence of diffusive fractal aggregation of TiO2 nanoparticles by femtosecond laser ablation at ambient conditions

NASA Astrophysics Data System (ADS)

Celardo, G. L.; Archetti, D.; Ferrini, G.; Gavioli, L.; Pingue, P.; Cavaliere, E.

2017-01-01

The specific mechanisms which lead to the formation of fractal nanostructures by pulsed laser deposition remain elusive despite intense research efforts, motivated mainly by the technological interest in obtaining tailored nanostructures with simple and scalable production methods. Here we focus on fractal nanostructures of titanium dioxide, TiO2, a strategic material for many applications, obtained by femtosecond laser ablation at ambient conditions. We compare a theoretical model of fractal formation with experimental data. The comparison of theory and experiment confirms that fractal aggregates are formed after landing of the ablated material on the substrate surface by a simple diffusive mechanism. We model the fractal formation through extensive Monte Carlo simulations based on a set of minimal assumptions: TiO2 nanoparticles arrive already formed on the substrate, then they diffuse in a size/mass independent way and stick irreversibly upon touching, thus forming fractal clusters. Despite its simplicity, our model explains the main features of the fractal structures arising from the complex interaction of large TiO2 nanoparticles with different substrates. Indeed our model is able to reproduce both the fractal dimensions and the area distributions of the nanostructures for different densities of the ablated material. Finally we discuss the role of the thermal conductivity of the substrate and the laser fluence on the properties of the fractal nanostructures. Our results represent an advancement towards controlling the production of fractal nanostructures by pulsed laser deposition.

A Fractal Permeability Model for Shale Oil Reservoir

NASA Astrophysics Data System (ADS)

Zhang, Tao; Dong, Mingzhe; Li, Yajun

2018-01-01

In this work, a fractal analytical model is proposed to predict the permeability of shale reservoir. The proposed model explicitly relates the permeability to the micro-structural parameters (tortuosity, pore area fractal dimensions, porosity and slip velocity coefficient) of shale.

Modelling groundwater fractal flow with fractional differentiation via Mittag-Leffler law

NASA Astrophysics Data System (ADS)

Ahokposi, D. P.; Atangana, Abdon; Vermeulen, D. P.

2017-04-01

Modelling the flow of groundwater within a network of fractures is perhaps one of the most difficult exercises within the field of geohydrology. This physical problem has attracted the attention of several scientists across the globe. Already two different types of differentiations have been used to attempt modelling this problem including the classical and the fractional differentiation. In this paper, we employed the most recent concept of differentiation based on the non-local and non-singular kernel called the generalized Mittag-Leffler function, to reshape the model of groundwater fractal flow. We presented the existence of positive solution of the new model. Using the fixed-point approach, we established the uniqueness of the positive solution. We solve the new model with three different numerical schemes including implicit, explicit and Crank-Nicholson numerical methods. Experimental data collected from four constant discharge tests conducted in a typical fractured crystalline rock aquifer of the Northern Limb (Bushveld Complex) in the Limpopo Province (South Africa) are compared with the numerical solutions. It is worth noting that the four boreholes (BPAC1, BPAC2, BPAC3, and BPAC4) are located on Faults.

The Legacy of Benoit Mandelbrot in Geophysics

NASA Astrophysics Data System (ADS)

Turcotte, D. L.

2001-12-01

The concept of fractals (fractional dimension) was introduced by Benoit Mandelbrot in his famous 1967 Science paper. The initial application was to the length of the coastline of Britain. A milestone in the appreciation of the fractal concept by geophysicists was the Union session of the AGU on fractals led off by Benoit in 1986. Although fractals have found important applications in almost every branch of the physical, biological, and social sciences, fractals have been particularly useful in geophysics. Drainage networks are fractal. The frequency-magnitude distribution of earthquakes is fractal. The scale invariance of landscapes and many other geological processes is due to the applicability of power-law (fractal) distributions. Clouds are often fractal. Porosity distributions are fractal. In an almost independent line of research, Benoit in collaboration with James Wallace and others developed the concept of self-affine fractals. The original applications were primarily to time series in hydrology and built on the foundation laid by Henry Hurst. Fractional Gaussian noises and fractional Brownian motions are ubiquitous in geophysics. These are expressed in terms of the power-law relation between the power-spectral density S and frequency f, S ~ f{ β }, examples are β = 0 (white noise), β = 1 (1/f noise), β = 2 (Brownian motion). Of particular importance in geophysics are fractional noises with β = 0.5, these are stationary but have long-range persistent and have a Hurst exponent H = 0.7. Examples include river flows, tree rings, sunspots, varves, etc. Two of Benoit Mandelbrot's major contributions in geophysics as in other fields are: (1) an appreciation of the importance of fat-tail, power-law (fractal) distributions and (2) an appreciation of the importance of self-similar long-range persistence in both stationary time series (noises) and nonstationary time series (walks).

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 Permeability Model Coupling Boundary-Layer Effect for Tight Oil Reservoirs

NASA Astrophysics Data System (ADS)

Wang, Fuyong; Liu, Zhichao; Jiao, Liang; Wang, Congle; Guo, Hu

A fractal permeability model coupling non-flowing boundary-layer effect for tight oil reservoirs was proposed. Firstly, pore structures of tight formations were characterized with fractal theory. Then, with the empirical equation of boundary-layer thickness, Hagen-Poiseuille equation and fractal theory, a fractal torturous capillary tube model coupled with boundary-layer effect was developed, and verified with experimental data. Finally, the parameters influencing effective liquid permeability were quantitatively investigated. The research results show that effective liquid permeability of tight formations is not only decided by pore structures, but also affected by boundary-layer distributions, and effective liquid permeability is the function of fluid type, fluid viscosity, pressure gradient, fractal dimension, tortuosity fractal dimension, minimum pore radius and maximum pore radius. For the tight formations dominated with nanoscale pores, boundary-layer effect can significantly reduce effective liquid permeability, especially under low pressure gradient.

Parameter Prediction of Hydraulic Fracture for Tight Reservoir Based on Micro-Seismic and History Matching

NASA Astrophysics Data System (ADS)

Zhang, Kai; Ma, Xiaopeng; Li, Yanlai; Wu, Haiyang; Cui, Chenyu; Zhang, Xiaoming; Zhang, Hao; Yao, Jun

Hydraulic fracturing is an important measure for the development of tight reservoirs. In order to describe the distribution of hydraulic fractures, micro-seismic diagnostic was introduced into petroleum fields. Micro-seismic events may reveal important information about static characteristics of hydraulic fracturing. However, this method is limited to reflect the distribution area of the hydraulic fractures and fails to provide specific parameters. Therefore, micro-seismic technology is integrated with history matching to predict the hydraulic fracture parameters in this paper. Micro-seismic source location is used to describe the basic shape of hydraulic fractures. After that, secondary modeling is considered to calibrate the parameters information of hydraulic fractures by using DFM (discrete fracture model) and history matching method. In consideration of fractal feature of hydraulic fracture, fractal fracture network model is established to evaluate this method in numerical experiment. The results clearly show the effectiveness of the proposed approach to estimate the parameters of hydraulic fractures.

Right-side-stretched multifractal spectra indicate small-worldness in networks

NASA Astrophysics Data System (ADS)

Oświȩcimka, Paweł; Livi, Lorenzo; Drożdż, Stanisław

2018-04-01

Complex network formalism allows to explain the behavior of systems composed by interacting units. Several prototypical network models have been proposed thus far. The small-world model has been introduced to mimic two important features observed in real-world systems: i) local clustering and ii) the possibility to move across a network by means of long-range links that significantly reduce the characteristic path length. A natural question would be whether there exist several ;types; of small-world architectures, giving rise to a continuum of models with properties (partially) shared with other models belonging to different network families. Here, we take advantage of the interplay between network theory and time series analysis and propose to investigate small-world signatures in complex networks by analyzing multifractal characteristics of time series generated from such networks. In particular, we suggest that the degree of right-sided asymmetry of multifractal spectra is linked with the degree of small-worldness present in networks. This claim is supported by numerical simulations performed on several parametric models, including prototypical small-world networks, scale-free, fractal and also real-world networks describing protein molecules. Our results also indicate that right-sided asymmetry emerges with the presence of the following topological properties: low edge density, low average shortest path, and high clustering coefficient.

Effects of Anisotropy on Scalar Field Ghost Dark Energy and the Non-Equilibrium Thermodynamics in Fractal Cosmology

NASA Astrophysics Data System (ADS)

Najafi, A.; Hossienkhani, H.

2017-10-01

Since the fractal cosmology has been created in early universe, therefore their models were mostly isotropic. The majority of previous studies had been based on FRW universe, while in the early universe, the best model for describing fractal cosmology is actually the anisotropic universe. Therefore in this work, by assuming the anisotropic universe, the cosmological implications of ghost and generalized ghost dark energy models with dark matter in fractal cosmology has been discussed. Moreover, the different kinds of dark energy models such as quintessence and tachyon field, with the generalized ghost dark energy in fractal universe has been investigated. In addition, we have reconstructed the Hubble parameter, H, the energy density, ρ, the deceleration parameter, q, the equations of state parameter, {ω }{{}D}, for both ghost and generalized ghost dark energy models. This correspondence allows us to reconstruct the potential and the dynamics of a fractal canonical scalar field according to the evolution of generalized ghost dark energy density. Eventually, thermodynamics of the cosmological apparent horizon in fractal cosmology was investigated and the validity of the Generalized second law of thermodynamics (GSLT) have been examined in an anisotropic universe. The results show the influence of the anisotropy on the GSLT of thermodynamics in a fractal cosmology.

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.

Focusing behavior of the fractal vector optical fields designed by fractal lattice growth model.

PubMed

Gao, Xu-Zhen; Pan, Yue; Zhao, Meng-Dan; Zhang, Guan-Lin; Zhang, Yu; Tu, Chenghou; Li, Yongnan; Wang, Hui-Tian

2018-01-22

We introduce a general fractal lattice growth model, significantly expanding the application scope of the fractal in the realm of optics. This model can be applied to construct various kinds of fractal "lattices" and then to achieve the design of a great diversity of fractal vector optical fields (F-VOFs) combinating with various "bases". We also experimentally generate the F-VOFs and explore their universal focusing behaviors. Multiple focal spots can be flexibly enginnered, and the optical tweezers experiment validates the simulated tight focusing fields, which means that this model allows the diversity of the focal patterns to flexibly trap and manipulate micrometer-sized particles. Furthermore, the recovery performance of the F-VOFs is also studied when the input fields and spatial frequency spectrum are obstructed, and the results confirm the robustness of the F-VOFs in both focusing and imaging processes, which is very useful in information transmission.

Phase transition in tumor growth: I avascular development

NASA Astrophysics Data System (ADS)

Izquierdo-Kulich, E.; Rebelo, I.; Tejera, E.; Nieto-Villar, J. M.

2013-12-01

We propose a mechanism for avascular tumor growth based on a simple chemical network. This model presents a logistic behavior and shows a “second order” phase transition. We prove the fractal origin of the empirical logistics and Gompertz constant and its relation to mitosis and apoptosis rate. Finally, the thermodynamics framework developed demonstrates the entropy production rate as a Lyapunov function during avascular tumor growth.

Quantitative metrics that describe river deltas and their channel networks

NASA Astrophysics Data System (ADS)

Edmonds, Douglas A.; Paola, Chris; Hoyal, David C. J. D.; Sheets, Ben A.

2011-12-01

Densely populated river deltas are losing land at an alarming rate and to successfully restore these environments we must understand the details of their morphology. Toward this end we present a set of five metrics that describe delta morphology: (1) the fractal dimension, (2) the distribution of island sizes, (3) the nearest-edge distance, (4) a synthetic distribution of sediment fluxes at the shoreline, and (5) the nourishment area. The nearest-edge distance is the shortest distance to channelized or unchannelized water from a given location on the delta and is analogous to the inverse of drainage density in tributary networks. The nourishment area is the downstream delta area supplied by the sediment coming through a given channel cross section and is analogous to catchment area in tributary networks. As a first step, we apply these metrics to four relatively simple, fluvially dominated delta networks. For all these deltas, the average nearest-edge distances are remarkably constant moving down delta suggesting that the network organizes itself to maintain a consistent distance to the nearest channel. Nourishment area distributions can be predicted from a river mouth bar model of delta growth, and also scale with the width of the channel and with the length of the longest channel, analogous to Hack's law for drainage basins. The four delta channel networks are fractal, but power laws and scale invariance appear to be less pervasive than in tributary networks. Thus, deltas may occupy an advantageous middle ground between complete similarity and complete dissimilarity, where morphologic differences indicate different behavior.

Fractual interrelationships in field and seismic data. Final report

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

NONE

1997-01-07

Fractals provide a description of physical patterns over a range of scales in both time and space. Studies presented herein examine the fractal characteristics of various geological variables such as deformed bed-lengths, fold relief, seismic reflection arrival time variations, drainage and topographic patterns, and fracture systems. The studies are also extended to consider the possibility that the fractal characteristics of these variables are interrelated. Fractal interrelationships observed in these studies provide a method for relating variations in the fractal characteristics of seismic reflection events from reservoir intervals to the fractal characteristics of reservoir fracture systems, faults, and fold distributions. Themore » work is motivated by current exploration and development interests to detect fractured reservoirs and to accurately predict flow rates and flow patterns within the fractured reservoir. Accurate prediction requires an understanding of several reservoir properties including the fractal geometry of the reservoir fracture network. Results of these studies provide a method to remotely assess the fractal characteristics of a fractured reservoir, and help guide field development activities. The most significant outgrowth of this research is that 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. Production from fractured reservoirs is the result of complex structural and stratigraphic controls; hence, the import of fractal characterization to the assessment of fractured reservoirs lies in its potential to quantitatively define interrelationships between subtle structural variation and production. The potential uses are illustrated using seismic data from the Granny Creek oil field in the Appalachian Plateau.« less

Optimization of hierarchical structure and nanoscale-enabled plasmonic refraction for window electrodes in photovoltaics.

PubMed

Han, Bing; Peng, Qiang; Li, Ruopeng; Rong, Qikun; Ding, Yang; Akinoglu, Eser Metin; Wu, Xueyuan; Wang, Xin; Lu, Xubing; Wang, Qianming; Zhou, Guofu; Liu, Jun-Ming; Ren, Zhifeng; Giersig, Michael; Herczynski, Andrzej; Kempa, Krzysztof; Gao, Jinwei

2016-09-26

An ideal network window electrode for photovoltaic applications should provide an optimal surface coverage, a uniform current density into and/or from a substrate, and a minimum of the overall resistance for a given shading ratio. Here we show that metallic networks with quasi-fractal structure provides a near-perfect practical realization of such an ideal electrode. We find that a leaf venation network, which possesses key characteristics of the optimal structure, indeed outperforms other networks. We further show that elements of hierarchal topology, rather than details of the branching geometry, are of primary importance in optimizing the networks, and demonstrate this experimentally on five model artificial hierarchical networks of varied levels of complexity. In addition to these structural effects, networks containing nanowires are shown to acquire transparency exceeding the geometric constraint due to the plasmonic refraction.

Holographic Characterization of Colloidal Fractal Aggregates

NASA Astrophysics Data System (ADS)

Wang, Chen; Cheong, Fook Chiong; Ruffner, David B.; Zhong, Xiao; Ward, Michael D.; Grier, David G.

In-line holographic microscopy images of micrometer-scale fractal aggregates can be interpreted with the Lorenz-Mie theory of light scattering and an effective-sphere model to obtain each aggregate's size and the population-averaged fractal dimension. We demonstrate this technique experimentally using model fractal clusters of polystyrene nanoparticles and fractal protein aggregates composed of bovine serum albumin and bovine pancreas insulin. This technique can characterize several thousand aggregates in ten minutes and naturally distinguishes aggregates from contaminants such as silicone oil droplets. Work supported by the SBIR program of the NSF.

A stress sensitivity model for the permeability of porous media based on bi-dispersed fractal theory

NASA Astrophysics Data System (ADS)

Tan, X.-H.; Liu, C.-Y.; Li, X.-P.; Wang, H.-Q.; Deng, H.

A stress sensitivity model for the permeability of porous media based on bidispersed fractal theory is established, considering the change of the flow path, the fractal geometry approach and the mechanics of porous media. It is noted that the two fractal parameters of the porous media construction perform differently when the stress changes. The tortuosity fractal dimension of solid cluster DcTσ become bigger with an increase of stress. However, the pore fractal dimension of solid cluster Dcfσ and capillary bundle Dpfσ remains the same with an increase of stress. The definition of normalized permeability is introduced for the analyzation of the impacts of stress sensitivity on permeability. The normalized permeability is related to solid cluster tortuosity dimension, pore fractal dimension, solid cluster maximum diameter, Young’s modulus and Poisson’s ratio. Every parameter has clear physical meaning without the use of empirical constants. Predictions of permeability of the model is accordant with the obtained experimental data. Thus, the proposed model can precisely depict the flow of fluid in porous media under stress.

Numerical Modeling of Large-Scale Rocky Coastline Evolution

NASA Astrophysics Data System (ADS)

Limber, P.; Murray, A. B.; Littlewood, R.; Valvo, L.

2008-12-01

Seventy-five percent of the world's ocean coastline is rocky. On large scales (i.e. greater than a kilometer), many intertwined processes drive rocky coastline evolution, including coastal erosion and sediment transport, tectonics, antecedent topography, and variations in sea cliff lithology. In areas such as California, an additional aspect of rocky coastline evolution involves submarine canyons that cut across the continental shelf and extend into the nearshore zone. These types of canyons intercept alongshore sediment transport and flush sand to abyssal depths during periodic turbidity currents, thereby delineating coastal sediment transport pathways and affecting shoreline evolution over large spatial and time scales. How tectonic, sediment transport, and canyon processes interact with inherited topographic and lithologic settings to shape rocky coastlines remains an unanswered, and largely unexplored, question. We will present numerical model results of rocky coastline evolution that starts with an immature fractal coastline. The initial shape is modified by headland erosion, wave-driven alongshore sediment transport, and submarine canyon placement. Our previous model results have shown that, as expected, an initial sediment-free irregularly shaped rocky coastline with homogeneous lithology will undergo smoothing in response to wave attack; headlands erode and mobile sediment is swept into bays, forming isolated pocket beaches. As this diffusive process continues, pocket beaches coalesce, and a continuous sediment transport pathway results. However, when a randomly placed submarine canyon is introduced to the system as a sediment sink, the end results are wholly different: sediment cover is reduced, which in turn increases weathering and erosion rates and causes the entire shoreline to move landward more rapidly. The canyon's alongshore position also affects coastline morphology. When placed offshore of a headland, the submarine canyon captures local sediment, increases weathering and erosion around the headland, and eventually changes the headland into an embayment! Improvements to our modeling approach include refining the initial conditions. To create a fractal, immature rocky coastline, self-similar river networks with random side branches were drawn on the shoreline domain. River networks and side branches were scaled according to Horton's law and Tokunaga statistics, respectively, and each river pathway was assigned a simple exponential longitudinal profile. Topography was generated around the river networks to create drainage basins and, on a larger scale, represent a mountainous, fluvially-sculpted landscape. The resultant morphology was then flooded to a given elevation, leaving a fractal rocky coastline. In addition to the simulated terrain, actual digital elevation models will also be used to derive the initial conditions. Elevation data from different mountainous geomorphic settings such as the decaying Appalachian Mountains or actively uplifting Sierra Nevada can be effectively flooded to a given sea level, resulting in a fractal and immature coastline that can be input to the numerical model. This approach will offer insight into how rocky coastlines in different geomorphic settings evolve, and provide a useful complement to results using the simulated terrain.

Polarization-phase tomography of biological fluids polycrystalline structure

NASA Astrophysics Data System (ADS)

Dubolazov, A. V.; Vanchuliak, O. Ya.; Garazdiuk, M.; Sidor, M. I.; Motrich, A. V.; Kostiuk, S. V.

2013-12-01

Our research is aimed at designing an experimental method of Fourier's laser polarization phasometry of the layers of human effusion for an express diagnostics during surgery and a differentiation of the degree of severity (acute - gangrenous) appendectomy by means of statistical, correlation and fractal analysis of the coherent scattered field. A model of generalized optical anisotropy of polycrystal networks of albumin and globulin of the effusion of appendicitis has been suggested and the method of Fourier's phasometry of linear (a phase shift between the orthogonal components of the laser wave amplitude) and circular (the angle of rotation of the polarization plane) birefringence with a spatial-frequency selection of the coordinate distributions for the differentiation of acute and gangrenous conditions have been analytically substantiated. Comparative studies of the efficacy of the methods of direct mapping of phase distributions and Fourier's phasometry of a laser radiation field transformed by the dendritic and spherolitic networks of albumin and globulin of the layers of effusion of appendicitis on the basis of complex statistical, correlation and fractal analysis of the structure of phase maps.

Fractal continuum model for tracer transport in a porous medium.

PubMed

Herrera-Hernández, E C; Coronado, M; Hernández-Coronado, H

2013-12-01

A model based on the fractal continuum approach is proposed to describe tracer transport in fractal porous media. The original approach has been extended to treat tracer transport and to include systems with radial and uniform flow, which are cases of interest in geoscience. The models involve advection due to the fluid motion in the fractal continuum and dispersion whose mathematical expression is taken from percolation theory. The resulting advective-dispersive equations are numerically solved for continuous and for pulse tracer injection. The tracer profile and the tracer breakthrough curve are evaluated and analyzed in terms of the fractal parameters. It has been found in this work that anomalous transport frequently appears, and a condition on the fractal parameter values to predict when sub- or superdiffusion might be expected has been obtained. The fingerprints of fractality on the tracer breakthrough curve in the explored parameter window consist of an early tracer breakthrough and long tail curves for the spherical and uniform flow cases, and symmetric short tailed curves for the radial flow case.

Application of Fractal theory for crash rate prediction: Insights from random parameters and latent class tobit models.

PubMed

Chand, Sai; Dixit, Vinayak V

2018-03-01

The repercussions from congestion and accidents on major highways can have significant negative impacts on the economy and environment. It is a primary objective of transport authorities to minimize the likelihood of these phenomena taking place, to improve safety and overall network performance. In this study, we use the Hurst Exponent metric from Fractal Theory, as a congestion indicator for crash-rate modeling. We analyze one month of traffic speed data at several monitor sites along the M4 motorway in Sydney, Australia and assess congestion patterns with the Hurst Exponent of speed (H speed ). Random Parameters and Latent Class Tobit models were estimated, to examine the effect of congestion on historical crash rates, while accounting for unobserved heterogeneity. Using a latent class modeling approach, the motorway sections were probabilistically classified into two segments, based on the presence of entry and exit ramps. This will allow transportation agencies to implement appropriate safety/traffic countermeasures when addressing accident hotspots or inadequately managed sections of motorway. Copyright © 2017 Elsevier Ltd. All rights reserved.

Vector calculus in non-integer dimensional space and its applications to fractal media

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2015-02-01

We suggest a generalization of vector calculus for the case of non-integer dimensional space. The first and second orders operations such as gradient, divergence, the scalar and vector Laplace operators for non-integer dimensional space are defined. For simplification we consider scalar and vector fields that are independent of angles. We formulate a generalization of vector calculus for rotationally covariant scalar and vector functions. This generalization allows us to describe fractal media and materials in the framework of continuum models with non-integer dimensional space. As examples of application of the suggested calculus, we consider elasticity of fractal materials (fractal hollow ball and fractal cylindrical pipe with pressure inside and outside), steady distribution of heat in fractal media, electric field of fractal charged cylinder. We solve the correspondent equations for non-integer dimensional space models.

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.

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.

Edible oil structures at low and intermediate concentrations. I. Modeling, computer simulation, and predictions for X ray scattering

NASA Astrophysics Data System (ADS)

Pink, David A.; Quinn, Bonnie; Peyronel, Fernanda; Marangoni, Alejandro G.

2013-12-01

Triacylglycerols (TAGs) are biologically important molecules which form the recently discovered highly anisotropic crystalline nanoplatelets (CNPs) and, ultimately, the large-scale fat crystal networks in edible oils. Identifying the hierarchies of these networks and how they spontaneously self-assemble is important to understanding their functionality and oil binding capacity. We have modelled CNPs and studied how they aggregate under the assumption that all CNPs are present before aggregation begins and that their solubility in the liquid oil is very low. We represented CNPs as rigid planar arrays of spheres with diameter ≈50 nm and defined the interaction between spheres in terms of a Hamaker coefficient, A, and a binding energy, VB. We studied three cases: weak binding, |VB|/kBT ≪ 1, physically realistic binding, VB = Vd(R, Δ), so that |VB|/kBT ≈ 1, and Strong binding with |VB|/kBT ≫ 1. We divided the concentration of CNPs, ϕ, with 0≤ϕ= 10-2 (solid fat content) ≤1, into two regions: Low and intermediate concentrations with 0<ϕ<0.25 and high concentrations with 0.25 < ϕ and considered only the first case. We employed Monte Carlo computer simulation to model CNP aggregation and analyzed them using static structure functions, S(q). We found that strong binding cases formed aggregates with fractal dimension, D, 1.7≤D ≤1.8, in accord with diffusion limited cluster-cluster aggregation (DLCA) and weak binding formed aggregates with D =3, indicating a random distribution of CNPs. We found that models with physically realistic intermediate binding energies formed linear multilayer stacks of CNPs (TAGwoods) with fractal dimension D =1 for ϕ =0.06,0.13, and 0.22. TAGwood lengths were greater at lower ϕ than at higher ϕ, where some of the aggregates appeared as thick CNPs. We increased the spatial scale and modelled the TAGwoods as rigid linear arrays of spheres of diameter ≈500 nm, interacting via the attractive van der Waals interaction. We found that TAGwoods aggregated via DLCA into clusters with fractal dimension D =1.7-1.8. As the simulations were run further, TAGwoods relaxed their positions in order to maximize the attractive interaction making the process look like reaction limited cluster-cluster aggregation with the fractal dimension increasing to D =2.0-2.1. For higher concentrations of CNPs, many TAGwood clusters were formed and, because of their weak interactions, were distributed randomly with D =3.0. We summarize the hierarchy of structures and make predictions for X-ray scattering.

The fractal feature and price trend in the gold future market at the Shanghai Futures Exchange (SFE)

NASA Astrophysics Data System (ADS)

Wu, Binghui; Duan, Tingting

2017-05-01

The price of gold future is affected by many factors, which include the fluctuation of gold price and the change of trading environment. Fractal analysis can help investors gain better understandings of the price fluctuation and make reasonable investment decisions in the gold future market. After analyzing gold future price from January 2th, 2014 to April 12th, 2016 at the Shanghai Futures Exchange (SFE) in China, the conclusion is drawn that the gold future market has sustainability in each trading day, with all Hurst indexes greater than 0.5. The changing features of Hurst index indicate the sustainability of gold future market is strengthened first and weakened then. As a complicatedly nonlinear system, the gold future market can be well reflected by Elman neural network, which is capable of memorizing previous prices and particularly suited for forecasting time series in comparison with other types of neural networks. After analyzing the price trend in the gold future market, the results show that the relative error between the actual value of gold future and the predictive value of Elman neural network is smaller. This model that has a better performance in data fitting and predication, can help investors analyze and foresee the price tendency in the gold future market.

Cascade model for fluvial geomorphology

NASA Technical Reports Server (NTRS)

Newman, W. I.; Turcotte, D. L.

1990-01-01

Erosional landscapes are generally scale invariant and fractal. Spectral studies provide quantitative confirmation of this statement. Linear theories of erosion will not generate scale-invariant topography. In order to explain the fractal behavior of landscapes a modified Fourier series has been introduced that is the basis for a renormalization approach. A nonlinear dynamical model has been introduced for the decay of the modified Fourier series coefficients that yield a fractal spectra. It is argued that a physical basis for this approach is that a fractal (or nearly fractal) distribution of storms (floods) continually renews erosional features on all scales.

Electronic shot noise in fractal conductors.

PubMed

Groth, C W; Tworzydło, J; Beenakker, C W J

2008-05-02

By solving a master equation in the Sierpiński lattice and in a planar random-resistor network, we determine the scaling with size L of the shot noise power P due to elastic scattering in a fractal conductor. We find a power-law scaling P proportional, variantL;{d_{f}-2-alpha}, with an exponent depending on the fractal dimension d_{f} and the anomalous diffusion exponent alpha. This is the same scaling as the time-averaged current I[over ], which implies that the Fano factor F=P/2eI[over ] is scale-independent. We obtain a value of F=1/3 for anomalous diffusion that is the same as for normal diffusion, even if there is no smallest length scale below which the normal diffusion equation holds. The fact that F remains fixed at 1/3 as one crosses the percolation threshold in a random-resistor network may explain recent measurements of a doping-independent Fano factor in a graphene flake.

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.

Simultaneous estimation of deterministic and fractal stochastic components in non-stationary time series

NASA Astrophysics Data System (ADS)

García, Constantino A.; Otero, Abraham; Félix, Paulo; Presedo, Jesús; Márquez, David G.

2018-07-01

In the past few decades, it has been recognized that 1 / f fluctuations are ubiquitous in nature. The most widely used mathematical models to capture the long-term memory properties of 1 / f fluctuations have been stochastic fractal models. However, physical systems do not usually consist of just stochastic fractal dynamics, but they often also show some degree of deterministic behavior. The present paper proposes a model based on fractal stochastic and deterministic components that can provide a valuable basis for the study of complex systems with long-term correlations. The fractal stochastic component is assumed to be a fractional Brownian motion process and the deterministic component is assumed to be a band-limited signal. We also provide a method that, under the assumptions of this model, is able to characterize the fractal stochastic component and to provide an estimate of the deterministic components present in a given time series. The method is based on a Bayesian wavelet shrinkage procedure that exploits the self-similar properties of the fractal processes in the wavelet domain. This method has been validated over simulated signals and over real signals with economical and biological origin. Real examples illustrate how our model may be useful for exploring the deterministic-stochastic duality of complex systems, and uncovering interesting patterns present in time series.

Evolution of fractality in space plasmas of interest to geomagnetic activity

NASA Astrophysics Data System (ADS)

Muñoz, Víctor; Domínguez, Macarena; Alejandro Valdivia, Juan; Good, Simon; Nigro, Giuseppina; Carbone, Vincenzo

2018-03-01

We studied the temporal evolution of fractality for geomagnetic activity, by calculating fractal dimensions from the Dst data and from a magnetohydrodynamic shell model for turbulent magnetized plasma, which may be a useful model to study geomagnetic activity under solar wind forcing. We show that the shell model is able to reproduce the relationship between the fractal dimension and the occurrence of dissipative events, but only in a certain region of viscosity and resistivity values. We also present preliminary results of the application of these ideas to the study of the magnetic field time series in the solar wind during magnetic clouds, which suggest that it is possible, by means of the fractal dimension, to characterize the complexity of the magnetic cloud structure.

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.

Optimization of hierarchical structure and nanoscale-enabled plasmonic refraction for window electrodes in photovoltaics

PubMed Central

Han, Bing; Peng, Qiang; Li, Ruopeng; Rong, Qikun; Ding, Yang; Akinoglu, Eser Metin; Wu, Xueyuan; Wang, Xin; Lu, Xubing; Wang, Qianming; Zhou, Guofu; Liu, Jun-Ming; Ren, Zhifeng; Giersig, Michael; Herczynski, Andrzej; Kempa, Krzysztof; Gao, Jinwei

2016-01-01

An ideal network window electrode for photovoltaic applications should provide an optimal surface coverage, a uniform current density into and/or from a substrate, and a minimum of the overall resistance for a given shading ratio. Here we show that metallic networks with quasi-fractal structure provides a near-perfect practical realization of such an ideal electrode. We find that a leaf venation network, which possesses key characteristics of the optimal structure, indeed outperforms other networks. We further show that elements of hierarchal topology, rather than details of the branching geometry, are of primary importance in optimizing the networks, and demonstrate this experimentally on five model artificial hierarchical networks of varied levels of complexity. In addition to these structural effects, networks containing nanowires are shown to acquire transparency exceeding the geometric constraint due to the plasmonic refraction. PMID:27667099

Fluvial drainage networks: the fractal approach as an improvement of quantitative geomorphic analyses

NASA Astrophysics Data System (ADS)

Melelli, Laura; Liucci, Luisa; Vergari, Francesca; Ciccacci, Sirio; Del Monte, Maurizio

2014-05-01

Drainage basins are primary landscape units for geomorphological investigations. Both hillslopes and river drainage system are fundamental components in drainage basins analysis. As other geomorphological systems, also the drainage basins aim to an equilibrium condition where the sequence of erosion, transport and sedimentation approach to a condition of minimum energy effort. This state is revealed by a typical geometry of landforms and of drainage net. Several morphometric indexes can measure how much a drainage basin is far from the theoretical equilibrium configuration, revealing possible external disarray. In active tectonic areas, the drainage basins have a primary importance in order to highlight style, amount and rate of tectonic impulses, and morphometric indexes allow to estimate the tectonic activity classes of different sectors in a study area. Moreover, drainage rivers are characterized by a self-similarity structure; this promotes the use of fractals theory to investigate the system. In this study, fractals techniques are employed together with quantitative geomorphological analysis to study the Upper Tiber Valley (UTV), a tectonic intermontane basin located in northern Apennines (Umbria, central Italy). The area is the result of different tectonic phases. From Late Pliocene until present time the UTV is strongly controlled by a regional uplift and by an extensional phase with different sets of normal faults playing a fundamental role in basin morphology. Thirty-four basins are taken into account for the quantitative analysis, twenty on the left side of the basin, the others on the right side. Using fractals dimension of drainage networks, Horton's laws results, concavity and steepness indexes, and hypsometric curves, this study aims to obtain an evolutionary model of the UTV, where the uplift is compared to local subsidence induced by normal fault activity. The results highlight a well defined difference between western and eastern tributary basins, suggesting a greater disequilibrium in the last ones. The quantitative analysis points out the segments of the basin boundaries where the fault activity is more efficient and the resulting geomorphological implications.

Not just fractal surfaces, but surface fractal aggregates: Derivation of the expression for the structure factor and its applications

NASA Astrophysics Data System (ADS)

Besselink, R.; Stawski, T. M.; Van Driessche, A. E. S.; Benning, L. G.

2016-12-01

Densely packed surface fractal aggregates form in systems with high local volume fractions of particles with very short diffusion lengths, which effectively means that particles have little space to move. However, there are no prior mathematical models, which would describe scattering from such surface fractal aggregates and which would allow the subdivision between inter- and intraparticle interferences of such aggregates. Here, we show that by including a form factor function of the primary particles building the aggregate, a finite size of the surface fractal interfacial sub-surfaces can be derived from a structure factor term. This formalism allows us to define both a finite specific surface area for fractal aggregates and the fraction of particle interfacial sub-surfaces at the perimeter of an aggregate. The derived surface fractal model is validated by comparing it with an ab initio approach that involves the generation of a "brick-in-a-wall" von Koch type contour fractals. Moreover, we show that this approach explains observed scattering intensities from in situ experiments that followed gypsum (CaSO4 ṡ 2H2O) precipitation from highly supersaturated solutions. Our model of densely packed "brick-in-a-wall" surface fractal aggregates may well be the key precursor step in the formation of several types of mosaic- and meso-crystals.

Fractal and Fourier analysis of the hepatic sinusoidal network in normal and cirrhotic rat liver

PubMed Central

Gaudio, Eugenio; Chaberek, Slawomir; Montella, Andrea; Pannarale, Luigi; Morini, Sergio; Novelli, Gilnardo; Borghese, Federica; Conte, Davide; Ostrowski, Kazimierz

2005-01-01

The organization of the hepatic microvascular network has been widely studied in recent years, especially with regard to cirrhosis. This research has enabled us to recognize the distinctive vascular patterns in the cirrhotic liver, compared with the normal liver, which may explain the cause of liver dysfunction and failure. The aim of this study was to compare normal and cirrhotic rat livers by means of a quantitative mathematical approach based on fractal and Fourier analyses performed on photomicrographs and therefore on discriminant analysis. Vascular corrosion casts of livers belonging to the following three experimental groups were studied by scanning electron microscopy: normal rats, CCl4-induced cirrhotic rats and cirrhotic rats after ligation of the bile duct. Photomicrographs were taken at a standard magnification; these images were used for the mathematical analysis. Our experimental design found that use of these different analyses reaches an efficiency of over 94%. Our analyses demonstrated a higher complexity of the normal hepatic sinusoidal network in comparison with the cirrhotic network. In particular, the morphological changes were more marked in the animals with bile duct-ligation cirrhosis compared with animals with CCl4-induced cirrhosis. The present findings based on fractal and Fourier analysis could increase our understanding of the pathophysiological alterations of the liver, and may have a diagnostic value in future clinical research. PMID:16050897

Fractal Risk Assessment of ISS Propulsion Module in Meteoroid and Orbital Debris Environments

NASA Technical Reports Server (NTRS)

Mog, Robert A.

2001-01-01

A unique and innovative risk assessment of the International Space Station (ISS) Propulsion Module is conducted using fractal modeling of the Module's response to the meteoroid and orbital debris environments. Both the environment models and structural failure modes due to the resultant hypervelocity impact phenomenology, as well as Module geometry, are investigated for fractal applicability. The fractal risk assessment methodology could produce a greatly simplified alternative to current methodologies, such as BUMPER analyses, while maintaining or increasing the number of complex scenarios that can be assessed. As a minimum, this innovative fractal approach will provide an independent assessment of existing methodologies in a unique way.

Allometric scaling in-vitro

NASA Astrophysics Data System (ADS)

Ahluwalia, Arti

2017-02-01

About two decades ago, West and coworkers established a model which predicts that metabolic rate follows a three quarter power relationship with the mass of an organism, based on the premise that tissues are supplied nutrients through a fractal distribution network. Quarter power scaling is widely considered a universal law of biology and it is generally accepted that were in-vitro cultures to obey allometric metabolic scaling, they would have more predictive potential and could, for instance, provide a viable substitute for animals in research. This paper outlines a theoretical and computational framework for establishing quarter power scaling in three-dimensional spherical constructs in-vitro, starting where fractal distribution ends. Allometric scaling in non-vascular spherical tissue constructs was assessed using models of Michaelis Menten oxygen consumption and diffusion. The models demonstrate that physiological scaling is maintained when about 5 to 60% of the construct is exposed to oxygen concentrations less than the Michaelis Menten constant, with a significant concentration gradient in the sphere. The results have important implications for the design of downscaled in-vitro systems with physiological relevance.

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.

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.

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.

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.

Fractal Inequality: A Social Network Analysis of Global and Regional International Student Mobility

ERIC Educational Resources Information Center

Macrander, Ashley

2017-01-01

Literature on global international student mobility (ISM) highlights the uneven nature of student flows--from the developing to the developed world--however, studies have yet to address whether this pattern is replicated within expanding regional networks. Utilizing social network analysis, UNESCO ISM data, and World Bank income classifications,…

A New Fractal Model of Chromosome and DNA Processes

NASA Astrophysics Data System (ADS)

Bouallegue, K.

Dynamic chromosome structure remains unknown. Can fractals and chaos be used as new tools to model, identify and generate a structure of chromosomes?Fractals and chaos offer a rich environment for exploring and modeling the complexity of nature. In a sense, fractal geometry is used to describe, model, and analyze the complex forms found in nature. Fractals have also been widely not only in biology but also in medicine. To this effect, a fractal is considered an object that displays self-similarity under magnification and can be constructed using a simple motif (an image repeated on ever-reduced scales).It is worth noting that the problem of identifying a chromosome has become a challenge to find out which one of the models it belongs to. Nevertheless, the several different models (a hierarchical coiling, a folded fiber, and radial loop) have been proposed for mitotic chromosome but have not reached a dynamic model yet.This paper is an attempt to solve topological problems involved in the model of chromosome and DNA processes. By combining the fractal Julia process and the numerical dynamical system, we have finally found out four main points. First, we have developed not only a model of chromosome but also a model of mitosis and one of meiosis. Equally important, we have identified the centromere position through the numerical model captured below. More importantly, in this paper, we have discovered the processes of the cell divisions of both mitosis and meiosis. All in all, the results show that this work could have a strong impact on the welfare of humanity and can lead to a cure of genetic diseases.

Anisotropic fractal media by vector calculus in non-integer dimensional space

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2014-08-01

A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.

Topological characterization of antireflective and hydrophobic rough surfaces: are random process theory and fractal modeling applicable?

NASA Astrophysics Data System (ADS)

Borri, Claudia; Paggi, Marco

2015-02-01

The random process theory (RPT) has been widely applied to predict the joint probability distribution functions (PDFs) of asperity heights and curvatures of rough surfaces. A check of the predictions of RPT against the actual statistics of numerically generated random fractal surfaces and of real rough surfaces has been only partially undertaken. The present experimental and numerical study provides a deep critical comparison on this matter, providing some insight into the capabilities and limitations in applying RPT and fractal modeling to antireflective and hydrophobic rough surfaces, two important types of textured surfaces. A multi-resolution experimental campaign using a confocal profilometer with different lenses is carried out and a comprehensive software for the statistical description of rough surfaces is developed. It is found that the topology of the analyzed textured surfaces cannot be fully described according to RPT and fractal modeling. The following complexities emerge: (i) the presence of cut-offs or bi-fractality in the power-law power-spectral density (PSD) functions; (ii) a more pronounced shift of the PSD by changing resolution as compared to what was expected from fractal modeling; (iii) inaccuracy of the RPT in describing the joint PDFs of asperity heights and curvatures of textured surfaces; (iv) lack of resolution-invariance of joint PDFs of textured surfaces in case of special surface treatments, not accounted for by fractal modeling.

Multifractal analysis and topological properties of a new family of weighted Koch networks

NASA Astrophysics Data System (ADS)

Huang, Da-Wen; Yu, Zu-Guo; Anh, Vo

2017-03-01

Weighted complex networks, especially scale-free networks, which characterize real-life systems better than non-weighted networks, have attracted considerable interest in recent years. Studies on the multifractality of weighted complex networks are still to be undertaken. In this paper, inspired by the concepts of Koch networks and Koch island, we propose a new family of weighted Koch networks, and investigate their multifractal behavior and topological properties. We find some key topological properties of the new networks: their vertex cumulative strength has a power-law distribution; there is a power-law relationship between their topological degree and weight strength; the networks have a high weighted clustering coefficient of 0.41004 (which is independent of the scaling factor c) in the limit of large generation t; the second smallest eigenvalue μ2 and the maximum eigenvalue μn are approximated by quartic polynomials of the scaling factor c for the general Laplacian operator, while μ2 is approximately a quartic polynomial of c and μn= 1.5 for the normalized Laplacian operator. Then, we find that weighted koch networks are both fractal and multifractal, their fractal dimension is influenced by the scaling factor c. We also apply these analyses to six real-world networks, and find that the multifractality in three of them are strong.

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.

Electrical conductivity modeling in fractal non-saturated porous media

NASA Astrophysics Data System (ADS)

Wei, W.; Cai, J.; Hu, X.; Han, Q.

2016-12-01

The variety of electrical conductivity in non-saturated conditions is important to study electric conduction in natural sedimentary rocks. The electrical conductivity in completely saturated porous media is a porosity-function representing the complex connected behavior of single conducting phases (pore fluid). For partially saturated conditions, the electrical conductivity becomes even more complicated since the connectedness of pore. Archie's second law is an empirical electrical conductivity-porosity and -saturation model that has been used to predict the formation factor of non-saturated porous rock. However, the physical interpretation of its parameters, e.g., the cementation exponent m and the saturation exponent n, remains questionable. On basis of our previous work, we combine the pore-solid fractal (PSF) model to build an electrical conductivity model in non-saturated porous media. Our theoretical porosity- and saturation-dependent models contain endmember properties, such as fluid electrical conductivities, pore fractal dimension and tortuosity fractal dimension (representing the complex degree of electrical flowing path). We find the presented model with non-saturation-dependent electrical conductivity datasets indicate excellent match between theory and experiments. This means the value of pore fractal dimension and tortuosity fractal dimension change from medium to medium and depends not only on geometrical properties of pore structure but also characteristics of electrical current flowing in the non-saturated porous media.

From Fractal Trees to Deltaic Networks

NASA Astrophysics Data System (ADS)

Cazanacli, D.; Wolinsky, M. A.; Sylvester, Z.; Cantelli, A.; Paola, C.

2013-12-01

Geometric networks that capture many aspects of natural deltas can be constructed from simple concepts from graph theory and normal probability distributions. Fractal trees with symmetrical geometries are the result of replicating two simple geometric elements, line segments whose lengths decrease and bifurcation angles that are commonly held constant. Branches could also have a thickness, which in the case of natural distributary systems is the equivalent of channel width. In river- or wave-dominated natural deltas, the channel width is a function of discharge. When normal variations around the mean values for length, bifurcating angles, and discharge are applied, along with either pruning of 'clashing' branches or merging (equivalent to channel confluence), fractal trees start resembling natural deltaic networks, except that the resulting channels are unnaturally straight. Introducing a bifurcation probability fewer, naturally curved channels are obtained. If there is no bifurcation, the direction of each new segment depends on the direction the previous segment upstream (correlated random walk) and, to a lesser extent, on a general direction of growth (directional bias). When bifurcation occurs, the resulting two directions also depend on the bifurcation angle and the discharge split proportions, with the dominant branch following the direction of the upstream parent channel closely. The bifurcation probability controls the channel density and, in conjunction with the variability of the directional angles, the overall curvature of the channels. The growth of the network in effect is associated with net delta progradation. The overall shape and shape evolution of the delta depend mainly on the bifurcation angle average size and angle variability coupled with the degree of dominant direction dependency (bias). The proposed algorithm demonstrates how, based on only a few simple rules, a wide variety of channel networks resembling natural deltas, can be replicated. Network Example

A fractal model for nuclear organization: current evidence and biological implications

PubMed Central

Bancaud, Aurélien; Lavelle, Christophe; Huet, Sébastien; Ellenberg, Jan

2012-01-01

Chromatin is a multiscale structure on which transcription, replication, recombination and repair of the genome occur. To fully understand any of these processes at the molecular level under physiological conditions, a clear picture of the polymorphic and dynamic organization of chromatin in the eukaryotic nucleus is required. Recent studies indicate that a fractal model of chromatin architecture is consistent with both the reaction-diffusion properties of chromatin interacting proteins and with structural data on chromatin interminglement. In this study, we provide a critical overview of the experimental evidence that support a fractal organization of chromatin. On this basis, we discuss the functional implications of a fractal chromatin model for biological processes and propose future experiments to probe chromatin organization further that should allow to strongly support or invalidate the fractal hypothesis. PMID:22790985

Average receiving scaling of the weighted polygon Koch networks with the weight-dependent walk

NASA Astrophysics Data System (ADS)

Ye, Dandan; Dai, Meifeng; Sun, Yanqiu; Shao, Shuxiang; Xie, Qi

2016-09-01

Based on the weighted Koch networks and the self-similarity of fractals, we present a family of weighted polygon Koch networks with a weight factor r(0 < r ≤ 1) . We study the average receiving time (ART) on weight-dependent walk (i.e., the walker moves to any of its neighbors with probability proportional to the weight of edge linking them), whose key step is to calculate the sum of mean first-passage times (MFPTs) for all nodes absorpt at a hub node. We use a recursive division method to divide the weighted polygon Koch networks in order to calculate the ART scaling more conveniently. We show that the ART scaling exhibits a sublinear or linear dependence on network order. Thus, the weighted polygon Koch networks are more efficient than expended Koch networks in receiving information. Finally, compared with other previous studies' results (i.e., Koch networks, weighted Koch networks), we find out that our models are more general.

Fractal modeling of fluidic leakage through metal sealing surfaces

NASA Astrophysics Data System (ADS)

Zhang, Qiang; Chen, Xiaoqian; Huang, Yiyong; Chen, Yong

2018-04-01

This paper investigates the fluidic leak rate through metal sealing surfaces by developing fractal models for the contact process and leakage process. An improved model is established to describe the seal-contact interface of two metal rough surface. The contact model divides the deformed regions by classifying the asperities of different characteristic lengths into the elastic, elastic-plastic and plastic regimes. Using the improved contact model, the leakage channel under the contact surface is mathematically modeled based on the fractal theory. The leakage model obtains the leak rate using the fluid transport theory in porous media, considering that the pores-forming percolation channels can be treated as a combination of filled tortuous capillaries. The effects of fractal structure, surface material and gasket size on the contact process and leakage process are analyzed through numerical simulations for sealed ring gaskets.

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

The fractal nature of vacuum arc cathode spots

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

Anders, Andre

2005-05-27

Cathode spot phenomena show many features of fractals, for example self-similar patterns in the emitted light and arc erosion traces. Although there have been hints on the fractal nature of cathode spots in the literature, the fractal approach to spot interpretation is underutilized. In this work, a brief review of spot properties is given, touching the differences between spot type 1 (on cathodes surfaces with dielectric layers) and spot type 2 (on metallic, clean surfaces) as well as the known spot fragment or cell structure. The basic properties of self-similarity, power laws, random colored noise, and fractals are introduced. Severalmore » points of evidence for the fractal nature of spots are provided. Specifically power laws are identified as signature of fractal properties, such as spectral power of noisy arc parameters (ion current, arc voltage, etc) obtained by fast Fourier transform. It is shown that fractal properties can be observed down to the cutoff by measurement resolution or occurrence of elementary steps in physical processes. Random walk models of cathode spot motion are well established: they go asymptotically to Brownian motion for infinitesimal step width. The power spectrum of the arc voltage noise falls as 1/f {sup 2}, where f is frequency, supporting a fractal spot model associated with Brownian motion.« less

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.

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.

Resolving Structural Variability in Network Models and the Brain

PubMed Central

Klimm, Florian; Bassett, Danielle S.; Carlson, Jean M.; Mucha, Peter J.

2014-01-01

Large-scale white matter pathways crisscrossing the cortex create a complex pattern of connectivity that underlies human cognitive function. Generative mechanisms for this architecture have been difficult to identify in part because little is known in general about mechanistic drivers of structured networks. Here we contrast network properties derived from diffusion spectrum imaging data of the human brain with 13 synthetic network models chosen to probe the roles of physical network embedding and temporal network growth. We characterize both the empirical and synthetic networks using familiar graph metrics, but presented here in a more complete statistical form, as scatter plots and distributions, to reveal the full range of variability of each measure across scales in the network. We focus specifically on the degree distribution, degree assortativity, hierarchy, topological Rentian scaling, and topological fractal scaling—in addition to several summary statistics, including the mean clustering coefficient, the shortest path-length, and the network diameter. The models are investigated in a progressive, branching sequence, aimed at capturing different elements thought to be important in the brain, and range from simple random and regular networks, to models that incorporate specific growth rules and constraints. We find that synthetic models that constrain the network nodes to be physically embedded in anatomical brain regions tend to produce distributions that are most similar to the corresponding measurements for the brain. We also find that network models hardcoded to display one network property (e.g., assortativity) do not in general simultaneously display a second (e.g., hierarchy). This relative independence of network properties suggests that multiple neurobiological mechanisms might be at play in the development of human brain network architecture. Together, the network models that we develop and employ provide a potentially useful starting point for the statistical inference of brain network structure from neuroimaging data. PMID:24675546

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

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.

Impact of network topology on self-organized criticality

NASA Astrophysics Data System (ADS)

Hoffmann, Heiko

2018-02-01

The general mechanisms behind self-organized criticality (SOC) are still unknown. Several microscopic and mean-field theory approaches have been suggested, but they do not explain the dependence of the exponents on the underlying network topology of the SOC system. Here, we first report the phenomena that in the Bak-Tang-Wiesenfeld (BTW) model, sites inside an avalanche area largely return to their original state after the passing of an avalanche, forming, effectively, critically arranged clusters of sites. Then, we hypothesize that SOC relies on the formation process of these clusters, and present a model of such formation. For low-dimensional networks, we show theoretically and in simulation that the exponent of the cluster-size distribution is proportional to the ratio of the fractal dimension of the cluster boundary and the dimensionality of the network. For the BTW model, in our simulations, the exponent of the avalanche-area distribution matched approximately our prediction based on this ratio for two-dimensional networks, but deviated for higher dimensions. We hypothesize a transition from cluster formation to the mean-field theory process with increasing dimensionality. This work sheds light onto the mechanisms behind SOC, particularly, the impact of the network topology.

Complex networks as an emerging property of hierarchical preferential attachment.

PubMed

Hébert-Dufresne, Laurent; Laurence, Edward; Allard, Antoine; Young, Jean-Gabriel; Dubé, Louis J

2015-12-01

Real complex systems are not rigidly structured; no clear rules or blueprints exist for their construction. Yet, amidst their apparent randomness, complex structural properties universally emerge. We propose that an important class of complex systems can be modeled as an organization of many embedded levels (potentially infinite in number), all of them following the same universal growth principle known as preferential attachment. We give examples of such hierarchy in real systems, for instance, in the pyramid of production entities of the film industry. More importantly, we show how real complex networks can be interpreted as a projection of our model, from which their scale independence, their clustering, their hierarchy, their fractality, and their navigability naturally emerge. Our results suggest that complex networks, viewed as growing systems, can be quite simple, and that the apparent complexity of their structure is largely a reflection of their unobserved hierarchical nature.

Complex networks as an emerging property of hierarchical preferential attachment

NASA Astrophysics Data System (ADS)

Hébert-Dufresne, Laurent; Laurence, Edward; Allard, Antoine; Young, Jean-Gabriel; Dubé, Louis J.

2015-12-01

Real complex systems are not rigidly structured; no clear rules or blueprints exist for their construction. Yet, amidst their apparent randomness, complex structural properties universally emerge. We propose that an important class of complex systems can be modeled as an organization of many embedded levels (potentially infinite in number), all of them following the same universal growth principle known as preferential attachment. We give examples of such hierarchy in real systems, for instance, in the pyramid of production entities of the film industry. More importantly, we show how real complex networks can be interpreted as a projection of our model, from which their scale independence, their clustering, their hierarchy, their fractality, and their navigability naturally emerge. Our results suggest that complex networks, viewed as growing systems, can be quite simple, and that the apparent complexity of their structure is largely a reflection of their unobserved hierarchical nature.

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.

Anisotropic fractal media by vector calculus in non-integer dimensional space

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

Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru

2014-08-15

A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensionalmore » space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.« 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).

Fractal markets: Liquidity and investors on different time horizons

NASA Astrophysics Data System (ADS)

Li, Da-Ye; Nishimura, Yusaku; Men, Ming

2014-08-01

In this paper, we propose a new agent-based model to study the source of liquidity and the “emergent” phenomenon in financial market with fractal structure. The model rests on fractal market hypothesis and agents with different time horizons of investments. What is interesting is that though the agent-based model reveals that the interaction between these heterogeneous agents affects the stability and liquidity of the financial market the real world market lacks detailed data to bring it to light since it is difficult to identify and distinguish the investors with different time horizons in the empirical approach. results show that in a relatively short period of time fractal market provides liquidity from investors with different horizons and the market gains stability when the market structure changes from uniformity to diversification. In the real world the fractal structure with the finite of horizons can only stabilize the market within limits. With the finite maximum horizons, the greater diversity of the investors and the fractal structure will not necessarily bring more stability to the market which might come with greater fluctuation in large time scale.

A user-friendly modified pore-solid fractal model

PubMed Central

Ding, Dian-yuan; Zhao, Ying; Feng, Hao; Si, Bing-cheng; Hill, Robert Lee

2016-01-01

The primary objective of this study was to evaluate a range of calculation points on water retention curves (WRC) instead of the singularity point at air-entry suction in the pore-solid fractal (PSF) model, which additionally considered the hysteresis effect based on the PSF theory. The modified pore-solid fractal (M-PSF) model was tested using 26 soil samples from Yangling on the Loess Plateau in China and 54 soil samples from the Unsaturated Soil Hydraulic Database. The derivation results showed that the M-PSF model is user-friendly and flexible for a wide range of calculation point options. This model theoretically describes the primary differences between the soil moisture desorption and the adsorption processes by the fractal dimensions. The M-PSF model demonstrated good performance particularly at the calculation points corresponding to the suctions from 100 cm to 1000 cm. Furthermore, the M-PSF model, used the fractal dimension of the particle size distribution, exhibited an accepted performance of WRC predictions for different textured soils when the suction values were ≥100 cm. To fully understand the function of hysteresis in the PSF theory, the role of allowable and accessible pores must be examined. PMID:27996013

Efficient RF energy harvesting by using a fractal structured rectenna system

NASA Astrophysics Data System (ADS)

Oh, Sechang; Ramasamy, Mouli; Varadan, Vijay K.

2014-04-01

A rectenna system delivers, collects, and converts RF energy into direct current to power the electronic devices or recharge batteries. It consists of an antenna for receiving RF power, an input filter for processing energy and impedance matching, a rectifier, an output filter, and a load resistor. However, the conventional rectenna systems have drawback in terms of power generation, as the single resonant frequency of an antenna can generate only low power compared to multiple resonant frequencies. A multi band rectenna system is an optimal solution to generate more power. This paper proposes the design of a novel rectenna system, which involves developing a multi band rectenna with a fractal structured antenna to facilitate an increase in energy harvesting from various sources like Wi-Fi, TV signals, mobile networks and other ambient sources, eliminating the limitation of a single band technique. The usage of fractal antennas effects certain prominent advantages in terms of size and multiple resonances. Even though, a fractal antenna incorporates multiple resonances, controlling the resonant frequencies is an important aspect to generate power from the various desired RF sources. Hence, this paper also describes the design parameters of the fractal antenna and the methods to control the multi band frequency.

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.

Effects of the soil pore network architecture on the soil's physical functionalities

NASA Astrophysics Data System (ADS)

Smet, Sarah; Beckers, Eléonore; Léonard, Angélique; Degré, Aurore

2017-04-01

The soil fluid movement's prediction is of major interest within an agricultural or environmental scope because many processes depend ultimately on the soil fluids dynamic. It is common knowledge that the soil microscopic pore network structure governs the inner-soil convective fluids flow. There isn't, however, a general methodthat consider the pore network structure as a variable in the prediction of thecore scale soil's physical functionalities. There are various possible representations of the microscopic pore network: sample scale averaged structural parameters, extrapolation of theoretic pore network, or use of all the information available by modeling within the observed pore network. Different representations implydifferent analyzing methodologies. To our knowledge, few studies have compared the micro-and macroscopic soil's characteristics for the same soil core sample. The objective of our study is to explore the relationship between macroscopic physical properties and microscopic pore network structure. The saturated hydraulic conductivity, the air permeability, the retention curve, and others classical physical parameters were measured for ten soil samples from an agricultural field. The pore network characteristics were quantified through the analyses of X-ray micro-computed tomographic images(micro-CT system Skyscan-1172) with a voxel size of 22 µm3. Some of the first results confirmed what others studies had reported. Then, the comparison between macroscopic properties and microscopic parameters suggested that the air movements depended mostly on the pore connectivity and tortuosity than on the total porosity volume. We have also found that the fractal dimension calculated from the X-ray images and the fractal dimension calculated from the retention curve were significantly different. Our communication will detailthose results and discuss the methodology: would the results be similar with a different voxel size? What are the calculated and measured parameters uncertainties? Sarah Smet, as a research fellow, acknowledges the support of the National Fund for Scientific Research (Brussels, Belgium).

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.

Simulation of extreme ground water flow in the fractal crack structure of Earth's crust - impact on catastrophic floods

NASA Astrophysics Data System (ADS)

Bukharov, Dmitriy; Aleksey, Kucherik; Tatyana, Trifonova

2014-05-01

Recently, the contribution of groundwater in catastrophic floods is the question under discussion [1,2]. The principal problem in such an approach - to analyze the transportation ways for groundwater in dynamics, and especially - the reasons of exit it on land surface. The crackness, being a characteristic property for all rocks, should be associated with the process in respect of unified dynamic system as a river water basin is, taking into account fundamental phenomena of the 3D-crack network development/modification (up to faults) as a transport groundwater system [3]. 2. In the system of fractal cracks (connected with the main channel for groundwater) the formation of extreme flow is possible, i.e. a devastating case occurs by instantaneous flash mechanism. The development of such a process is related to two factors. First, within the main channel of propagation of the groundwater when a motion is turbulent. In accordance with the theory of Kolmogorov [4], we assume that such a turbulence is isotropic. The fact means that both velocity and pressure fields in the water flow have pulsations related to the non-linear energy transfer between the vortices. This approach allows us to determine both that a maximum possible size of the vortices defined by characteristic dimensions of the underground channel and another - a minimum size of their due to process of dissipation. Energy transfer in the eddies formed near a border, is a complex nonlinear process, which we described by using a modernized Prandtl semi-empirical model [5]. Second, the mechanism of groundwater propagation in the system of cracks extending from the main underground channel is described in the frames of the fractal geometry methods [6]. The approach allows to determine the degree of similarity in the crack system, i.e. the ratio of mean diameters and lengths of cracks/faults for each step of decomposition. The fact results in integrated quantitative characteristics of 3D-network in all, by fractal dimension. Formation of fractal cracks (in coupling of fault length and it number) ensures an optimal traveling network for propagation of water, but changes in external conditions can lead to the formation of hydroblow with extreme water flow formation on surface, i.e. a flash event arise. 3. The proposed approach allows to carry out the modeling in different spatial scales, to determine the features of hydrodynamic processes for generate extreme water flow, when it is going out on the land surface, and results in catastrophic water phenomenon development. 1. Trifonova T.A., Arakelian M.M., Arakelian S.M. European Geosciences Union General Assembly 2013, Vienna, Austria, 2013. http://www.egu2013.eu ; 2. Arakelian S.M., Trifonova T.A., Arakelian M.M. IGU Kyoto Regional Conference (KRC), Kyoto, Japan, 2013, www.igu-kyoto2013.org. 3.Trifonova T. A.. // Izv. RAS, series on geography, 2008, No.1, pp.28-36. 4. Kolmogorov A.N. //Bulletin of Soviet Academy of Science, 1941. V. 30, No.4. pp. 299-303. 5.Volynov M.A. // Fundamental research No.10. 2013, pp. 1676-1688. 6. Mandelbrot B.B. // Institute of computer research ISBN 5-93972-108-7 (2002).

Topographic and Roughness Characteristics of the Vastitas Borealis Formation on Mars Described by Fractal Statistics

NASA Technical Reports Server (NTRS)

Garneau, S.; Plaut, J. J.

2000-01-01

The surface roughness of the Vastitas Borealis Formation on Mars was analyzed with fractal statistics. Root mean square slopes and fractal dimensions were calculated for 74 topographic profiles. Results have implications for radar scattering models.

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.

[A method to estimate the short-term fractal dimension of heart rate variability based on wavelet transform].

PubMed

Zhonggang, Liang; Hong, Yan

2006-10-01

A new method of calculating fractal dimension of short-term heart rate variability signals is presented. The method is based on wavelet transform and filter banks. The implementation of the method is: First of all we pick-up the fractal component from HRV signals using wavelet transform. Next, we estimate the power spectrum distribution of fractal component using auto-regressive model, and we estimate parameter 7 using the least square method. Finally according to formula D = 2- (gamma-1)/2 estimate fractal dimension of HRV signal. To validate the stability and reliability of the proposed method, using fractional brown movement simulate 24 fractal signals that fractal value is 1.6 to validate, the result shows that the method has stability and reliability.

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.

Viscoelastic and fractal characteristics of a supramolecular hydrogel hybridized with clay nanoparticles.

PubMed

Song, Fei; Zhang, Li-Ming; Shi, Jun-Feng; Li, Nan-Nan

2010-12-01

The supramolecular hydrogels derived from low-molecular-mass gelators represent a unique class of soft matters and have important potential applications in biomedical fields, separation technology and cosmetic science. However, they suffer usually from weak mechanical and viscoelastic properties. In this work, we carry out the in situ hybridization of clay nanoparticles (Laponite RD) into the supramolecular hydrogel formed from a low-molecular-mass hydrogelator, 2,6-di[N-(carboxyethyl carbonyl)amino]pyridine (DAP), and investigate the viscoelastic and structural characteristics of resultant hybrid hydrogel. It was found that a small concentration of Laponite RD could lead to a significant increase in the storage modulus, loss modulus or complex viscosity. Compared with neat DAP hydrogel, the hybrid hydrogel has a greater hydrogel strength and a lower relaxation exponent. In particular, the enhancement of the clay nanoparticles to the viscoelastic properties of the DAP hydrogel is more effective in the case of higher DAP concentration. By relating its macroscopic elastic properties to a scaling fractal model, such a hybrid hydrogel was confirmed to be in the strong-link regime and to have a more complex network structure with a higher fractal dimension when compared with neat DAP hydrogel. Copyright © 2010 Elsevier B.V. All rights reserved.

Evolving random fractal Cantor superlattices for the infrared using a genetic algorithm

PubMed Central

Bossard, Jeremy A.; Lin, Lan; Werner, Douglas H.

2016-01-01

Ordered and chaotic superlattices have been identified in Nature that give rise to a variety of colours reflected by the skin of various organisms. In particular, organisms such as silvery fish possess superlattices that reflect a broad range of light from the visible to the UV. Such superlattices have previously been identified as ‘chaotic’, but we propose that apparent ‘chaotic’ natural structures, which have been previously modelled as completely random structures, should have an underlying fractal geometry. Fractal geometry, often described as the geometry of Nature, can be used to mimic structures found in Nature, but deterministic fractals produce structures that are too ‘perfect’ to appear natural. Introducing variability into fractals produces structures that appear more natural. We suggest that the ‘chaotic’ (purely random) superlattices identified in Nature are more accurately modelled by multi-generator fractals. Furthermore, we introduce fractal random Cantor bars as a candidate for generating both ordered and ‘chaotic’ superlattices, such as the ones found in silvery fish. A genetic algorithm is used to evolve optimal fractal random Cantor bars with multiple generators targeting several desired optical functions in the mid-infrared and the near-infrared. We present optimized superlattices demonstrating broadband reflection as well as single and multiple pass bands in the near-infrared regime. PMID:26763335

Reverse Engineering of Oxygen Transport in the Lung: Adaptation to Changing Demands and Resources through Space-Filling Networks

PubMed Central

Hou, Chen; Gheorghiu, Stefan; Huxley, Virginia H.; Pfeifer, Peter

2010-01-01

The space-filling fractal network in the human lung creates a remarkable distribution system for gas exchange. Landmark studies have illuminated how the fractal network guarantees minimum energy dissipation, slows air down with minimum hardware, maximizes the gas- exchange surface area, and creates respiratory flexibility between rest and exercise. In this paper, we investigate how the fractal architecture affects oxygen transport and exchange under varying physiological conditions, with respect to performance metrics not previously studied. We present a renormalization treatment of the diffusion-reaction equation which describes how oxygen concentrations drop in the airways as oxygen crosses the alveolar membrane system. The treatment predicts oxygen currents across the lung at different levels of exercise which agree with measured values within a few percent. The results exhibit wide-ranging adaptation to changing process parameters, including maximum oxygen uptake rate at minimum alveolar membrane permeability, the ability to rapidly switch from a low oxygen uptake rate at rest to high rates at exercise, and the ability to maintain a constant oxygen uptake rate in the event of a change in permeability or surface area. We show that alternative, less than space-filling architectures perform sub-optimally and that optimal performance of the space-filling architecture results from a competition between underexploration and overexploration of the surface by oxygen molecules. PMID:20865052

A model study of aggregates composed of spherical soot monomers with an acentric carbon shell

NASA Astrophysics Data System (ADS)

Luo, Jie; Zhang, Yongming; Zhang, Qixing

2018-01-01

Influences of morphology on the optical properties of soot particles have gained increasing attentions. However, studies on the effect of the way primary particles are coated on the optical properties is few. Aimed to understand how the primary particles are coated affect the optical properties of soot particles, the coated soot particle was simulated using the acentric core-shell monomers model (ACM), which was generated by randomly moving the cores of concentric core-shell monomers (CCM) model. Single scattering properties of the CCM model with identical fractal parameters were calculated 50 times at first to evaluate the optical diversities of different realizations of fractal aggregates with identical parameters. The results show that optical diversities of different realizations for fractal aggregates with identical parameters cannot be eliminated by averaging over ten random realizations. To preserve the fractal characteristics, 10 realizations of each model were generated based on the identical 10 parent fractal aggregates, and then the results were averaged over each 10 realizations, respectively. The single scattering properties of all models were calculated using the numerically exact multiple-sphere T-matrix (MSTM) method. It is found that the single scattering properties of randomly coated soot particles calculated using the ACM model are extremely close to those using CCM model and homogeneous aggregate (HA) model using Maxwell-Garnett effective medium theory. Our results are different from previous studies. The reason may be that the differences in previous studies were caused by fractal characteristics but not models. Our findings indicate that how the individual primary particles are coated has little effect on the single scattering properties of soot particles with acentric core-shell monomers. This work provides a suggestion for scattering model simplification and model selection.

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-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.

Determination of Uniaxial Compressive Strength of Ankara Agglomerate Considering Fractal Geometry of Blocks

NASA Astrophysics Data System (ADS)

Coskun, Aycan; Sonmez, Harun; Ercin Kasapoglu, K.; Ozge Dinc, S.; Celal Tunusluoglu, M.

2010-05-01

The uniaxial compressive strength (UCS) of rock material is a crucial parameter to be used for design stages of slopes, tunnels and foundations to be constructed in/on geological medium. However, preparation of high quality cores from geological mixtures or fragmented rocks such as melanges, fault rocks, coarse pyroclastic rocks, breccias and sheared serpentinites is often extremely difficult. According to the studies performed in literature, this type of geological materials may be grouped as welded and unwelded birmocks. Success of preparation of core samples from welded bimrocks is slightly better than unwelded ones. Therefore, some studies performed on the welded bimrocks to understand the mechanical behavior of geological mixture materials composed of stronger and weaker components (Gokceoglu, 2002; Sonmez et al., 2004; Sonmez et al., 2006; Kahraman, et al., 2008). The overall strength of bimrocks are generally depends on strength contrast between blocks and matrix; types and strength of matrix; type, size, strength, shape and orientation of blocks and volumetric block proportion. In previously proposed prediction models, while UCS of unwelded bimrocks may be determined by decreasing the UCS of matrix considering the volumetric block proportion, the welded ones can be predicted by considering both UCS of matrix and blocks together (Lindquist, 1994; Lindquist and Goodman, 1994; Sonmez et al., 2006 and Sonmez et al., 2009). However, there is a few attempts were performed about the effect of blocks shape and orientation on the strength of bimrock (Linqduist, 1994 and Kahraman, et al., 2008). In this study, Ankara agglomerate, which is composed of andesite blocks and surrounded weak tuff matrix, was selected as study material. Image analyses were performed on bottom, top and side faces of cores to identify volumetric block portions. In addition to the image analyses, andesite blocks on bottom, top and side faces were digitized for determination of fractal dimensions. To determine fractal dimensions of more than hundred andesite blocks in cores, a computer program namely FRACRUN were developed. Fractal geometry has been used as practical and popular tool to define particularly irregular shaped bodies in literature since the theory of fractal was developed by Mandelbrot (1967) (Hyslip and Vallejo, 1997; Kruhl and Nega, 1996; Bagde etal., 2002; Gulbin and Evangulova, 2003; Pardini, 2003; Kolay and Kayabali, 2006; Hamdi, 2008; Zorlu, 2009 and Sezer, 2009). Although there are some methods to determine fractal dimensions, square grid-cell count method for 2D and segment count method for 1D were followed in the algorithm of FRACRUN. FRACRUN has capable of determine fractal dimensions of many closed polygons on a single surface. In the study, a database composed of uniaxial compressive strength, volumetric block proportion, fractal dimensions and number of blocks for each core was established. Finally, prediction models were developed by regression analyses and compared with the empirical equations proposed by Sonmez et al. (2006). Acknowledgement This study is a product of ongoing project supported by TUBITAK (The Scientific and Technological Research Council of Turkey - Project No: 108Y002). References Bagde, M.N., Raina, A.K., Chakraborty, A.K., Jethwa, J.L., 2002. Rock mass characterization by fractal dimension. Engineering Geology 63, 141-155. Gokceoglu, C., 2002. A fuzzy triangular chart to predict the uniaxial compressive strength of the Ankara agglomerates from their petrographic composition. Engineering Geology, 66 (1-2), 39-51. Gulbin, Y.L., Evangulova, E.B., 2003. Morphometry of quartz aggregates in granites: fractal images referring to nucleation and growth processes. Mathematical Geology 35 (7), 819-833 Hamdi, E., 2008. A fractal description of simulated 3D discontinuity networks. Rock Mechanics and Rock Engineering 41, 587-599. Hyslip, J.P., Vallejo, L.E., 1997. Fractals analysis of the roughness and size distribution of granular materials. Engineering Geology 48, 231-244. Kahraman, S., Alber, M., Fener, M. and Gunaydin, O. 2008. Evaluating the geomechanical properties of Misis fault breccia (Turkey). Int. J. Rock Mech. Min. Sci, 45, (8), 1469-1479. Kolay, E., Kayabali, K., 2006. Investigation of the effect of aggregate shape and surface roughness on the slake durability index using the fractal dimension approach. Engineering Geology 86, 271-294. Kruhl, J.H., Nega, M., 1996. The fractal shape of sutured quartz grain boundaries: application as a geothermometer. Geologische Rundschau 85, 38-43. Lindquist E.S. 1994. The strength, deformation properties of melange. PhD thesis, University of California, Berkeley, 1994. 264p. Lindquist E.S. and Goodman R.E. 1994. The strength and deformation properties of the physical model m!elange. In: Nelson PP, Laubach SE, editors. Proceedings of the First North American Rock Mechanics Conference (NARMS), Austin, Texas. Rotterdam: AA Balkema; 1994. Pardini, G., 2003. Fractal scaling of surface roughness in artificially weathered smectite rich soil regoliths. Geoderma 117, 157-167. Sezer E., 2009. A computer program for fractal dimension (FRACEK) with application on type of mass movement characterization. Computers and Geosciences (doi:10.1016/j.cageo.2009.04.006). Sonmez H, Tuncay E, and Gokceoglu C., 2004. Models to predict the uniaxial compressive strength and the modulus of elasticity for Ankara Agglomerate. Int. J. Rock Mech. Min. Sci., 41 (5), 717-729. Sonmez, H., Gokceoglu, C., Medley, E.W., Tuncay, E., and Nefeslioglu, H.A., 2006. Estimating the uniaxial compressive strength of a volcanic bimrock. Int. J. Rock Mech. Min. Sci., 43 (4), 554-561. Zorlu K., 2008. Description of the weathering states of building stones by fractal geometry and fuzzy inference system in the Olba ancient city (Southern Turkey). Engineering Geology 101 (2008) 124-133.

Fractal pharmacokinetics.

PubMed

Pereira, Luis M

2010-06-01

Pharmacokinetics (PK) has been traditionally dealt with under the homogeneity assumption. However, biological systems are nowadays comprehensively understood as being inherently fractal. Specifically, the microenvironments where drug molecules interact with membrane interfaces, metabolic enzymes or pharmacological receptors, are unanimously recognized as unstirred, space-restricted, heterogeneous and geometrically fractal. Therefore, classical Fickean diffusion and the notion of the compartment as a homogeneous kinetic space must be revisited. Diffusion in fractal spaces has been studied for a long time making use of fractional calculus and expanding on the notion of dimension. Combining this new paradigm with the need to describe and explain experimental data results in defining time-dependent rate constants with a characteristic fractal exponent. Under the one-compartment simplification this strategy is straightforward. However, precisely due to the heterogeneity of the underlying biology, often at least a two-compartment model is required to address macroscopic data such as drug concentrations. This simple modelling step-up implies significant analytical and numerical complications. However, a few methods are available that make possible the original desideratum. In fact, exploring the full range of parametric possibilities and looking at different drugs and respective biological concentrations, it may be concluded that all PK modelling approaches are indeed particular cases of the fractal PK theory.

Nonextensivity in a Dark Maximum Entropy Landscape

NASA Astrophysics Data System (ADS)

Leubner, M. P.

2011-03-01

Nonextensive statistics along with network science, an emerging branch of graph theory, are increasingly recognized as potential interdisciplinary frameworks whenever systems are subject to long-range interactions and memory. Such settings are characterized by non-local interactions evolving in a non-Euclidean fractal/multi-fractal space-time making their behavior nonextensive. After summarizing the theoretical foundations from first principles, along with a discussion of entropy bifurcation and duality in nonextensive systems, we focus on selected significant astrophysical consequences. Those include the gravitational equilibria of dark matter (DM) and hot gas in clustered structures, the dark energy(DE) negative pressure landscape governed by the highest degree of mutual correlations and the hierarchy of discrete cosmic structure scales, available upon extremizing the generalized nonextensive link entropy in a homogeneous growing network.

Networks of gold nanoparticles and bacteriophage as biological sensors and cell-targeting agents

PubMed Central

Souza, Glauco R.; Christianson, Dawn R.; Staquicini, Fernanda I.; Ozawa, Michael G.; Snyder, Evan Y.; Sidman, Richard L.; Miller, J. Houston; Arap, Wadih; Pasqualini, Renata

2006-01-01

Biological molecular assemblies are excellent models for the development of nanoengineered systems with desirable biomedical properties. Here we report an approach for fabrication of spontaneous, biologically active molecular networks consisting of bacteriophage (phage) directly assembled with gold (Au) nanoparticles (termed Au–phage). We show that when the phage are engineered so that each phage particle displays a peptide, such networks preserve the cell surface receptor binding and internalization attributes of the displayed peptide. The spontaneous organization of these targeted networks can be manipulated further by incorporation of imidazole (Au–phage–imid), which induces changes in fractal structure and near-infrared optical properties. The networks can be used as labels for enhanced fluorescence and dark-field microscopy, surface-enhanced Raman scattering detection, and near-infrared photon-to-heat conversion. Together, the physical and biological features within these targeted networks offer convenient multifunctional integration within a single entity with potential for nanotechnology-based biomedical applications. PMID:16434473

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.

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 ...

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.

Computer simulation of viscous fingering in Sierpinski carpet

NASA Astrophysics Data System (ADS)

Ju-ping, Tian; Kai-lun, Yao

1998-09-01

A new method-mapping dilation method is proposed in this paper to construct Sierpinski carpet. Viscous fingering (VF) in Sierpinski carpet, based on the assumption that bond radii are beta distribution, is investigated by means of successive over-relaxation techniques. The topology and the geometry of the porous media have a strong effect on displacement processes. In the Sierpinski network, the VF pattern of porous media in the limit M → ∞ is found to be similar to the diffusion-limited-aggregation pattern. The fractal dimension for VF in fractal space is calculated and the fractal dimension D can be reasonably regarded as a useful parameter to evaluate the sweep efficiencies and oil recoveries. We have also found that the geometry of the porous medium also has strong effects on the displacement processes and the structure of the VF. Moreover, we find that the sweep efficiency of the displacement processes mainly depends upon the length of the network system and also on the viscosity ratio M. This shows that the current method can be used to solve VF problems in complex structures if the structures are self-similar, or they can be reduced to a self-similar structure.

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.

Model for growth of fractal solid state surface and possibility of its verification by means of atomic force microscopy

NASA Astrophysics Data System (ADS)

Kulikov, D. A.; Potapov, A. A.; Rassadin, A. E.; Stepanov, A. V.

2017-10-01

In the paper, methods of verification of models for growth of solid state surface by means of atomic force microscopy are suggested. Simulation of growth of fractals with cylindrical generatrix on the solid state surface is presented. Our mathematical model of this process is based on generalization of the Kardar-Parisi-Zhang equation. Corner stones of this generalization are both conjecture of anisotropy of growth of the surface and approximation of small angles. The method of characteristics has been applied to solve the Kardar-Parisi-Zhang equation. Its solution should be considered up to the gradient catastrophe. The difficulty of nondifferentiability of fractal initial generatrix has been overcome by transition from a mathematical fractal to a physical one.

Scale effect challenges in urban hydrology highlighted with a Fully Distributed Model and High-resolution rainfall data

NASA Astrophysics Data System (ADS)

Ichiba, Abdellah; Gires, Auguste; Tchiguirinskaia, Ioulia; Schertzer, Daniel; Bompard, Philippe; Ten Veldhuis, Marie-Claire

2017-04-01

Nowadays, there is a growing interest on small-scale rainfall information, provided by weather radars, to be used in urban water management and decision-making. Therefore, an increasing interest is in parallel devoted to the development of fully distributed and grid-based models following the increase of computation capabilities, the availability of high-resolution GIS information needed for such models implementation. However, the choice of an appropriate implementation scale to integrate the catchment heterogeneity and the whole measured rainfall variability provided by High-resolution radar technologies still issues. This work proposes a two steps investigation of scale effects in urban hydrology and its effects on modeling works. In the first step fractal tools are used to highlight the scale dependency observed within distributed data used to describe the catchment heterogeneity, both the structure of the sewer network and the distribution of impervious areas are analyzed. Then an intensive multi-scale modeling work is carried out to understand scaling effects on hydrological model performance. Investigations were conducted using a fully distributed and physically based model, Multi-Hydro, developed at Ecole des Ponts ParisTech. The model was implemented at 17 spatial resolutions ranging from 100 m to 5 m and modeling investigations were performed using both rain gauge rainfall information as well as high resolution X band radar data in order to assess the sensitivity of the model to small scale rainfall variability. Results coming out from this work demonstrate scale effect challenges in urban hydrology modeling. In fact, fractal concept highlights the scale dependency observed within distributed data used to implement hydrological models. Patterns of geophysical data change when we change the observation pixel size. The multi-scale modeling investigation performed with Multi-Hydro model at 17 spatial resolutions confirms scaling effect on hydrological model performance. Results were analyzed at three ranges of scales identified in the fractal analysis and confirmed in the modeling work. The sensitivity of the model to small-scale rainfall variability was discussed as well.

Fundamental Fractal Antenna Design Process

NASA Astrophysics Data System (ADS)

Zhu, L. P.; Kim, T. C.; Kakas, G. D.

2017-12-01

Antenna designers are always looking to come up with new ideas to push the envelope for new antennas, using a smaller volume while striving for higher bandwidth, wider bandwidth, and antenna gain. One proposed method of increasing bandwidth or shrinking antenna size is via the use of fractal geometry, which gives rise to fractal antennas. Fractals are those fun shapes that if one zooms in or zoom out, the structure is always the same. Design a new type of antenna based on fractal antenna design by utilize the Design of Experiment (DOE) will be shown in fractal antenna design process. Investigate conformal fractal antenna design for patterns, dimensions, and size, of the antenna but maintaining or improving the antenna performance. Research shows an antenna designer how to create basic requirements of the fractal antenna through a step by step process, and provides how to optimize the antenna design with the model prediction, lab measurement, and actual results from the compact range measurement on the antenna patterns.

Fractal characteristic in the wearing of cutting tool

NASA Astrophysics Data System (ADS)

Mei, Anhua; Wang, Jinghui

1995-11-01

This paper studies the cutting tool wear with fractal geometry. The wearing image of the flank has been collected by machine vision which consists of CCD camera and personal computer. After being processed by means of preserving smoothing, binary making and edge extracting, the clear boundary enclosing the worn area has been obtained. The fractal dimension of the worn surface is calculated by the methods called `Slit Island' and `Profile'. The experiments and calciating give the conclusion that the worn surface is enclosed by a irregular boundary curve with some fractal dimension and characteristics of self-similarity. Furthermore, the relation between the cutting velocity and the fractal dimension of the worn region has been submitted. This paper presents a series of methods for processing and analyzing the fractal information in the blank wear, which can be applied to research the projective relation between the fractal structure and the wear state, and establish the fractal model of the cutting tool wear.

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.

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.

Investigating the effect of suspensions nanostructure on the thermophysical properties of nanofluids

NASA Astrophysics Data System (ADS)

Tesfai, Waka; Singh, Pawan K.; Masharqa, Salim J. S.; Souier, Tewfik; Chiesa, Matteo; Shatilla, Youssef

2012-12-01

The effect of fractal dimensions and Feret diameter of aggregated nanoparticle on predicting the thermophysical properties of nanofluids is demonstrated. The fractal dimensions and Feret diameter distributions of particle agglomerates are quantified from scanning electron and probe microscope imaging of yttria nanofluids. The results are compared with the fractal dimensions calculated by fitting the rheological properties of yttria nanofluids against the modified Krieger-Dougherty model. Nanofluids of less than 1 vol. % particle loading are found to have fractal dimensions of below 1.8, which is typical for diffusion controlled cluster formation. By contrast, an increase in the particle loading increases the fractal dimension to 2.0-2.2. The fractal dimensions obtained from both methods are employed to predict the thermal conductivity of the nanofluids using the modified Maxwell-Garnet (M-G) model. The prediction from rheology is found inadequate and might lead up to 8% error in thermal conductivity for an improper choice of aspect ratio. Nevertheless, the prediction of the modified M-G model from the imaging is found to agree well with the experimentally observed effective thermal conductivity of the nanofluids. In addition, this study opens a new window on the study of aggregate kinetics, which is critical in tuning the properties of multiphase systems.

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.

Relationship between the anomalous diffusion and the fractal dimension of the environment

NASA Astrophysics Data System (ADS)

Zhokh, Alexey; Trypolskyi, Andrey; Strizhak, Peter

2018-03-01

In this letter, we provide an experimental study highlighting a relation between the anomalous diffusion and the fractal dimension of the environment using the methanol anomalous transport through the porous solid pellets with various pores geometries and different chemical compositions. The anomalous diffusion exponent was derived from the non-integer order of the time-fractional diffusion equation that describes the methanol anomalous transport through the solid media. The surface fractal dimension was estimated from the nitrogen adsorption isotherms using the Frenkel-Halsey-Hill method. Our study shows that decreasing the fractal dimension leads to increasing the anomalous diffusion exponent, whereas the anomalous diffusion constant is independent on the fractal dimension. We show that the obtained results are in a good agreement with the anomalous diffusion model on a fractal mesh.

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

Applications of fractals in ecology.

PubMed

Sugihara, G; M May, R

1990-03-01

Fractal models describe the geometry of a wide variety of natural objects such as coastlines, island chains, coral reefs, satellite ocean-color images and patches of vegetation. Cast in the form of modified diffusion models, they can mimic natural and artificial landscapes having different types of complexity of shape. This article provides a brief introduction to fractals and reports on how they can be used by ecologists to answer a variety of basic questions, about scale, measurement and hierarchy in, ecological systems. Copyright © 1990. Published by Elsevier Ltd.

Multifractal to monofractal evolution of the London street network.

PubMed

Murcio, Roberto; Masucci, A Paolo; Arcaute, Elsa; Batty, Michael

2015-12-01

We perform a multifractal analysis of the evolution of London's street network from 1786 to 2010. First, we show that a single fractal dimension, commonly associated with the morphological description of cities, does not suffice to capture the dynamics of the system. Instead, for a proper characterization of such a dynamics, the multifractal spectrum needs to be considered. Our analysis reveals that London evolves from an inhomogeneous fractal structure, which can be described in terms of a multifractal, to a homogeneous one, which converges to monofractality. We argue that London's multifractal to monofractal evolution might be a special outcome of the constraint imposed on its growth by a green belt. Through a series of simulations, we show that multifractal objects, constructed through diffusion limited aggregation, evolve toward monofractality if their growth is constrained by a nonpermeable boundary.

[Modeling continuous scaling of NDVI based on fractal theory].

PubMed

Luan, Hai-Jun; Tian, Qing-Jiu; Yu, Tao; Hu, Xin-Li; Huang, Yan; Du, Ling-Tong; Zhao, Li-Min; Wei, Xi; Han, Jie; Zhang, Zhou-Wei; Li, Shao-Peng

2013-07-01

Scale effect was one of the very important scientific problems of remote sensing. The scale effect of quantitative remote sensing can be used to study retrievals' relationship between different-resolution images, and its research became an effective way to confront the challenges, such as validation of quantitative remote sensing products et al. Traditional up-scaling methods cannot describe scale changing features of retrievals on entire series of scales; meanwhile, they are faced with serious parameters correction issues because of imaging parameters' variation of different sensors, such as geometrical correction, spectral correction, etc. Utilizing single sensor image, fractal methodology was utilized to solve these problems. Taking NDVI (computed by land surface radiance) as example and based on Enhanced Thematic Mapper Plus (ETM+) image, a scheme was proposed to model continuous scaling of retrievals. Then the experimental results indicated that: (a) For NDVI, scale effect existed, and it could be described by fractal model of continuous scaling; (2) The fractal method was suitable for validation of NDVI. All of these proved that fractal was an effective methodology of studying scaling of quantitative remote sensing.

The Buildup of a Scale-free Photospheric Magnetic Network

NASA Astrophysics Data System (ADS)

Thibault, K.; Charbonneau, P.; Crouch, A. D.

2012-10-01

We use a global Monte Carlo simulation of the formation of the solar photospheric magnetic network to investigate the origin of the scale invariance characterizing magnetic flux concentrations visible on high-resolution magnetograms. The simulations include spatially and temporally homogeneous injection of small-scale magnetic elements over the whole photosphere, as well as localized episodic injection associated with the emergence and decay of active regions. Network elements form in response to cumulative pairwise aggregation or cancellation of magnetic elements, undergoing a random walk on the sphere and advected on large spatial scales by differential rotation and a poleward meridional flow. The resulting size distribution of simulated network elements is in very good agreement with observational inferences. We find that the fractal index and size distribution of network elements are determined primarily by these post-emergence surface mechanisms, and carry little or no memory of the scales at which magnetic flux is injected in the simulation. Implications for models of dynamo action in the Sun are briefly discussed.

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.

Association of the Fractal Dimension of Retinal Arteries and Veins with Quantitative Brain MRI Measures in HIV-Infected and Uninfected Women

PubMed Central

Crystal, Howard A.; Holman, Susan; Lui, Yvonne W.; Baird, Alison E.; Yu, Hua; Klein, Ronald; Rojas-Soto, Diana Marcella; Gustafson, Deborah R.; Stebbins, Glenn T.

2016-01-01

Objective The fractal dimension of retinal arteries and veins is a measure of the complexity of the vascular tree. We hypothesized that retinal fractal dimension would be associated with brain volume and white matter integrity in HIV-infected women. Design Nested case-control within longitudinal cohort study. Methods Women were recruited from the Brooklyn site of the Women’s Interagency HIV study (WIHS); 34 HIV-infected and 21 HIV-uninfected women with analyzable MRIs and retinal photographs were included. Fractal dimension was determined using the SIVA software program on skeletonized retinal images. The relationship between predictors (retinal vascular measures) and outcomes (quantitative MRI measures) were analyzed with linear regression models. All models included age, intracranial volume, and both arterial and venous fractal dimension. Some models were adjusted for blood pressure, race/ethnicity, and HIV-infection. Results The women were 45.6 ± 7.3 years of age. Higher arterial dimension was associated with larger cortical volumes, but higher venous dimension was associated with smaller cortical volumes. In fully adjusted models, venous dimension was significantly associated with fractional anisotropy (standardized β = -0.41, p = 0.009) and total gray matter volume (β = -0.24, p = 0.03), and arterial dimension with mean diffusivity (β = -0.33,.p = 0.04) and fractional anisotropy (β = 0.34, p = 0.03). HIV-infection was not associated with any retinal or MRI measure. Conclusions Higher venous fractal dimension was associated with smaller cortical volumes and lower fractional anisotropy, whereas higher arterial fractal dimension was associated with the opposite patterns. Longitudinal studies are needed to validate this finding. PMID:27158911

Carbon black networking in elastomers monitored by simultaneous rheological and dielectric investigations.

PubMed

Steinhauser, Dagmar; Möwes, Markus; Klüppel, Manfred

2016-12-14

The rheo-dielectric response of carbon black filled elastomer melts is investigated by dielectric relaxation spectroscopy in the frequency range from 0.1 Hz up to 10 MHz during oszillatory shearing in a plate-plate rheometer. Various concentrations and types of carbon blacks dispersed in a non-crosslinked EPDM melt are considered. It is demonstrated that during heat treatment at low strain amplitude a pronounced flocculation of filler particles takes place leading to a successive increase of the shear modulus and conductivity. Followed up by a strain sweep, the filler network breaks up and both quantities decrease simultaneously with increasing strain amplitude. Two relaxation times, obtained from a Cole-Cole fit of the dielectric spectra, are identified, which both decrease strongly with increasing flocculation time. This behaviour is analyzed in the frame of fractal network models, describing the effect of structural disorder of the conducting carbon black network on the diffusive charge transport. Significant deviations from the predictions of percolation theory are observed, which are traced back to a superimposed cluster-cluster aggregation process (CCA). During flocculation, a universal scaling behaviour holds between the conductivity and the corresponding high frequency relaxation time, which fits all the measured data. The scaling exponent agrees fairly well with the prediction obtained from CCA. It is demonstrated that the underlying basic mechanism is a change of the correlation length of the filler network, i.e. the size of the fractal heterogeneities. This decreases during flocculation due to the formation of additional conductive paths, making the system more homogeneous. An addition less pronounced effect is found from nanoscopic gaps between adjacent filler particles, which decrease during flocculation. The same universal scaling behaviour, as obtained for flocculation, is found for temperature-dependent dielectric measurements of the cured crosslinked systems, which are heated from room temperature up to 200 °C. Thereby, the conductivity decreases significantly and the relaxation time increases, indicating that the filler network breaks up randomly due to the thermal expansion of the rubber matrix.

Carbon black networking in elastomers monitored by simultaneous rheological and dielectric investigations

NASA Astrophysics Data System (ADS)

Steinhauser, Dagmar; Möwes, Markus; Klüppel, Manfred

2016-12-01

The rheo-dielectric response of carbon black filled elastomer melts is investigated by dielectric relaxation spectroscopy in the frequency range from 0.1 Hz up to 10 MHz during oszillatory shearing in a plate-plate rheometer. Various concentrations and types of carbon blacks dispersed in a non-crosslinked EPDM melt are considered. It is demonstrated that during heat treatment at low strain amplitude a pronounced flocculation of filler particles takes place leading to a successive increase of the shear modulus and conductivity. Followed up by a strain sweep, the filler network breaks up and both quantities decrease simultaneously with increasing strain amplitude. Two relaxation times, obtained from a Cole-Cole fit of the dielectric spectra, are identified, which both decrease strongly with increasing flocculation time. This behaviour is analyzed in the frame of fractal network models, describing the effect of structural disorder of the conducting carbon black network on the diffusive charge transport. Significant deviations from the predictions of percolation theory are observed, which are traced back to a superimposed cluster-cluster aggregation process (CCA). During flocculation, a universal scaling behaviour holds between the conductivity and the corresponding high frequency relaxation time, which fits all the measured data. The scaling exponent agrees fairly well with the prediction obtained from CCA. It is demonstrated that the underlying basic mechanism is a change of the correlation length of the filler network, i.e. the size of the fractal heterogeneities. This decreases during flocculation due to the formation of additional conductive paths, making the system more homogeneous. An addition less pronounced effect is found from nanoscopic gaps between adjacent filler particles, which decrease during flocculation. The same universal scaling behaviour, as obtained for flocculation, is found for temperature-dependent dielectric measurements of the cured crosslinked systems, which are heated from room temperature up to 200 °C. Thereby, the conductivity decreases significantly and the relaxation time increases, indicating that the filler network breaks up randomly due to the thermal expansion of the rubber matrix.

Universal inverse power-law distribution for temperature and rainfall in the UK region

NASA Astrophysics Data System (ADS)

Selvam, A. M.

2014-06-01

Meteorological parameters, such as temperature, rainfall, pressure, etc., exhibit selfsimilar space-time fractal fluctuations generic to dynamical systems in nature such as fluid flows, spread of forest fires, earthquakes, etc. The power spectra of fractal fluctuations display inverse power-law form signifying long-range correlations. A general systems theory model predicts universal inverse power-law form incorporating the golden mean for the fractal fluctuations. The model predicted distribution was compared with observed distribution of fractal fluctuations of all size scales (small, large and extreme values) in the historic month-wise temperature (maximum and minimum) and total rainfall for the four stations Oxford, Armagh, Durham and Stornoway in the UK region, for data periods ranging from 92 years to 160 years. For each parameter, the two cumulative probability distributions, namely cmax and cmin starting from respectively maximum and minimum data value were used. The results of the study show that (i) temperature distributions (maximum and minimum) follow model predicted distribution except for Stornowy, minimum temperature cmin. (ii) Rainfall distribution for cmin follow model predicted distribution for all the four stations. (iii) Rainfall distribution for cmax follows model predicted distribution for the two stations Armagh and Stornoway. The present study suggests that fractal fluctuations result from the superimposition of eddy continuum fluctuations.

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.

River Networks and Human Activities: Global Fractal Analysis Using Nightlight Data

NASA Astrophysics Data System (ADS)

McCurley, K. 4553; Fang, Y.; Ceola, S.; Paik, K.; McGrath, G. S.; Montanari, A.; Rao, P. S.; Jawitz, J. W.

2016-12-01

River networks hold an important historical role in affecting human population distribution. In this study, we link the geomorphological structure of river networks to the pattern of human activities at a global scale. We use nightlights as a valuable proxy for the presence of human settlements and economic activity, and we employ HydroSHEDS as the main data source on river networks. We test the hypotheses that, analogous to Horton's laws, human activities (magnitude of nightlights) also show scaling relationship with stream order, and that the intensity of human activities decrease as the distance from the basin outlet increase. Our results demonstrate that the distribution of human activities shows a fractal structure, with power-law scaling between human activities and stream order. This relationship is robust among global river basins. Human activities are more concentrated in larger order basins, but show large variation in equivalent order basins, with higher population density emergent in the basins connected with high-order rivers. For all global river basins longer than 400km, the average intensity of human activities decrease as the distance to the outlets increases, albeit with signatures of large cities at varied distances. The power spectrum of human width (area) function is found to exhibit power law scaling, with a scaling exponent that indicates enrichment of low frequency variation. The universal fractal structure of human activities may reflect an optimum arrangement for humans in river basins to better utilize the water resources, ecological assets, and geographic advantages. The generalized patterns of human activities could be applied to better understand hydrologic and biogeochemical responses in river basins, and to advance catchment management.

Relaxation dynamics of a multihierarchical polymer network

NASA Astrophysics Data System (ADS)

Jurjiu, Aurel; Biter, Teodor Lucian; Turcu, Flaviu

2017-01-01

In this work, we study the relaxation dynamics of a multihierarchical polymer network built by replicating the Vicsek fractal in dendrimer shape. The relaxation dynamics is investigated in the framework of the generalized Gaussian structure model by employing both Rouse and Zimm approaches. In the Rouse-type approach, we show the iterative procedure whereby the whole eigenvalue spectrum of the connectivity matrix of the multihierarchical structure can be obtained. Remarkably, the general picture that emerges from both approaches, even though we have a mixed growth algorithm, is that the obtained multihierarchical structure preserves the individual relaxation behaviors of its components. The theoretical findings with respect to the splitting of the intermediate domain of the relaxation quantities are well supported by experimental results.

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).

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.

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.

Revisiting Horton's laws with considerations of the directly drained VS source area

NASA Astrophysics Data System (ADS)

Yang, Soohyun; Paik, Kyungrock

2015-04-01

River networks have been regarded as excellent examples of self-similar patterns in nature. Fractal characteristics of river networks have been quantified through scaling relations between several morphologic variables (e.g., Hack, 1957; Flint, 1974). In particular, Horton's legendary study on scaling properties between numbers and lengths of streams in different orders (Horton, 1945) has significantly influenced research studies in this subject. Today, Horton's laws are referred to the log-linear relationships of three variables across stream orders, i.e., number, length, and area which is later added by Schumm (1956). In a closer look, there is a conceptual inconsistency between their definitions though. While length is defined as the length of stream of a specific order only, area by its definition includes drainage area of lower order streams. To deal with this inconsistency, there was an attempt to distinguish the average area drained directly by the stream of a particular order in the Hortonian formulation (Marani et al., 1991; Beer and Borgas, 1993). Nevertheless, there remains an interesting problem in the definition of directly drained area for 1st order and for the rest orders in these studies. While the whole area of 1st order stream is regarded as the directly drained area in these studies, for a channel to form it needs the minimum drainage area named source area. In this study, we evaluate how significant considering this zero order area separately is in understanding overall river network organization. To this end, we define new expression for the directly drained area and revisit Horton's laws with a generalized formulation. To test the proposed ideas, several river networks extracted from digital elevation models (DEMs) are analyzed. References Beer, T., & Borgas, M. (1993). Horton's laws and the fractal nature of streams. Water Resources Research, 29(5), 1475-1487. Flint, J. J. (1974). Stream gradient as a function of order, magnitude, and discharge. Water Resources Research, 10(5), 969-973. Hack, J. T. (1957). Studies of longitudinal river profiles in Virginia and Maryland. US, Geological Survey Professional Paper, 294. Horton, R. E. (1945). Erosional development of streams and their drainage basins; hydrophysical approach to quantitative morphology. Geological Society of America Bulletin, 56(3), 275-370. Marani, A., Rigon, R., & Rinaldo, A. (1991). A note on fractal channel networks. Water Resources Research, 27(12), 3041-3049. Schumm, S. A. (1956). Evolution of drainage systems and slopes in badlands at Perth Amboy, New Jersey. Geological Society of America Bulletin, 67(5), 597-646.

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.

Fractal dynamics of earthquakes

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

Bak, P.; Chen, K.

1995-05-01

Many objects in nature, from mountain landscapes to electrical breakdown and turbulence, have a self-similar fractal spatial structure. It seems obvious that to understand the origin of self-similar structures, one must understand the nature of the dynamical processes that created them: temporal and spatial properties must necessarily be completely interwoven. This is particularly true for earthquakes, which have a variety of fractal aspects. The distribution of energy released during earthquakes is given by the Gutenberg-Richter power law. The distribution of epicenters appears to be fractal with dimension D {approx} 1--1.3. The number of after shocks decay as a function ofmore » time according to the Omori power law. There have been several attempts to explain the Gutenberg-Richter law by starting from a fractal distribution of faults or stresses. But this is a hen-and-egg approach: to explain the Gutenberg-Richter law, one assumes the existence of another power-law--the fractal distribution. The authors present results of a simple stick slip model of earthquakes, which evolves to a self-organized critical state. Emphasis is on demonstrating that empirical power laws for earthquakes indicate that the Earth`s crust is at the critical state, with no typical time, space, or energy scale. Of course the model is tremendously oversimplified; however in analogy with equilibrium phenomena they do not expect criticality to depend on details of the model (universality).« less

SAXS analysis of single- and multi-core iron oxide magnetic nanoparticles

PubMed Central

Szczerba, Wojciech; Costo, Rocio; Morales, Maria del Puerto; Thünemann, Andreas F.

2017-01-01

This article reports on the characterization of four superparamagnetic iron oxide nanoparticles stabilized with dimercaptosuccinic acid, which are suitable candidates for reference materials for magnetic properties. Particles p1 and p2 are single-core particles, while p3 and p4 are multi-core particles. Small-angle X-ray scattering analysis reveals a lognormal type of size distribution for the iron oxide cores of the particles. Their mean radii are 6.9 nm (p1), 10.6 nm (p2), 5.5 nm (p3) and 4.1 nm (p4), with narrow relative distribution widths of 0.08, 0.13, 0.08 and 0.12. The cores are arranged as a clustered network in the form of dense mass fractals with a fractal dimension of 2.9 in the multi-core particles p3 and p4, but the cores are well separated from each other by a protecting organic shell. The radii of gyration of the mass fractals are 48 and 44 nm, and each network contains 117 and 186 primary particles, respectively. The radius distributions of the primary particle were confirmed with transmission electron microscopy. All particles contain purely maghemite, as shown by X-ray absorption fine structure spectroscopy. PMID:28381973

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.

Self-Organized Criticality Systems

NASA Astrophysics Data System (ADS)

Aschwanden, M. J.

2013-07-01

Contents: (1) Introduction - Norma B. Crosby --- (2) Theoretical Models of SOC Systems - Markus J. Aschwanden --- (3) SOC and Fractal Geometry - R. T. James McAteer --- (4) Percolation Models of Self-Organized Critical Phenomena - Alexander V. Milovanov --- (5) Criticality and Self-Organization in Branching Processes: Application to Natural Hazards - Álvaro Corral, Francesc Font-Clos --- (6) Power Laws of Recurrence Networks - Yong Zou, Jobst Heitzig, Jürgen Kurths --- (7) SOC computer simolations - Gunnar Pruessner --- (8) SOC Laboratory Experiments - Gunnar Pruessner --- (9) Self-Organizing Complex Earthquakes: Scaling in Data, Models, and Forecasting - Michael K. Sachs et al. --- (10) Wildfires and the Forest-Fire Model - Stefan Hergarten --- (11) SOC in Landslides - Stefan Hergarten --- (12) SOC and Solar Flares - Paul Charbonneau --- (13) SOC Systems in Astrophysics - Markus J. Aschwanden ---

Recent advances in coding theory for near error-free communications

NASA Technical Reports Server (NTRS)

Cheung, K.-M.; Deutsch, L. J.; Dolinar, S. J.; Mceliece, R. J.; Pollara, F.; Shahshahani, M.; Swanson, L.

1991-01-01

Channel and source coding theories are discussed. The following subject areas are covered: large constraint length convolutional codes (the Galileo code); decoder design (the big Viterbi decoder); Voyager's and Galileo's data compression scheme; current research in data compression for images; neural networks for soft decoding; neural networks for source decoding; finite-state codes; and fractals for data compression.

Fractal active contour model for segmenting the boundary of man-made target in nature scenes

NASA Astrophysics Data System (ADS)

Li, Min; Tang, Yandong; Wang, Lidi; Shi, Zelin

2006-02-01

In this paper, a novel geometric active contour model based on the fractal dimension feature to extract the boundary of man-made target in nature scenes is presented. In order to suppress the nature clutters, an adaptive weighting function is defined using the fractal dimension feature. Then the weighting function is introduced into the geodesic active contour model to detect the boundary of man-made target. Curve driven by our proposed model can evolve gradually from the initial position to the boundary of man-made target without being disturbed by nature clutters, even if the initial curve is far away from the true boundary. Experimental results validate the effectiveness and feasibility of our model.

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.

Detecting Blind Fault with Fractal and Roughness Factors from High Resolution LiDAR DEM at Taiwan

NASA Astrophysics Data System (ADS)

Cheng, Y. S.; Yu, T. T.

2014-12-01

There is no obvious fault scarp associated with blind fault. The traditional method of mapping this unrevealed geological structure is the cluster of seismicity. Neither the seismic event nor the completeness of cluster could be captured by network to chart the location of the entire possible active blind fault within short period of time. High resolution DEM gathered by LiDAR could denote actual terrain information despite the existence of plantation. 1-meter interval DEM of mountain region at Taiwan is utilized by fractal, entropy and roughness calculating with MATLAB code. By jointing these handing, the regions of non-sediment deposit are charted automatically. Possible blind fault associated with Chia-Sen earthquake at southern Taiwan is served as testing ground. GIS layer help in removing the difference from various geological formation, then multi-resolution fractal index is computed around the target region. The type of fault movement controls distribution of fractal index number. The scale of blind fault governs degree of change in fractal index. Landslide induced by rainfall and/or earthquake possesses larger degree of geomorphology alteration than blind fault; special treatment in removing these phenomena is required. Highly weathered condition at Taiwan should erase the possible trace remained upon DEM from the ruptured of blind fault while reoccurrence interval is higher than hundreds of years. This is one of the obstacle in finding possible blind fault at Taiwan.

A mathematics for medicine: The Network Effect

PubMed Central

West, Bruce J.

2014-01-01

The theory of medicine and its complement systems biology are intended to explain the workings of the large number of mutually interdependent complex physiologic networks in the human body and to apply that understanding to maintaining the functions for which nature designed them. Therefore, when what had originally been made as a simplifying assumption or a working hypothesis becomes foundational to understanding the operation of physiologic networks it is in the best interests of science to replace or at least update that assumption. The replacement process requires, among other things, an evaluation of how the new hypothesis affects modern day understanding of medical science. This paper identifies linear dynamics and Normal statistics as being such arcane assumptions and explores some implications of their retirement. Specifically we explore replacing Normal with fractal statistics and examine how the latter are related to non-linear dynamics and chaos theory. The observed ubiquity of inverse power laws in physiology entails the need for a new calculus, one that describes the dynamics of fractional phenomena and captures the fractal properties of the statistics of physiological time series. We identify these properties as a necessary consequence of the complexity resulting from the network dynamics and refer to them collectively as The Network Effect. PMID:25538622

An information dimension of weighted complex networks

NASA Astrophysics Data System (ADS)

Wen, Tao; Jiang, Wen

2018-07-01

The fractal and self-similarity are important properties in complex networks. Information dimension is a useful dimension for complex networks to reveal these properties. In this paper, an information dimension is proposed for weighted complex networks. Based on the box-covering algorithm for weighted complex networks (BCANw), the proposed method can deal with the weighted complex networks which appear frequently in the real-world, and it can get the influence of the number of nodes in each box on the information dimension. To show the wide scope of information dimension, some applications are illustrated, indicating that the proposed method is effective and feasible.

Unified Mie and fractal scattering by cells and experimental study on application in optical characterization of cellular and subcellular structures.

PubMed

Xu, Min; Wu, Tao T; Qu, Jianan Y

2008-01-01

A unified Mie and fractal model for light scattering by biological cells is presented. This model is shown to provide an excellent global agreement with the angular dependent elastic light scattering spectroscopy of cells over the whole visible range (400 to 700 nm) and at all scattering angles (1.1 to 165 deg) investigated. Mie scattering from the bare cell and the nucleus is found to dominate light scattering in the forward directions, whereas the random fluctuation of the background refractive index within the cell, behaving as a fractal random continuous medium, is found to dominate light scattering at other angles. Angularly dependent elastic light scattering spectroscopy aided by the unified Mie and fractal model is demonstrated to be an effective noninvasive approach to characterize biological cells and their internal structures. The acetowhitening effect induced by applying acetic acid on epithelial cells is investigated as an example. The changes in morphology and refractive index of epithelial cells, nuclei, and subcellular structures after the application of acetic acid are successfully probed and quantified using the proposed approach. The unified Mie and fractal model may serve as the foundation for optical detection of precancerous and cancerous changes in biological cells and tissues based on light scattering techniques.

Fractal growth mechanism of sp3-bonded 5H-BN microcones by plasma-assisted pulsed-laser chemical vapor deposition

NASA Astrophysics Data System (ADS)

Komatsu, Shojiro; Kazami, Daisuke; Tanaka, Hironori; Moriyoshi, Yusuke; Shiratani, Masaharu; Okada, Katsuyuki

2006-08-01

Here we propose a repetitive photochemical reaction and diffusion model for the fractal pattern formation of sp3-bonded 5H-BN microcones in laser-assisted plasma chemical vapor deposition, which was observed experimentally and reported previously. This model describing the behavior of the surface density of precursor species gave explanations to (1) the "line-drawing" nature of the patterns, (2) the origin of the scale-invariant self-similarity (fractality) of the pattern, and (3) the temperature-dependent uniform to fractal transition. The results have implications for controlling the self-organized arrangements of electron-emitter cones at the micro-and nanoscale by adjusting macroscopically the boundary condition (LX,LY) for the deposition, which will be very effective in improving the electron field emission properties.

Interactions between a fractal tree-like object and hydrodynamic turbulence: flow structure and characteristic mixing length

NASA Astrophysics Data System (ADS)

Meneveau, C. V.; Bai, K.; Katz, J.

2011-12-01

The vegetation canopy has a significant impact on various physical and biological processes such as forest microclimate, rainfall evaporation distribution and climate change. Most scaled laboratory experimental studies have used canopy element models that consist of rigid vertical strips or cylindrical rods that can be typically represented through only one or a few characteristic length scales, for example the diameter and height for cylindrical rods. However, most natural canopies and vegetation are highly multi-scale with branches and sub-branches, covering a wide range of length scales. Fractals provide a convenient idealization of multi-scale objects, since their multi-scale properties can be described in simple ways (Mandelbrot 1982). While fractal aspects of turbulence have been studied in several works in the past decades, research on turbulence generated by fractal objects started more recently. We present an experimental study of boundary layer flow over fractal tree-like objects. Detailed Particle-Image-Velocimetry (PIV) measurements are carried out in the near-wake of a fractal-like tree. The tree is a pre-fractal with five generations, with three branches and a scale reduction factor 1/2 at each generation. Its similarity fractal dimension (Mandelbrot 1982) is D ~ 1.58. Detailed mean velocity and turbulence stress profiles are documented, as well as their downstream development. We then turn attention to the turbulence mixing properties of the flow, specifically to the question whether a mixing length-scale can be identified in this flow, and if so, how it relates to the geometric length-scales in the pre-fractal object. Scatter plots of mean velocity gradient (shear) and Reynolds shear stress exhibit good linear relation at all locations in the flow. Therefore, in the transverse direction of the wake evolution, the Boussinesq eddy viscosity concept is appropriate to describe the mixing. We find that the measured mixing length increases with increasing streamwise locations. Conversely, the measured eddy viscosity and mixing length decrease with increasing elevation, which differs from eddy viscosity and mixing length behaviors of traditional boundary layers or canopies studied before. In order to find an appropriate length for the flow, several models based on the notion of superposition of scales are proposed and examined. One approach is based on spectral distributions. Another more practical approach is based on length-scale distributions evaluated using fractal geometry tools. These proposed models agree well with the measured mixing length. The results indicate that information about multi-scale clustering of branches as it occurs in fractals has to be incorporated into models of the mixing length for flows through canopies with multiple scales. The research is supported by National Science Foundation grant ATM-0621396 and AGS-1047550.

Time irreversibility and intrinsics revealing of series with complex network approach

NASA Astrophysics Data System (ADS)

Xiong, Hui; Shang, Pengjian; Xia, Jianan; Wang, Jing

2018-06-01

In this work, we analyze time series on the basis of the visibility graph algorithm that maps the original series into a graph. By taking into account the all-round information carried by the signals, the time irreversibility and fractal behavior of series are evaluated from a complex network perspective, and considered signals are further classified from different aspects. The reliability of the proposed analysis is supported by numerical simulations on synthesized uncorrelated random noise, short-term correlated chaotic systems and long-term correlated fractal processes, and by the empirical analysis on daily closing prices of eleven worldwide stock indices. Obtained results suggest that finite size has a significant effect on the evaluation, and that there might be no direct relation between the time irreversibility and long-range correlation of series. Similarity and dissimilarity between stock indices are also indicated from respective regional and global perspectives, showing the existence of multiple features of underlying systems.

Integrating landscape ecology and geoinformatics to decipher landscape dynamics for regional planning.

PubMed

Dikou, Angela; Papapanagiotou, Evangelos; Troumbis, Andreas

2011-09-01

We used remote sensing and GIS in conjunction with multivariate statistical methods to: (i) quantify landscape composition (land cover types) and configuration (patch density, diversity, fractal dimension, contagion) for five coastal watersheds of Kalloni gulf, Lesvos Island, Greece, in 1945, 1960, 1971, 1990 and 2002/2003, (ii) evaluate the relative importance of physical (slope, geologic substrate, stream order) and human (road network, population density) variables on landscape composition and configuration, and (iii) characterize processes that led to land cover changes through land cover transitions between these five successive periods in time. Distributions of land cover types did not differ among the five time periods at the five watersheds studied because the largest cumulative changes between 1945 and 2002/2003 did not take place at dominant land cover types. Landscape composition related primarily to the physical attributes of the landscape. Nevertheless, increase in population density and the road network were found to increase heterogeneity of the landscape mosaic (patchiness), complexity of patch shape (fractal dimension), and patch disaggregation (contagion). Increase in road network was also found to increase landscape diversity due to the creation of new patches. The main processes involved in land cover changes were plough-land abandonment and ecological succession. Landscape dynamics during the last 50 years corroborate the ecotouristic-agrotouristic model for regional development to reverse trends in agricultural land abandonment and human population decline and when combined with hypothetical regulatory approaches could predict how this landscape could develop in the future, thus, providing a valuable tool to regional planning.

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.

Wetting characteristics of 3-dimensional nanostructured fractal surfaces

NASA Astrophysics Data System (ADS)

Davis, Ethan; Liu, Ying; Jiang, Lijia; Lu, Yongfeng; Ndao, Sidy

2017-01-01

This article reports the fabrication and wetting characteristics of 3-dimensional nanostructured fractal surfaces (3DNFS). Three distinct 3DNFS surfaces, namely cubic, Romanesco broccoli, and sphereflake were fabricated using two-photon direct laser writing. Contact angle measurements were performed on the multiscale fractal surfaces to characterize their wetting properties. Average contact angles ranged from 66.8° for the smooth control surface to 0° for one of the fractal surfaces. The change in wetting behavior was attributed to modification of the interfacial surface properties due to the inclusion of 3-dimensional hierarchical fractal nanostructures. However, this behavior does not exactly obey existing surface wetting models in the literature. Potential applications for these types of surfaces in physical and biological sciences are also discussed.

Average geodesic distance of skeleton networks of Sierpinski tetrahedron

NASA Astrophysics Data System (ADS)

Yang, Jinjin; Wang, Songjing; Xi, Lifeng; Ye, Yongchao

2018-04-01

The average distance is concerned in the research of complex networks and is related to Wiener sum which is a topological invariant in chemical graph theory. In this paper, we study the skeleton networks of the Sierpinski tetrahedron, an important self-similar fractal, and obtain their asymptotic formula for average distances. To provide the formula, we develop some technique named finite patterns of integral of geodesic distance on self-similar measure for the Sierpinski tetrahedron.

Fractal dust constrains the collisional history of comets

NASA Astrophysics Data System (ADS)

Fulle, M.; Blum, J.

2017-07-01

The fractal dust particles observed by Rosetta cannot form in the physical conditions observed today in comet 67P/Churyumov-Gerasimenko (67P hereinafter), being instead consistent with models of the pristine dust aggregates coagulated in the solar nebula. Since bouncing collisions in the protoplanetary disc restructure fractals into compact aggregates (pebbles), the only way to preserve fractals in a comet is the gentle gravitational collapse of a mixture of pebbles and fractals, which must occur before their mutual collision speeds overcome ≈1 m s-1. This condition fixes the pebble radius to ≲1 cm, as confirmed by Comet Nucleus Infrared and Visible Analyser onboard Philae. Here, we show that the flux of fractal particles measured by Rosetta constrains the 67P nucleus in a random packing of cm-sized pebbles, with all the voids among them filled by fractal particles. This structure is inconsistent with any catastrophic collision, which would have compacted or dispersed most fractals, thus leaving empty most voids in the reassembled nucleus. Comets are less numerous than current estimates, as confirmed by lacking small craters on Pluto and Charon. Bilobate comets accreted at speeds <1 m s-1 from cometesimals born in the same disc stream.

Magnetorheological response of highly filled magnetoactive elastomers from perspective of mechanical energy density: Fractal aggregates above the nanometer scale?

PubMed

Sorokin, Vladislav V; Belyaeva, Inna A; Shamonin, Mikhail; Kramarenko, Elena Yu

2017-06-01

The dynamic shear modulus of magnetoactive elastomers containing 70 and 80 mass % of carbonyl iron microparticles is measured as a function of strain amplitude via dynamic torsion oscillations in various magnetic fields. The results are presented in terms of the mechanical energy density and considered in the framework of the conventional Kraus model. The form exponent of the Kraus model is further related to a physical model of Huber et al. [Huber et al., J. Phys.: Condens. Matter 8, 409 (1996)10.1088/0953-8984/8/29/003] that uses a realistic representation for the cluster network possessing fractal structure. Two mechanical loading regimes are identified. At small strain amplitudes the exponent β of the Kraus model changes in an externally applied magnetic field due to rearrangement of ferromagnetic-filler particles, while at large strain amplitudes, the exponent β seems to be independent of the magnetic field. The critical mechanical energy characterizing the transition between these two regimes grows with the increasing magnetic field. Similarities between agglomeration and deagglomeration of magnetic filler under simultaneously applied magnetic field and mechanical shear and the concept of jamming transition are discussed. It is proposed that the magnetic field should be considered as an additional parameter to the jamming phase diagram of rubbers filled with magnetic particles.

Forest Fires, Oil Spills, and Fractal Geometry: An Investigation in Two Parts. Part 2: Using Fractal Complexity to Analyze Mathematical Models.

ERIC Educational Resources Information Center

Biehl, L. Charles

1999-01-01

Presents an activity that utilizes the mathematical models of forest fires and oil spills that were generated (in the first part of this activity, published in the November 1998 issue) by students using probability and cellular automata. (ASK)

Fractal dynamics in physiology: Alterations with disease and aging

PubMed Central

Goldberger, Ary L.; Amaral, Luis A. N.; Hausdorff, Jeffrey M.; Ivanov, Plamen Ch.; Peng, C.-K.; Stanley, H. Eugene

2002-01-01

According to classical concepts of physiologic control, healthy systems are self-regulated to reduce variability and maintain physiologic constancy. Contrary to the predictions of homeostasis, however, the output of a wide variety of systems, such as the normal human heartbeat, fluctuates in a complex manner, even under resting conditions. Scaling techniques adapted from statistical physics reveal the presence of long-range, power-law correlations, as part of multifractal cascades operating over a wide range of time scales. These scaling properties suggest that the nonlinear regulatory systems are operating far from equilibrium, and that maintaining constancy is not the goal of physiologic control. In contrast, for subjects at high risk of sudden death (including those with heart failure), fractal organization, along with certain nonlinear interactions, breaks down. Application of fractal analysis may provide new approaches to assessing cardiac risk and forecasting sudden cardiac death, as well as to monitoring the aging process. Similar approaches show promise in assessing other regulatory systems, such as human gait control in health and disease. Elucidating the fractal and nonlinear mechanisms involved in physiologic control and complex signaling networks is emerging as a major challenge in the postgenomic era. PMID:11875196

Fast, Statistical Model of Surface Roughness for Ion-Solid Interaction Simulations and Efficient Code Coupling

NASA Astrophysics Data System (ADS)

Drobny, Jon; Curreli, Davide; Ruzic, David; Lasa, Ane; Green, David; Canik, John; Younkin, Tim; Blondel, Sophie; Wirth, Brian

2017-10-01

Surface roughness greatly impacts material erosion, and thus plays an important role in Plasma-Surface Interactions. Developing strategies for efficiently introducing rough surfaces into ion-solid interaction codes will be an important step towards whole-device modeling of plasma devices and future fusion reactors such as ITER. Fractal TRIDYN (F-TRIDYN) is an upgraded version of the Monte Carlo, BCA program TRIDYN developed for this purpose that includes an explicit fractal model of surface roughness and extended input and output options for file-based code coupling. Code coupling with both plasma and material codes has been achieved and allows for multi-scale, whole-device modeling of plasma experiments. These code coupling results will be presented. F-TRIDYN has been further upgraded with an alternative, statistical model of surface roughness. The statistical model is significantly faster than and compares favorably to the fractal model. Additionally, the statistical model compares well to alternative computational surface roughness models and experiments. Theoretical links between the fractal and statistical models are made, and further connections to experimental measurements of surface roughness are explored. This work was supported by the PSI-SciDAC Project funded by the U.S. Department of Energy through contract DOE-DE-SC0008658.

Human Age Recognition by Electrocardiogram Signal Based on Artificial Neural Network

NASA Astrophysics Data System (ADS)

Dasgupta, Hirak

2016-12-01

The objective of this work is to make a neural network function approximation model to detect human age from the electrocardiogram (ECG) signal. The input vectors of the neural network are the Katz fractal dimension of the ECG signal, frequencies in the QRS complex, male or female (represented by numeric constant) and the average of successive R-R peak distance of a particular ECG signal. The QRS complex has been detected by short time Fourier transform algorithm. The successive R peak has been detected by, first cutting the signal into periods by auto-correlation method and then finding the absolute of the highest point in each period. The neural network used in this problem consists of two layers, with Sigmoid neuron in the input and linear neuron in the output layer. The result shows the mean of errors as -0.49, 1.03, 0.79 years and the standard deviation of errors as 1.81, 1.77, 2.70 years during training, cross validation and testing with unknown data sets, respectively.

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.

Chimera states in networks of logistic maps with hierarchical connectivities

NASA Astrophysics Data System (ADS)

zur Bonsen, Alexander; Omelchenko, Iryna; Zakharova, Anna; Schöll, Eckehard

2018-04-01

Chimera states are complex spatiotemporal patterns consisting of coexisting domains of coherence and incoherence. We study networks of nonlocally coupled logistic maps and analyze systematically how the dilution of the network links influences the appearance of chimera patterns. The network connectivities are constructed using an iterative Cantor algorithm to generate fractal (hierarchical) connectivities. Increasing the hierarchical level of iteration, we compare the resulting spatiotemporal patterns. We demonstrate that a high clustering coefficient and symmetry of the base pattern promotes chimera states, and asymmetric connectivities result in complex nested chimera patterns.

Path tortuosity in everyday movements of elderly persons increases fall prediction beyond knowledge of fall history, medication use, and standardized gait and balance assessments.

PubMed

Kearns, William D; Fozard, James L; Becker, Marion; Jasiewicz, Jan M; Craighead, Jeffrey D; Holtsclaw, Lori; Dion, Charles

2012-09-01

We hypothesized that variability in voluntary movement paths of assisted living facility (ALF) residents would be greater in the week preceding a fall compared with residents who did not fall. Prospective, observational study using telesurveillance technology. Two ALFs. The sample consisted of 69 older ALF residents (53 female) aged 76.9 (SD ± 11.9 years). Daytime movement in ALF common use areas was automatically tracked using a commercially available ultra-wideband radio real-time location sensor network with a spatial resolution of approximately 20 cm. Movement path variability (tortuosity) was gauged using fractal dimension (fractal D). A logistic regression was performed predicting movement related falls from fractal D, presence of a fall in the prior year, psychoactive medication use, and movement path length. Fallers and non-fallers were also compared on activities of daily living requiring supervision or assistance, performance on standardized static and dynamic balance, and stride velocity assessments gathered at the start of a 1-year fall observation period. Fall risk due to cognitive deficit was assessed by the Mini Mental Status Examination (MMSE), and by clinical dementia diagnoses from participant's activities of daily living health record. Logistic regression analysis revealed odds of falling increased 2.548 (P = .021) for every 0.1 increase in fractal D, and having a fall in the prior year increased odds of falling by 7.36 (P = .006). There was a trend for longer movement paths to reduce the odds of falling (OR .976 P = .08) but it was not significant. Number of psychoactive medications did not contribute significantly to fall prediction in the model. Fallers had more variable stride-to-stride velocities and required more activities of daily living assistance. High fractal D levels can be detected using commercially available telesurveillance technologies and offers a new tool for health services administrators seeking to reduce falls at their facilities. Copyright © 2012 American Medical Directors Association. Published by Elsevier Inc. All rights reserved.

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.

Multifractal modeling, segmentation, prediction, and statistical validation of posterior fossa tumors

NASA Astrophysics Data System (ADS)

Islam, Atiq; Iftekharuddin, Khan M.; Ogg, Robert J.; Laningham, Fred H.; Sivakumar, Bhuvaneswari

2008-03-01

In this paper, we characterize the tumor texture in pediatric brain magnetic resonance images (MRIs) and exploit these features for automatic segmentation of posterior fossa (PF) tumors. We focus on PF tumor because of the prevalence of such tumor in pediatric patients. Due to varying appearance in MRI, we propose to model the tumor texture with a multi-fractal process, such as a multi-fractional Brownian motion (mBm). In mBm, the time-varying Holder exponent provides flexibility in modeling irregular tumor texture. We develop a detailed mathematical framework for mBm in two-dimension and propose a novel algorithm to estimate the multi-fractal structure of tissue texture in brain MRI based on wavelet coefficients. This wavelet based multi-fractal feature along with MR image intensity and a regular fractal feature obtained using our existing piecewise-triangular-prism-surface-area (PTPSA) method, are fused in segmenting PF tumor and non-tumor regions in brain T1, T2, and FLAIR MR images respectively. We also demonstrate a non-patient-specific automated tumor prediction scheme based on these image features. We experimentally show the tumor discriminating power of our novel multi-fractal texture along with intensity and fractal features in automated tumor segmentation and statistical prediction. To evaluate the performance of our tumor prediction scheme, we obtain ROCs and demonstrate how sharply the curves reach the specificity of 1.0 sacrificing minimal sensitivity. Experimental results show the effectiveness of our proposed techniques in automatic detection of PF tumors in pediatric MRIs.

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.

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.

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

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.

Fractal based curves in musical creativity: A critical annotation

NASA Astrophysics Data System (ADS)

Georgaki, Anastasia; Tsolakis, Christos

In this article we examine fractal curves and synthesis algorithms in musical composition and research. First we trace the evolution of different approaches for the use of fractals in music since the 80's by a literature review. Furthermore, we review representative fractal algorithms and platforms that implement them. Properties such as self-similarity (pink noise), correlation, memory (related to the notion of Brownian motion) or non correlation at multiple levels (white noise), can be used to develop hierarchy of criteria for analyzing different layers of musical structure. L-systems can be applied in the modelling of melody in different musical cultures as well as in the investigation of musical perception principles. Finally, we propose a critical investigation approach for the use of artificial or natural fractal curves in systematic musicology.

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/

Complexity and multifractality of neuronal noise in mouse and human hippocampal epileptiform dynamics.

PubMed

Serletis, Demitre; Bardakjian, Berj L; Valiante, Taufik A; Carlen, Peter L

2012-10-01

Fractal methods offer an invaluable means of investigating turbulent nonlinearity in non-stationary biomedical recordings from the brain. Here, we investigate properties of complexity (i.e. the correlation dimension, maximum Lyapunov exponent, 1/f(γ) noise and approximate entropy) and multifractality in background neuronal noise-like activity underlying epileptiform transitions recorded at the intracellular and local network scales from two in vitro models: the whole-intact mouse hippocampus and lesional human hippocampal slices. Our results show evidence for reduced dynamical complexity and multifractal signal features following transition to the ictal epileptiform state. These findings suggest that pathological breakdown in multifractal complexity coincides with loss of signal variability or heterogeneity, consistent with an unhealthy ictal state that is far from the equilibrium of turbulent yet healthy fractal dynamics in the brain. Thus, it appears that background noise-like activity successfully captures complex and multifractal signal features that may, at least in part, be used to classify and identify brain state transitions in the healthy and epileptic brain, offering potential promise for therapeutic neuromodulatory strategies for afflicted patients suffering from epilepsy and other related neurological disorders.

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.

Retinal Vascular Fractal Dimension, Childhood IQ, and Cognitive Ability in Old Age: The Lothian Birth Cohort Study 1936

PubMed Central

Taylor, Adele M.; MacGillivray, Thomas J.; Henderson, Ross D.; Ilzina, Lasma; Dhillon, Baljean; Starr, John M.; Deary, Ian J.

2015-01-01

Purpose Cerebral microvascular disease is associated with dementia. Differences in the topography of the retinal vascular network may be a marker for cerebrovascular disease. The association between cerebral microvascular state and non-pathological cognitive ageing is less clear, particularly because studies are rarely able to adjust for pre-morbid cognitive ability level. We measured retinal vascular fractal dimension (D f) as a potential marker of cerebral microvascular disease. We examined the extent to which it contributes to differences in non-pathological cognitive ability in old age, after adjusting for childhood mental ability. Methods Participants from the Lothian Birth Cohort 1936 Study (LBC1936) had cognitive ability assessments and retinal photographs taken of both eyes aged around 73 years (n = 648). IQ scores were available from childhood. Retinal vascular D f was calculated with monofractal and multifractal analysis, performed on custom-written software. Multiple regression models were applied to determine associations between retinal vascular D f and general cognitive ability (g), processing speed, and memory. Results Only three out of 24 comparisons (two eyes × four D f parameters × three cognitive measures) were found to be significant. This is little more than would be expected by chance. No single association was verified by an equivalent association in the contralateral eye. Conclusions The results show little evidence that fractal measures of retinal vascular differences are associated with non-pathological cognitive ageing. PMID:25816017

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.

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.

Breathing of voltage dependent anion channel as revealed by the fractal property of its gating

NASA Astrophysics Data System (ADS)

Manna, Smarajit; Banerjee, Jyotirmoy; Ghosh, Subhendu

2007-12-01

The gating of voltage dependent anion channel (VDAC) depends on the movement of voltage sensors in the transmembrane region, but the actual mechanism is still not well understood. With a view to understand the phenomenon we have analyzed the current recordings of VDAC in lipid bilayer membrane (BLM) and found that the data show self-similarity and fractal characteristics. We look for the microscopic and molecular basis of fractal behavior of gating of VDAC. A model describing the oscillatory dynamics of voltage sensors of VDAC in the transmembrane region under applied potential has been proposed which gives rise to the aforesaid fractal behavior.

From standard alpha-stable Lévy motions to horizontal visibility networks: dependence of multifractal and Laplacian spectrum

NASA Astrophysics Data System (ADS)

Zou, Hai-Long; Yu, Zu-Guo; Anh, Vo; Ma, Yuan-Lin

2018-05-01

In recent years, researchers have proposed several methods to transform time series (such as those of fractional Brownian motion) into complex networks. In this paper, we construct horizontal visibility networks (HVNs) based on the -stable Lévy motion. We aim to study the relations of multifractal and Laplacian spectrum of transformed networks on the parameters and of the -stable Lévy motion. First, we employ the sandbox algorithm to compute the mass exponents and multifractal spectrum to investigate the multifractality of these HVNs. Then we perform least squares fits to find possible relations of the average fractal dimension , the average information dimension and the average correlation dimension against using several methods of model selection. We also investigate possible dependence relations of eigenvalues and energy on , calculated from the Laplacian and normalized Laplacian operators of the constructed HVNs. All of these constructions and estimates will help us to evaluate the validity and usefulness of the mappings between time series and networks, especially between time series of -stable Lévy motions and HVNs.

Energy Spectral Behaviors of Communication Networks of Open-Source Communities

PubMed Central

Yang, Jianmei; Yang, Huijie; Liao, Hao; Wang, Jiangtao; Zeng, Jinqun

2015-01-01

Large-scale online collaborative production activities in open-source communities must be accompanied by large-scale communication activities. Nowadays, the production activities of open-source communities, especially their communication activities, have been more and more concerned. Take CodePlex C # community for example, this paper constructs the complex network models of 12 periods of communication structures of the community based on real data; then discusses the basic concepts of quantum mapping of complex networks, and points out that the purpose of the mapping is to study the structures of complex networks according to the idea of quantum mechanism in studying the structures of large molecules; finally, according to this idea, analyzes and compares the fractal features of the spectra in different quantum mappings of the networks, and concludes that there are multiple self-similarity and criticality in the communication structures of the community. In addition, this paper discusses the insights and application conditions of different quantum mappings in revealing the characteristics of the structures. The proposed quantum mapping method can also be applied to the structural studies of other large-scale organizations. PMID:26047331

Fractals, Coherence and Brain Dynamics

NASA Astrophysics Data System (ADS)

Vitiello, Giuseppe

2010-11-01

I show that the self-similarity property of deterministic fractals provides a direct connection with the space of the entire analytical functions. Fractals are thus described in terms of coherent states in the Fock-Bargmann representation. Conversely, my discussion also provides insights on the geometrical properties of coherent states: it allows to recognize, in some specific sense, fractal properties of coherent states. In particular, the relation is exhibited between fractals and q-deformed coherent states. The connection with the squeezed coherent states is also displayed. In this connection, the non-commutative geometry arising from the fractal relation with squeezed coherent states is discussed and the fractal spectral properties are identified. I also briefly discuss the description of neuro-phenomenological data in terms of squeezed coherent states provided by the dissipative model of brain and consider the fact that laboratory observations have shown evidence that self-similarity characterizes the brain background activity. This suggests that a connection can be established between brain dynamics and the fractal self-similarity properties on the basis of the relation discussed in this report between fractals and squeezed coherent states. Finally, I do not consider in this paper the so-called random fractals, namely those fractals obtained by randomization processes introduced in their iterative generation. Since self-similarity is still a characterizing property in many of such random fractals, my conjecture is that also in such cases there must exist a connection with the coherent state algebraic structure. In condensed matter physics, in many cases the generation by the microscopic dynamics of some kind of coherent states is involved in the process of the emergence of mesoscopic/macroscopic patterns. The discussion presented in this paper suggests that also fractal generation may provide an example of emergence of global features, namely long range correlation at mesoscopic/macroscopic level, from microscopic local deformation processes. In view of the wide spectrum of application of both, fractal studies and coherent state physics, spanning from solid state physics to laser physics, quantum optics, complex dynamical systems and biological systems, the results presented in the present report may lead to interesting practical developments in many research sectors.

A diffusivity model for predicting VOC diffusion in porous building materials based on fractal theory.

PubMed

Liu, Yanfeng; Zhou, Xiaojun; Wang, Dengjia; Song, Cong; Liu, Jiaping

2015-12-15

Most building materials are porous media, and the internal diffusion coefficients of such materials have an important influences on the emission characteristics of volatile organic compounds (VOCs). The pore structure of porous building materials has a significant impact on the diffusion coefficient. However, the complex structural characteristics bring great difficulties to the model development. The existing prediction models of the diffusion coefficient are flawed and need to be improved. Using scanning electron microscope (SEM) observations and mercury intrusion porosimetry (MIP) tests of typical porous building materials, this study developed a new diffusivity model: the multistage series-connection fractal capillary-bundle (MSFC) model. The model considers the variable-diameter capillaries formed by macropores connected in series as the main mass transfer paths, and the diameter distribution of the capillary bundles obeys a fractal power law in the cross section. In addition, the tortuosity of the macrocapillary segments with different diameters is obtained by the fractal theory. Mesopores serve as the connections between the macrocapillary segments rather than as the main mass transfer paths. The theoretical results obtained using the MSFC model yielded a highly accurate prediction of the diffusion coefficients and were in a good agreement with the VOC concentration measurements in the environmental test chamber. Copyright © 2015 Elsevier B.V. All rights reserved.

Chaos in a dynamic model of traffic flows in an origin-destination network.

PubMed

Zhang, Xiaoyan; Jarrett, David F.

1998-06-01

In this paper we investigate the dynamic behavior of road traffic flows in an area represented by an origin-destination (O-D) network. Probably the most widely used model for estimating the distribution of O-D flows is the gravity model, [J. de D. Ortuzar and L. G. Willumsen, Modelling Transport (Wiley, New York, 1990)] which originated from an analogy with Newton's gravitational law. The conventional gravity model, however, is static. The investigation in this paper is based on a dynamic version of the gravity model proposed by Dendrinos and Sonis by modifying the conventional gravity model [D. S. Dendrinos and M. Sonis, Chaos and Social-Spatial Dynamics (Springer-Verlag, Berlin, 1990)]. The dynamic model describes the variations of O-D flows over discrete-time periods, such as each day, each week, and so on. It is shown that when the dimension of the system is one or two, the O-D flow pattern either approaches an equilibrium or oscillates. When the dimension is higher, the behavior found in the model includes equilibria, oscillations, periodic doubling, and chaos. Chaotic attractors are characterized by (positive) Liapunov exponents and fractal dimensions.(c) 1998 American Institute of Physics.

Fractal: An Educational Model for the Convergence of Formal and Non-Formal Education

ERIC Educational Resources Information Center

Enríquez, Larisa

2017-01-01

For the last two decades, different authors have mentioned the need to have new pedagogies that respond better to current times, which are surrounded by a complex set of issues such as mobility, interculturality, curricular flexibility, accreditation and academic coverage. Fractal is an educational model proposal for online learning that is formed…

Synthetic Minority Oversampling Technique and Fractal Dimension for Identifying Multiple Sclerosis

NASA Astrophysics Data System (ADS)

Zhang, Yu-Dong; Zhang, Yin; Phillips, Preetha; Dong, Zhengchao; Wang, Shuihua

Multiple sclerosis (MS) is a severe brain disease. Early detection can provide timely treatment. Fractal dimension can provide statistical index of pattern changes with scale at a given brain image. In this study, our team used susceptibility weighted imaging technique to obtain 676 MS slices and 880 healthy slices. We used synthetic minority oversampling technique to process the unbalanced dataset. Then, we used Canny edge detector to extract distinguishing edges. The Minkowski-Bouligand dimension was a fractal dimension estimation method and used to extract features from edges. Single hidden layer neural network was used as the classifier. Finally, we proposed a three-segment representation biogeography-based optimization to train the classifier. Our method achieved a sensitivity of 97.78±1.29%, a specificity of 97.82±1.60% and an accuracy of 97.80±1.40%. The proposed method is superior to seven state-of-the-art methods in terms of sensitivity and accuracy.

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.

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.

Characterization of complex networks by higher order neighborhood properties

NASA Astrophysics Data System (ADS)

Andrade, R. F. S.; Miranda, J. G. V.; Pinho, S. T. R.; Lobão, T. P.

2008-01-01

A concept of higher order neighborhood in complex networks, introduced previously [Phys. Rev. E 73, 046101 (2006)], is systematically explored to investigate larger scale structures in complex networks. The basic idea is to consider each higher order neighborhood as a network in itself, represented by a corresponding adjacency matrix, and to settle a plenty of new parameters in order to obtain a best characterization of the whole network. Usual network indices are then used to evaluate the properties of each neighborhood. The identification of high order neighborhoods is also regarded as intermediary step towards the evaluation of global network properties, like the diameter, average shortest path between node, and network fractal dimension. Results for a large number of typical networks are presented and discussed.

Fractal Measure and Microscopic Modeling of Osseointegration.

PubMed

Santos, Leonardo Cavalcanti Bezerra; Carvalho, Alessandra Albuquerque; Leão, Jair Carneiro; Neto, Paulo Jose; Stosic, Tatijana; Stosic, Borko

2015-01-01

In this study, the process of osseointegration on titanium implant surfaces with different physicochemical treatments subjected to a simulated corporal fluid submersion was evaluated using the concept of fractal dimension. It was found that different treatments led to rather different calcium phosphate crystal growth patterns, with fractal dimension ranging from 1.68 to 1.93. The observed crystal patterns may be explained by a general deposition, diffusion, and aggregation growth mechanism, where diffusing particle sticking probability plays a fundamental role.

Test-Retest Reliability of fMRI Brain Activity during Memory Encoding

PubMed Central

Brandt, David J.; Sommer, Jens; Krach, Sören; Bedenbender, Johannes; Kircher, Tilo; Paulus, Frieder M.; Jansen, Andreas

2013-01-01

The mechanisms underlying hemispheric specialization of memory are not completely understood. Functional magnetic resonance imaging (fMRI) can be used to develop and test models of hemispheric specialization. In particular for memory tasks however, the interpretation of fMRI results is often hampered by the low reliability of the data. In the present study we therefore analyzed the test-retest reliability of fMRI brain activation related to an implicit memory encoding task, with a particular focus on brain activity of the medial temporal lobe (MTL). Fifteen healthy subjects were scanned with fMRI on two sessions (average retest interval 35 days) using a commonly applied novelty encoding paradigm contrasting known and unknown stimuli. To assess brain lateralization, we used three different stimuli classes that differed in their verbalizability (words, scenes, fractals). Test-retest reliability of fMRI brain activation was assessed by an intraclass-correlation coefficient (ICC), describing the stability of inter-individual differences in the brain activation magnitude over time. We found as expected a left-lateralized brain activation network for the words paradigm, a bilateral network for the scenes paradigm, and predominantly right-hemispheric brain activation for the fractals paradigm. Although these networks were consistently activated in both sessions on the group level, across-subject reliabilities were only poor to fair (ICCs ≤ 0.45). Overall, the highest ICC values were obtained for the scenes paradigm, but only in strongly activated brain regions. In particular the reliability of brain activity of the MTL was poor for all paradigms. In conclusion, for novelty encoding paradigms the interpretation of fMRI results on a single subject level is hampered by its low reliability. More studies are needed to optimize the retest reliability of fMRI activation for memory tasks. PMID:24367338

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.

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.

Fractional viscoelasticity in fractal and non-fractal media: Theory, experimental validation, and uncertainty analysis

NASA Astrophysics Data System (ADS)

Mashayekhi, Somayeh; Miles, Paul; Hussaini, M. Yousuff; Oates, William S.

2018-02-01

In this paper, fractional and non-fractional viscoelastic models for elastomeric materials are derived and analyzed in comparison to experimental results. The viscoelastic models are derived by expanding thermodynamic balance equations for both fractal and non-fractal media. The order of the fractional time derivative is shown to strongly affect the accuracy of the viscoelastic constitutive predictions. Model validation uses experimental data describing viscoelasticity of the dielectric elastomer Very High Bond (VHB) 4910. Since these materials are known for their broad applications in smart structures, it is important to characterize and accurately predict their behavior across a large range of time scales. Whereas integer order viscoelastic models can yield reasonable agreement with data, the model parameters often lack robustness in prediction at different deformation rates. Alternatively, fractional order models of viscoelasticity provide an alternative framework to more accurately quantify complex rate-dependent behavior. Prior research that has considered fractional order viscoelasticity lacks experimental validation and contains limited links between viscoelastic theory and fractional order derivatives. To address these issues, we use fractional order operators to experimentally validate fractional and non-fractional viscoelastic models in elastomeric solids using Bayesian uncertainty quantification. The fractional order model is found to be advantageous as predictions are significantly more accurate than integer order viscoelastic models for deformation rates spanning four orders of magnitude.

Universal Inverse Power-Law Distribution for Fractal Fluctuations in Dynamical Systems: Applications for Predictability of Inter-Annual Variability of Indian and USA Region Rainfall

NASA Astrophysics Data System (ADS)

Selvam, A. M.

2017-01-01

Dynamical systems in nature exhibit self-similar fractal space-time fluctuations on all scales indicating long-range correlations and, therefore, the statistical normal distribution with implicit assumption of independence, fixed mean and standard deviation cannot be used for description and quantification of fractal data sets. The author has developed a general systems theory based on classical statistical physics for fractal fluctuations which predicts the following. (1) The fractal fluctuations signify an underlying eddy continuum, the larger eddies being the integrated mean of enclosed smaller-scale fluctuations. (2) The probability distribution of eddy amplitudes and the variance (square of eddy amplitude) spectrum of fractal fluctuations follow the universal Boltzmann inverse power law expressed as a function of the golden mean. (3) Fractal fluctuations are signatures of quantum-like chaos since the additive amplitudes of eddies when squared represent probability densities analogous to the sub-atomic dynamics of quantum systems such as the photon or electron. (4) The model predicted distribution is very close to statistical normal distribution for moderate events within two standard deviations from the mean but exhibits a fat long tail that are associated with hazardous extreme events. Continuous periodogram power spectral analyses of available GHCN annual total rainfall time series for the period 1900-2008 for Indian and USA stations show that the power spectra and the corresponding probability distributions follow model predicted universal inverse power law form signifying an eddy continuum structure underlying the observed inter-annual variability of rainfall. On a global scale, man-made greenhouse gas related atmospheric warming would result in intensification of natural climate variability, seen immediately in high frequency fluctuations such as QBO and ENSO and even shorter timescales. Model concepts and results of analyses are discussed with reference to possible prediction of climate change. Model concepts, if correct, rule out unambiguously, linear trends in climate. Climate change will only be manifested as increase or decrease in the natural variability. However, more stringent tests of model concepts and predictions are required before applications to such an important issue as climate change. Observations and simulations with climate models show that precipitation extremes intensify in response to a warming climate (O'Gorman in Curr Clim Change Rep 1:49-59, 2015).

A fractal derivative model for the characterization of anomalous diffusion in magnetic resonance imaging

NASA Astrophysics Data System (ADS)

Liang, Yingjie; Ye, Allen Q.; Chen, Wen; Gatto, Rodolfo G.; Colon-Perez, Luis; Mareci, Thomas H.; Magin, Richard L.

2016-10-01

Non-Gaussian (anomalous) diffusion is wide spread in biological tissues where its effects modulate chemical reactions and membrane transport. When viewed using magnetic resonance imaging (MRI), anomalous diffusion is characterized by a persistent or 'long tail' behavior in the decay of the diffusion signal. Recent MRI studies have used the fractional derivative to describe diffusion dynamics in normal and post-mortem tissue by connecting the order of the derivative with changes in tissue composition, structure and complexity. In this study we consider an alternative approach by introducing fractal time and space derivatives into Fick's second law of diffusion. This provides a more natural way to link sub-voxel tissue composition with the observed MRI diffusion signal decay following the application of a diffusion-sensitive pulse sequence. Unlike previous studies using fractional order derivatives, here the fractal derivative order is directly connected to the Hausdorff fractal dimension of the diffusion trajectory. The result is a simpler, computationally faster, and more direct way to incorporate tissue complexity and microstructure into the diffusional dynamics. Furthermore, the results are readily expressed in terms of spectral entropy, which provides a quantitative measure of the overall complexity of the heterogeneous and multi-scale structure of biological tissues. As an example, we apply this new model for the characterization of diffusion in fixed samples of the mouse brain. These results are compared with those obtained using the mono-exponential, the stretched exponential, the fractional derivative, and the diffusion kurtosis models. Overall, we find that the order of the fractal time derivative, the diffusion coefficient, and the spectral entropy are potential biomarkers to differentiate between the microstructure of white and gray matter. In addition, we note that the fractal derivative model has practical advantages over the existing models from the perspective of computational accuracy and efficiency.

The relevance of network micro-structure for neural dynamics.

PubMed

Pernice, Volker; Deger, Moritz; Cardanobile, Stefano; Rotter, Stefan

2013-01-01

The activity of cortical neurons is determined by the input they receive from presynaptic neurons. Many previous studies have investigated how specific aspects of the statistics of the input affect the spike trains of single neurons and neurons in recurrent networks. However, typically very simple random network models are considered in such studies. Here we use a recently developed algorithm to construct networks based on a quasi-fractal probability measure which are much more variable than commonly used network models, and which therefore promise to sample the space of recurrent networks in a more exhaustive fashion than previously possible. We use the generated graphs as the underlying network topology in simulations of networks of integrate-and-fire neurons in an asynchronous and irregular state. Based on an extensive dataset of networks and neuronal simulations we assess statistical relations between features of the network structure and the spiking activity. Our results highlight the strong influence that some details of the network structure have on the activity dynamics of both single neurons and populations, even if some global network parameters are kept fixed. We observe specific and consistent relations between activity characteristics like spike-train irregularity or correlations and network properties, for example the distributions of the numbers of in- and outgoing connections or clustering. Exploiting these relations, we demonstrate that it is possible to estimate structural characteristics of the network from activity data. We also assess higher order correlations of spiking activity in the various networks considered here, and find that their occurrence strongly depends on the network structure. These results provide directions for further theoretical studies on recurrent networks, as well as new ways to interpret spike train recordings from neural circuits.

Beyond Scale-Free Small-World Networks: Cortical Columns for Quick Brains

NASA Astrophysics Data System (ADS)

Stoop, Ralph; Saase, Victor; Wagner, Clemens; Stoop, Britta; Stoop, Ruedi

2013-03-01

We study to what extent cortical columns with their particular wiring boost neural computation. Upon a vast survey of columnar networks performing various real-world cognitive tasks, we detect no signs of enhancement. It is on a mesoscopic—intercolumnar—scale that the existence of columns, largely irrespective of their inner organization, enhances the speed of information transfer and minimizes the total wiring length required to bind distributed columnar computations towards spatiotemporally coherent results. We suggest that brain efficiency may be related to a doubly fractal connectivity law, resulting in networks with efficiency properties beyond those by scale-free networks.

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.

Fractal-like kinetics, a possible link between preconditioning and sepsis immunodepression. On the chemical basis of innate immunity.

PubMed

Vasilescu, C; Olteanu, M; Flondor, P

2012-01-01

In a recent paper the authors hypothesized that the so called fractal-like enzyme kinetics of intracellular reactions may explain the preconditioning effect in biology (Vasilescu C, Olteanu M, Flondor P, Revue Roumaine de Chimie. 2011; 56(7): 751-7). Inside cells the reaction kinetics is very well described by fractal-like kinetics. In the present work some clinical implications of this model are analyzed. Endotoxin tolerance is a particular case of preconditioning and shows similarities with the immunodepression seen in some sepsis patients. This idea offers a theoretical support for modulation of the enzymatic activity of the cell by changing the fractal dimension of the cytoskeleton.

Toward a Time-Domain Fractal Lightning Simulation

NASA Astrophysics Data System (ADS)

Liang, C.; Carlson, B. E.; Lehtinen, N. G.; Cohen, M.; Lauben, D.; Inan, U. S.

2010-12-01

Electromagnetic simulations of lightning are useful for prediction of lightning properties and exploration of the underlying physical behavior. Fractal lightning models predict the spatial structure of the discharge, but thus far do not provide much information about discharge behavior in time and therefore cannot predict electromagnetic wave emissions or current characteristics. Here we develop a time-domain fractal lightning simulation from Maxwell's equations, the method of moments with the thin wire approximation, an adaptive time-stepping scheme, and a simplified electrical model of the lightning channel. The model predicts current pulse structure and electromagnetic wave emissions and can be used to simulate the entire duration of a lightning discharge. The model can be used to explore the electrical characteristics of the lightning channel, the temporal development of the discharge, and the effects of these characteristics on observable electromagnetic wave emissions.

Fractal and chaotic laws on seismic dissipated energy in an energy system of engineering structures

NASA Astrophysics Data System (ADS)

Cui, Yu-Hong; Nie, Yong-An; Yan, Zong-Da; Wu, Guo-You

1998-09-01

Fractal and chaotic laws of engineering structures are discussed in this paper, it means that the intrinsic essences and laws on dynamic systems which are made from seismic dissipated energy intensity E d and intensity of seismic dissipated energy moment I e are analyzed. Based on the intrinsic characters of chaotic and fractal dynamic system of E d and I e, three kinds of approximate dynamic models are rebuilt one by one: index autoregressive model, threshold autoregressive model and local-approximate autoregressive model. The innate laws, essences and systematic error of evolutional behavior I e are explained over all, the short-term behavior predictability and long-term behavior probability of which are analyzed in the end. That may be valuable for earthquake-resistant theory and analysis method in practical engineering structures.

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.

Pond fractals in a tidal flat.

PubMed

Cael, B B; Lambert, Bennett; Bisson, Kelsey

2015-11-01

Studies over the past decade have reported power-law distributions for the areas of terrestrial lakes and Arctic melt ponds, as well as fractal relationships between their areas and coastlines. Here we report similar fractal structure of ponds in a tidal flat, thereby extending the spatial and temporal scales on which such phenomena have been observed in geophysical systems. Images taken during low tide of a tidal flat in Damariscotta, Maine, reveal a well-resolved power-law distribution of pond sizes over three orders of magnitude with a consistent fractal area-perimeter relationship. The data are consistent with the predictions of percolation theory for unscreened perimeters and scale-free cluster size distributions and are robust to alterations of the image processing procedure. The small spatial and temporal scales of these data suggest this easily observable system may serve as a useful model for investigating the evolution of pond geometries, while emphasizing the generality of fractal behavior in geophysical surfaces.

Pond fractals in a tidal flat

NASA Astrophysics Data System (ADS)

Cael, B. B.; Lambert, Bennett; Bisson, Kelsey

2015-11-01

Studies over the past decade have reported power-law distributions for the areas of terrestrial lakes and Arctic melt ponds, as well as fractal relationships between their areas and coastlines. Here we report similar fractal structure of ponds in a tidal flat, thereby extending the spatial and temporal scales on which such phenomena have been observed in geophysical systems. Images taken during low tide of a tidal flat in Damariscotta, Maine, reveal a well-resolved power-law distribution of pond sizes over three orders of magnitude with a consistent fractal area-perimeter relationship. The data are consistent with the predictions of percolation theory for unscreened perimeters and scale-free cluster size distributions and are robust to alterations of the image processing procedure. The small spatial and temporal scales of these data suggest this easily observable system may serve as a useful model for investigating the evolution of pond geometries, while emphasizing the generality of fractal behavior in geophysical surfaces.

On the Relationship of the Fractal Dimension of Structure with the State of Drying Drops of Crystallizing Solutions (Thermodynamic and Experimental Modeling)

NASA Astrophysics Data System (ADS)

Golovanova, O. A.; Chikanova, E. S.; Fedoseev, V. B.

2018-05-01

The processes occurring in aqueous salt solutions have been investigated based on thermodynamic and experimental modeling. The self-organization in a drying drop of dehydrated liquids is analyzed using the fractal theory, due to which the quantitative characteristics of the crystallization processes in a small volume are obtained.

Fractal-like kinetics of intracellular enzymatic reactions: a chemical framework of endotoxin tolerance and a possible non-specific contribution of macromolecular crowding to cross-tolerance.

PubMed

Vasilescu, Catalin; Olteanu, Mircea; Flondor, Paul; Calin, George A

2013-09-14

The response to endotoxin (LPS), and subsequent signal transduction lead to the production of cytokines such as tumor necrosis factor-α (TNF-α) by innate immune cells. Cells or organisms pretreated with endotoxin enter into a transient state of hyporesponsiveness, referred to as endotoxin tolerance (ET) which represents a particular case of negative preconditioning. Despite recent progress in understanding the molecular basis of ET, there is no consensus yet on the primary mechanism responsible for ET and for the more complex cases of cross tolerance. In this study, we examined the consequences of the macromolecular crowding (MMC) and of fractal-like kinetics (FLK) of intracellular enzymatic reactions on the LPS signaling machinery. We hypothesized that this particular type of enzyme kinetics may explain the development of ET phenomenon. Our aim in the present study was to characterize the chemical kinetics framework in ET and determine whether fractal-like kinetics explains, at least in part, ET. We developed an ordinary differential equations (ODE) mathematical model that took into account the links between the MMC and the LPS signaling machinery leading to ET. We proposed that the intracellular fractal environment (MMC) contributes to ET and developed two mathematical models of enzyme kinetics: one based on Kopelman's fractal-like kinetics framework and the other based on Savageau's power law model. Kopelman's model provides a good image of the potential influence of a fractal intracellular environment (MMC) on ET. The Savageau power law model also partially explains ET. The computer simulations supported the hypothesis that MMC and FLK may play a role in ET. The model highlights the links between the organization of the intracellular environment, MMC and the LPS signaling machinery leading to ET. Our FLK-based model does not minimize the role of the numerous negative regulatory factors. It simply draws attention to the fact that macromolecular crowding can contribute significantly to the induction of ET by imposing geometric constrains and a particular chemical kinetic for the intracellular reactions.

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.

A Complex Story: Universal Preference vs. Individual Differences Shaping Aesthetic Response to Fractals Patterns

PubMed Central

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. PMID:27252634

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.

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.

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.

Fractal dimension of interfaces in Edwards-Anderson spin glasses for up to six space dimensions.

PubMed

Wang, Wenlong; Moore, M A; Katzgraber, Helmut G

2018-03-01

The fractal dimension of domain walls produced by changing the boundary conditions from periodic to antiperiodic in one spatial direction is studied using both the strong-disorder renormalization group algorithm and the greedy algorithm for the Edwards-Anderson Ising spin-glass model for up to six space dimensions. We find that for five or fewer space dimensions, the fractal dimension is lower than the space dimension. This means that interfaces are not space filling, thus implying that replica symmetry breaking is absent in space dimensions fewer than six. However, the fractal dimension approaches the space dimension in six dimensions, indicating that replica symmetry breaking occurs above six dimensions. In two space dimensions, the strong-disorder renormalization group results for the fractal dimension are in good agreement with essentially exact numerical results, but the small difference is significant. We discuss the origin of this close agreement. For the greedy algorithm there is analytical expectation that the fractal dimension is equal to the space dimension in six dimensions and our numerical results are consistent with this expectation.

Temporal behavior of a solute cloud in a fractal heterogeneous porous medium at different scales

NASA Astrophysics Data System (ADS)

Ross, Katharina; Attinger, Sabine

2010-05-01

Water pollution is still a very real problem and the need for efficient models for flow and solute transport in heterogeneous porous or fractured media is evident. In our study we focus on solute transport in heterogeneous fractured media. In heterogeneous fractured media the shape of the pores and fractures in the subsurface might be modeled as a fractal network or a heterogeneous structure with infinite correlation length. To derive explicit results for larger scale or effective transport parameters in such structures is the aim of this work. To describe flow and transport we investigate the temporal behavior of transport coefficients of solute movement through a spatially heterogeneous medium. It is necessary to distinguish between two fundamentally different quantities characterizing the solute dispersion: The effective dispersion coefficient Deff(t) represents the physical (observable) dispersion in one given realization of the medium. It is conceptually different from the mathematically simpler ensemble dispersion coefficient Dens(t) which characterizes the (abstract) dispersion with respect to the set of all possible realizations of the medium. In the framework of a stochastic approach DENTZ ET AL. (2000 I[2] & II[3]) derive explicit expressions for the temporal behavior of the center-of-mass velocity and the dispersion of the concentration distribution, using a second order perturbation expansion. In their model the authors assume a finite correlation length of the heterogeneities and use a GAUSSIAN correlation function. In a first step, we model the fractured medium as a heterogeneous porous medium with infinite correlation length and neglect single fractures. ZHAN & WHEATCRAFT (1996[4]) analyze the macrodispersivity tensor in fractal porous media using a non-integer exponent which consists of the HURST coefficient and the fractal dimension D. To avoid this non-integer exponent for numerical reasons we extend the study of DENTZ ET AL. (2000 I[2] & II[3]) and derive explicit expressions for the center-of-mass velocity and the longitudinal dispersion coefficient for isotropic and anisotropic media as well as for point-like (where the extent of the source distribution is small compared to the correlation lengths of the heterogeneities) and spatially extended injections. Our results clearly show that the difference between Deff and Dens persists for all times. In other words, ensemble mixing and effective mixing coefficients do not approach the same asymptotic limit. The center-of-mass fluctuations between different flow paths for a plume traveling through the medium never become irrelevant and ergodicity breaks down in such media. Our ongoing work concerns the investigation of the transversal dispersion coefficient and the extension of the upscaling method coarse graining[1] to heterogeneous fractal porous media with embedded single fractures. References [1]ATTINGER, S. (2003): Generalized coarse graining procedures for flow in porous media, Computational Geosciences, 7 (4), pp. 253-273. [2]DENTZ, M. / KINZELBACH, H. / ATTINGER, S. and W. KINZELBACH (2000): Temporal behavior of a solute cloud in a heterogeneous porous medium: 1. Point-like injection, Water Resources Research, 36 (12), pp. 3591-3604. [3]DENTZ, M. / KINZELBACH, H. / ATTINGER, S. and W. KINZELBACH (2000): Temporal behavior of a solute cloud in a heterogeneous porous medium: 2. Spatially extended injection, Water Resources Research, 36 (12), pp. 3605-3614. [4]ZHAN, H. and S. W. WHEATCRAFT (1996): Macrodispersivity tensor for nonreactive solute transport in isotropic and anisotropic fractal porous media: Analytical solutions, Water Resources Research, 32 (12), pp. 3461-3474.

Stochastic simulation of karst conduit networks

NASA Astrophysics Data System (ADS)

Pardo-Igúzquiza, Eulogio; Dowd, Peter A.; Xu, Chaoshui; Durán-Valsero, Juan José

2012-01-01

Karst aquifers have very high spatial heterogeneity. Essentially, they comprise a system of pipes (i.e., the network of conduits) superimposed on rock porosity and on a network of stratigraphic surfaces and fractures. This heterogeneity strongly influences the hydraulic behavior of the karst and it must be reproduced in any realistic numerical model of the karst system that is used as input to flow and transport modeling. However, the directly observed karst conduits are only a small part of the complete karst conduit system and knowledge of the complete conduit geometry and topology remains spatially limited and uncertain. Thus, there is a special interest in the stochastic simulation of networks of conduits that can be combined with fracture and rock porosity models to provide a realistic numerical model of the karst system. Furthermore, the simulated model may be of interest per se and other uses could be envisaged. The purpose of this paper is to present an efficient method for conditional and non-conditional stochastic simulation of karst conduit networks. The method comprises two stages: generation of conduit geometry and generation of topology. The approach adopted is a combination of a resampling method for generating conduit geometries from templates and a modified diffusion-limited aggregation method for generating the network topology. The authors show that the 3D karst conduit networks generated by the proposed method are statistically similar to observed karst conduit networks or to a hypothesized network model. The statistical similarity is in the sense of reproducing the tortuosity index of conduits, the fractal dimension of the network, the direction rose of directions, the Z-histogram and Ripley's K-function of the bifurcation points (which differs from a random allocation of those bifurcation points). The proposed method (1) is very flexible, (2) incorporates any experimental data (conditioning information) and (3) can easily be modified when implemented in a hydraulic inverse modeling procedure. Several synthetic examples are given to illustrate the methodology and real conduit network data are used to generate simulated networks that mimic real geometries and topology.

Edge detection of optical subaperture image based on improved differential box-counting method

NASA Astrophysics Data System (ADS)

Li, Yi; Hui, Mei; Liu, Ming; Dong, Liquan; Kong, Lingqin; Zhao, Yuejin

2018-01-01

Optical synthetic aperture imaging technology is an effective approach to improve imaging resolution. Compared with monolithic mirror system, the image of optical synthetic aperture system is often more complex at the edge, and as a result of the existence of gap between segments, which makes stitching becomes a difficult problem. So it is necessary to extract the edge of subaperture image for achieving effective stitching. Fractal dimension as a measure feature can describe image surface texture characteristics, which provides a new approach for edge detection. In our research, an improved differential box-counting method is used to calculate fractal dimension of image, then the obtained fractal dimension is mapped to grayscale image to detect edges. Compared with original differential box-counting method, this method has two improvements as follows: by modifying the box-counting mechanism, a box with a fixed height is replaced by a box with adaptive height, which solves the problem of over-counting the number of boxes covering image intensity surface; an image reconstruction method based on super-resolution convolutional neural network is used to enlarge small size image, which can solve the problem that fractal dimension can't be calculated accurately under the small size image, and this method may well maintain scale invariability of fractal dimension. The experimental results show that the proposed algorithm can effectively eliminate noise and has a lower false detection rate compared with the traditional edge detection algorithms. In addition, this algorithm can maintain the integrity and continuity of image edge in the case of retaining important edge information.

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.

Temporal evolution of soil moisture statistical fractal and controls by soil texture and regional groundwater flow

NASA Astrophysics Data System (ADS)

Ji, Xinye; Shen, Chaopeng; Riley, William J.

2015-12-01

Soil moisture statistical fractal is an important tool for downscaling remotely-sensed observations and has the potential to play a key role in multi-scale hydrologic modeling. The fractal was first introduced two decades ago, but relatively little is known regarding how its scaling exponents evolve in time in response to climatic forcings. Previous studies have neglected the process of moisture re-distribution due to regional groundwater flow. In this study we used a physically-based surface-subsurface processes model and numerical experiments to elucidate the patterns and controls of fractal temporal evolution in two U.S. Midwest basins. Groundwater flow was found to introduce large-scale spatial structure, thereby reducing the scaling exponents (τ), which has implications for the transferability of calibrated parameters to predict τ. However, the groundwater effects depend on complex interactions with other physical controls such as soil texture and land use. The fractal scaling exponents, while in general showing a seasonal mode that correlates with mean moisture content, display hysteresis after storm events that can be divided into three phases, consistent with literature findings: (a) wetting, (b) re-organizing, and (c) dry-down. Modeling experiments clearly show that the hysteresis is attributed to soil texture, whose "patchiness" is the primary contributing factor. We generalized phenomenological rules for the impacts of rainfall, soil texture, groundwater flow, and land use on τ evolution. Grid resolution has a mild influence on the results and there is a strong correlation between predictions of τ from different resolutions. Overall, our results suggest that groundwater flow should be given more consideration in studies of the soil moisture statistical fractal, especially in regions with a shallow water table.

Fractal analysis of urban catchments and their representation in semi-distributed models: imperviousness and sewer system

NASA Astrophysics Data System (ADS)

Gires, Auguste; Tchiguirinskaia, Ioulia; Schertzer, Daniel; Ochoa-Rodriguez, Susana; Willems, Patrick; Ichiba, Abdellah; Wang, Lipen; Pina, Rui; Van Assel, Johan; Bruni, Guendalina; Murla Tuyls, Damian; ten Veldhuis, Marie-Claire

2017-04-01

Land use distribution and sewer system geometry exhibit complex scale dependent patterns in urban environment. This scale dependency is even more visible in a rasterized representation where only a unique class is affected to each pixel. Such features are well grasped with fractal tools, which are based scale invariance and intrinsically designed to characterise and quantify the space filled by a geometrical set exhibiting complex and tortuous patterns. Fractal tools have been widely used in hydrology but seldom in the specific context of urban hydrology. In this paper, they are used to analyse surface and sewer data from 10 urban or peri-urban catchments located in 5 European countries in the framework of the NWE Interreg RainGain project (www.raingain.eu). The aim was to characterise urban catchment properties accounting for the complexity and inhomogeneity typical of urban water systems. Sewer system density and imperviousness (roads or buildings), represented in rasterized maps of 2 m x 2 m pixels, were analysed to quantify their fractal dimension, characteristic of scaling invariance. It appears that both sewer density and imperviousness exhibit scale invariant features that can be characterized with the help of fractal dimensions ranging from 1.6 to 2, depending on the catchment. In a given area, consistent results were found for the two geometrical features, yielding a robust and innovative way of quantifying the level of urbanization. The representation of imperviousness in operational semi-distributed hydrological models for these catchments was also investigated by computing fractal dimensions of the geometrical sets made up of the sub-catchments with coefficients of imperviousness greater than a range of thresholds. It enables to quantify how well spatial structures of imperviousness are represented in the urban hydrological models.

Degree of time dependency of kinetic coefficient as a function of adsorbate concentration; new insights from adsorption of tetracycline onto monodispersed starch-stabilized magnetic nanocomposite.

PubMed

Okoli, Chukwunonso P; Ofomaja, Augustine E

2018-07-15

The realization that the observed kinetic coefficient (k obs ) varies with time in most real-time adsorption system, as against the constant value conceived in the most widely-applied adsorption kinetic models, have attracted much attention in recent time. Understanding the factors that control the extent/degree of time dependency (otherwise known as fractal-like kinetics), is therefore central in taking manipulative advantage of this phenomenon in critical adsorption applications. This study therefore deployed non-fractal-like and fractal-like kinetic approach to study the adsorption of tetracycline on monodispersed starch-stabilized magnetite nanocomposite (MSM). MSM was synthesized by in-situ coprecipitation of magnetite in the presence of starch, and successfully characterized with classical solid-state techniques. Isotherm studies indicated that MSM has heterogenous surface adsorption sites. Equilibrium and kinetic data indicated the existence of π-cation interaction as the underlying mechanism, while pH study revealed that tetracycline was adsorbed in its zwitterion form. Though the non-fractal kinetic models exhibited some level of relevance in explaining the tetracycline adsorption interactions, the best fitting of the fractal-like pseudo second order model to the adsorption kinetic data, indicated that the real-time adsorption kinetics occurred in fractal-like manner. The study also revealed that the degree of time dependency of k obs had negative correlation with the initial tetracycline concentration. Apart from developing a low-cost strategy for addressing tetracycline water pollution, the result of this study serves a positive step towards gaining manipulative control of adsorption mechanism in potential application of MSM for targeted drug delivery and controlled release of tetracycline antibiotics. Copyright © 2018 Elsevier Ltd. All rights reserved.

Velocity Profiles of Slow Blood Flow in a Narrow Tube

NASA Astrophysics Data System (ADS)

Chen, Jinyu; Huang, Zuqia; Zhuang, Fengyuan; Zhang, Hui

1998-04-01

A fractal model is introduced into the slow blood motion. When blood flows slowly in a narrow tube, red cell aggregation results in the formation of an approximately cylindrical core of red cells. By introducing the fractal model and using the power law relation between area fraction φ and distance from tube axis ρ, rigorous velocity profiles of the fluid in and outside the aggregated core and of the core itself are obtained analytically for different fractal dimensions. It shows a blunted velocity distribution for a relatively large fractal dimension (D ˜ 2), which can be observed in normal blood; a pathological velocity profile for moderate dimension (D = 1), which is similar to the Segre-Silberberg effect; and a parabolic profile for negligible red cell concentration (D = 0), which likes in the Poiseuille flow. The project supported by the National Basic Research Project "Nonlinear Science", National Natural Science Foundation of China and the State Education Commission through the Foundation of Doctoral Training

Morphogenesis and Complexity of the Tumor Patterns

NASA Astrophysics Data System (ADS)

Izquierdo-Kulich, E.; Nieto-Villar, J. M.

A mechanism to describe the apoptosis process at mesoscopic level through p53 is proposed in this paper. A deterministic model given by three differential equations is deduced from the mesoscopic approach, which exhibits sustained oscillations caused by a supercritical Andronov-Hopf bifurcation. Taking as hypothesis that the p53 sustained oscillation is the fundamental mechanism for apoptosis regulation; the model predicts that it is necessary a strict control of p53 to stimulated it, which is an important consideration to established new therapy strategy to fight cancer. The mathematical modeling of tumor growth allows us to describe the most important regularities of these systems. A stochastic model, based on the most important processes that take place at the level of individual cells, is proposed to predict the dynamical behavior of the expected radius of the tumor and its fractal dimension. It was found that the tumor has a characteristic fractal dimension, which contains the necessary information to predict the tumor growth until it reaches a stationary state. The mathematical modeling of tumor growth is an approach to explain the complex nature of these systems. A model that describes tumor growth was obtained by using a mesoscopic formalism and fractal dimension. This model theoretically predicts the relation between the morphology of the cell pattern and the mitosis/apoptosis quotient that helps to predict tumor growth from tumoral cells fractal dimension. The relation between the tumor macroscopic morphology and the cell pattern morphology is also determined. This could explain why the interface fractal dimension decreases with the increase of the cell pattern fractal dimension and consequently with the increase of the mitosis/apoptosis relation. Indexes to characterize tumoral cell proliferation and invasion capacities are proposed and used to predict the growth of different types of tumors. These indexes also show that the proliferation capacity is directly proportional to the invasion capacity. The proposed model assumes: i) only interface cells proliferate and invade the host, and ii) the fractal dimension of tumoral cell patterns, can reproduce the Gompertzian growth law. A mathematical model was obtained to describe the relation between the tissue morphology of cervix carcinoma and both dynamic processes of mitosis and apoptosis, and an expression to quantify the tumor aggressiveness, which in this context is associated with the tumor growth rate. The proposed model was applied to Stage III cervix carcinoma in vivo studies. In this study we found that the apoptosis rate was significantly smaller in the tumor tissues and both the mitosis rate and aggressiveness index decrease with Stage III patient's age. These quantitative results correspond to observed behavior in clinical and genetics studies. Finally, the entropy production rate was determined for avascular tumor growth. The proposed formula relates the fractal dimension of the tumor contour with the quotient between mitosis and apoptosis rate, which can be used to characterize the degree of proliferation of tumor cells. The entropy production rate was determined for fourteen tumor cell lines as a physical function of cancer robustness. The entropy production rate is a hallmark that allows us the possibility of prognosis of tumor proliferation and invasion capacities, key factors to improve cancer therapy.

Distance-weighted city growth.

PubMed

Rybski, Diego; García Cantú Ros, Anselmo; Kropp, Jürgen P

2013-04-01

Urban agglomerations exhibit complex emergent features of which Zipf's law, i.e., a power-law size distribution, and fractality may be regarded as the most prominent ones. We propose a simplistic model for the generation of citylike structures which is solely based on the assumption that growth is more likely to take place close to inhabited space. The model involves one parameter which is an exponent determining how strongly the attraction decays with the distance. In addition, the model is run iteratively so that existing clusters can grow (together) and new ones can emerge. The model is capable of reproducing the size distribution and the fractality of the boundary of the largest cluster. Although the power-law distribution depends on both, the imposed exponent and the iteration, the fractality seems to be independent of the former and only depends on the latter. Analyzing land-cover data, we estimate the parameter-value γ≈2.5 for Paris and its surroundings.

Gelation Kinetics and Network Structure of Cellulose Nanocrystals in Aqueous Solution.

PubMed

Peddireddy, Karthik R; Capron, Isabelle; Nicolai, Taco; Benyahia, Lazhar

2016-10-10

Cellulose nanocrystals (CNC) are rod-like biosourced nanoparticles that are widely used in a range of applications. Charged CNC was obtained by acid extraction from cotton and dispersed in aqueous solution using ultrasound and characterized by light scattering. Aggregation and gelation of CNC induced by addition of NaCl was investigated by light scattering as a function of the NaCl concentration (30-70 mM), the CNC concentration (0.5-5 g/L), and the temperature (10-60 °C). Formation of fractal aggregates was observed that grow with time until they percolate and form a weak system spanning network. The aggregation rate and gel time were found to decrease very steeply with increasing NaCl concentration and more weakly with increasing CNC concentration. A decrease of the gel time was also observed with increasing temperature for T > 20 °C. The structure of the CNC networks was studied using confocal laser scanning microscopy and light scattering. The local structure of the networks was fractal and reflected that of the constituting aggregates. The gels were homogeneous on length scales larger than the correlation length, which decreased with increasing CNC concentration. The CNC gels flowed when tilted for C < 12 g/L and sedimentation was observed macroscopically for C < 4 g/L due to the collapse of the CNC network under gravity. The speed and extent of sedimentation was investigated as a function of the ionic strength and the CNC concentration. Gelled CNC could be completely redispersed by applying ultrasound.

VESGEN Software for Mapping and Quantification of Vascular Regulators

NASA Technical Reports Server (NTRS)

Parsons-Wingerter, Patricia A.; Vickerman, Mary B.; Keith, Patricia A.

2012-01-01

VESsel GENeration (VESGEN) Analysis is an automated software that maps and quantifies effects of vascular regulators on vascular morphology by analyzing important vessel parameters. Quantification parameters include vessel diameter, length, branch points, density, and fractal dimension. For vascular trees, measurements are reported as dependent functions of vessel branching generation. VESGEN maps and quantifies vascular morphological events according to fractal-based vascular branching generation. It also relies on careful imaging of branching and networked vascular form. It was developed as a plug-in for ImageJ (National Institutes of Health, USA). VESGEN uses image-processing concepts of 8-neighbor pixel connectivity, skeleton, and distance map to analyze 2D, black-and-white (binary) images of vascular trees, networks, and tree-network composites. VESGEN maps typically 5 to 12 (or more) generations of vascular branching, starting from a single parent vessel. These generations are tracked and measured for critical vascular parameters that include vessel diameter, length, density and number, and tortuosity per branching generation. The effects of vascular therapeutics and regulators on vascular morphology and branching tested in human clinical or laboratory animal experimental studies are quantified by comparing vascular parameters with control groups. VESGEN provides a user interface to both guide and allow control over the users vascular analysis process. An option is provided to select a morphological tissue type of vascular trees, network or tree-network composites, which determines the general collections of algorithms, intermediate images, and output images and measurements that will be produced.

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.

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…

Discriminating topology in galaxy distributions using network analysis

NASA Astrophysics Data System (ADS)

Hong, Sungryong; Coutinho, Bruno C.; Dey, Arjun; Barabási, Albert-L.; Vogelsberger, Mark; Hernquist, Lars; Gebhardt, Karl

2016-07-01

The large-scale distribution of galaxies is generally analysed using the two-point correlation function. However, this statistic does not capture the topology of the distribution, and it is necessary to resort to higher order correlations to break degeneracies. We demonstrate that an alternate approach using network analysis can discriminate between topologically different distributions that have similar two-point correlations. We investigate two galaxy point distributions, one produced by a cosmological simulation and the other by a Lévy walk. For the cosmological simulation, we adopt the redshift z = 0.58 slice from Illustris and select galaxies with stellar masses greater than 108 M⊙. The two-point correlation function of these simulated galaxies follows a single power law, ξ(r) ˜ r-1.5. Then, we generate Lévy walks matching the correlation function and abundance with the simulated galaxies. We find that, while the two simulated galaxy point distributions have the same abundance and two-point correlation function, their spatial distributions are very different; most prominently, filamentary structures, absent in Lévy fractals. To quantify these missing topologies, we adopt network analysis tools and measure diameter, giant component, and transitivity from networks built by a conventional friends-of-friends recipe with various linking lengths. Unlike the abundance and two-point correlation function, these network quantities reveal a clear separation between the two simulated distributions; therefore, the galaxy distribution simulated by Illustris is not a Lévy fractal quantitatively. We find that the described network quantities offer an efficient tool for discriminating topologies and for comparing observed and theoretical distributions.

Mathematical models used in segmentation and fractal methods of 2-D ultrasound images

NASA Astrophysics Data System (ADS)

Moldovanu, Simona; Moraru, Luminita; Bibicu, Dorin

2012-11-01

Mathematical models are widely used in biomedical computing. The extracted data from images using the mathematical techniques are the "pillar" achieving scientific progress in experimental, clinical, biomedical, and behavioural researches. This article deals with the representation of 2-D images and highlights the mathematical support for the segmentation operation and fractal analysis in ultrasound images. A large number of mathematical techniques are suitable to be applied during the image processing stage. The addressed topics cover the edge-based segmentation, more precisely the gradient-based edge detection and active contour model, and the region-based segmentation namely Otsu method. Another interesting mathematical approach consists of analyzing the images using the Box Counting Method (BCM) to compute the fractal dimension. The results of the paper provide explicit samples performed by various combination of methods.

[Perinatal model of human transition from hypogravity to the earth's gravity based on the electromyogram nonlinear characteristics].

PubMed

Meĭgal, A Iu; Voroshilov, A S

2009-01-01

Interferential electromyogram (iEMG) was analyzed in healthy newborn infants (n=29) during the first 24 hours of life as a model of transition from hypogravity (intrauterine immersion) to the Earth's gravity (postnatal period). Nonlinear instruments of iEMG analysis (correlation dimension, entropy and fractal dimension) reflected the complexity, chaotic character and predictability of signals from the leg and arm antagonistic muscles. Except for m. gastrocnemius, in all other musles iEMG fractal dimension was shown to grow as the postnatal period extended. Low fractal and correlation dimensions and entropy marked flexor muscles, particularly against low iEMG amplitude suggesting a better congenital programming for the flexors as compared to the extensors. It is concluded that the early ontogenesis model can be practicable in studying the evolution and states of antigravity functions.

Validation and sensitivity of the FINE Bayesian network for forecasting aquatic exposure to nano-silver.

PubMed

Money, Eric S; Barton, Lauren E; Dawson, Joseph; Reckhow, Kenneth H; Wiesner, Mark R

2014-03-01

The adaptive nature of the Forecasting the Impacts of Nanomaterials in the Environment (FINE) Bayesian network is explored. We create an updated FINE model (FINEAgNP-2) for predicting aquatic exposure concentrations of silver nanoparticles (AgNP) by combining the expert-based parameters from the baseline model established in previous work with literature data related to particle behavior, exposure, and nano-ecotoxicology via parameter learning. We validate the AgNP forecast from the updated model using mesocosm-scale field data and determine the sensitivity of several key variables to changes in environmental conditions, particle characteristics, and particle fate. Results show that the prediction accuracy of the FINEAgNP-2 model increased approximately 70% over the baseline model, with an error rate of only 20%, suggesting that FINE is a reliable tool to predict aquatic concentrations of nano-silver. Sensitivity analysis suggests that fractal dimension, particle diameter, conductivity, time, and particle fate have the most influence on aquatic exposure given the current knowledge; however, numerous knowledge gaps can be identified to suggest further research efforts that will reduce the uncertainty in subsequent exposure and risk forecasts. Copyright © 2013 Elsevier B.V. All rights reserved.

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.

Wavelet detection of singularities in the presence of fractal noise

NASA Astrophysics Data System (ADS)

Noel, Steven E.; Gohel, Yogesh J.; Szu, Harold H.

1997-04-01

Here we detect singularities with generalized quadrature processing using the recently developed Hermitian Hat wavelet. Our intended application is radar target detection for the optimal fuzzing of ship self-defense munitions. We first develop a wavelet-based fractal noise model to represent sea clutter. We then investigate wavelet shrinkage as a way to reduce and smooth the noise before attempting wavelet detection. Finally, we use the complex phase of the Hermitian Hat wavelet to detect a simulated target singularity in the presence of our fractal noise.

Fabrication of rippled surfaces for diffraction gratings by plastic deformation of platinum foils and metallic glasses

NASA Astrophysics Data System (ADS)

Korsukov, V. E.; Malygin, G. A.; Korsukova, M. M.; Nyapshaev, I. A.; Obidov, B. A.

2015-12-01

Thin platinum foils and metallic glass ribbons with a fractal surface consisting of different-scale unidirectionally oriented ripples have been fabricated using special thermoplastic processing. The general fractal dimension of the rippled surface and dimensions along and across the ripples have been measured. The optical spectra of a PRK-4 lamp using rippled Pt(111) foils as reflective diffraction gratings have been determined. A model describing the mechanism of the formation of surface unidirectional fractal structures during deformation has been proposed.

Mathematics of Failures in Complex Systems: Characterization and Mitigation of Service Failures in Complex Dynamic Systems

DTIC Science & Technology

2007-06-30

fractal dimensions and Lyapunov exponents . Fractal dimensions characterize geometri- cal complexity of dynamics (e.g., spatial distribution of points along...ant classi3ers (e.g., Lyapunov exponents , and fractal dimensions). The 3rst three steps show how chaotic systems may be separated from stochastic...correlated random walk in which a ¼ 2H, where H is the Hurst exponen interval 0pHp1 with the case H ¼ 0:5 corresponding to a simple rando This model has been

Condensation versus diffusion. A spatial-scale-independent theory of aggregate structures in edible oils: applications to model systems and commercial shortenings studied via rheology and USAXS

NASA Astrophysics Data System (ADS)

Pink, David A.; Peyronel, Fernanda; Quinn, Bonnie; Singh, Pratham; Marangoni, Alejandro G.

2015-09-01

Understanding how solid fats structures come about in edible oils and quantifying their structures is of fundamental importance in developing edible oils with pre-selected characteristics. We considered the great range of fractal dimensions, from 1.91 to 2.90, reported from rheological measurements. We point out that, if the structures arise via DLA/RLA or DLCA/RLCA, as has been established using ultra small angle x-ray scattering (USAXS), we would expect fractal dimensions in the range ~1.7 to 2.1, and ~2.5 or ~3.0. We present new data for commercial fats and show that the fractal dimensions deduced lie outside these values. We have developed a model in which competition between two processes can lead to the range of fractal dimensions observed. The two processes are (i) the rate at which the solid fat particles are created as the temperature is decreased, and (ii) the rate at which these particles diffuse, thereby meeting and forming aggregates. We assumed that aggregation can take place essentially isotropically and we identified two characteristic times: a time characterizing the rate of creation of solid fats, {τ\\text{create}}(T)\\equiv 1/{{R}S}(T) , where {{R}S}(T) is the rate of solid condensation (cm3 s-1), and the diffusion time of solid fats, {τ\\text{diff}}≤ft(T,{{c}S}\\right)=< {{r}2}> /6{D}≤ft(T,{{c}S}\\right) , where {D}≤ft(T,{{c}S}\\right) is their diffusion coefficient and < {{r}2}> is the typical average distance that fats must move in order to aggregate. The intent of this model is to show that a simple process can lead to a wide range of fractal dimensions. We showed that in the limit of very fast solid creation, {τ\\text{create}}\\ll {τ\\text{diff}} the fractal dimension is predicted to be that of DLCA, ~1.7, relaxing to that of RLCA, 2.0-2.1, and that in the limit of very slow solid creation, {τ\\text{create}}\\gg {τ\\text{diff}} , the fractal dimension is predicted to be that obtained via DLA, ~2.5, relaxing to that of RLA, 3.0. We predict that, given a system which satisfies our model assumptions and which can either be cooled rapidly or cooled slowly to yield fractal dimensions {{D}\\text{rapid}} and {{D}\\text{slow}}~ then {{D}\\text{rapid}}≤slant {{D}\\text{slow}} . This is supported by both rheological [1] and USAXS measurements [2, 3] even though the latter models do not conform to the assumptions of those presented here.

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.

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.

Transformation of the System of Values of Autonomous Learning for English Acquisition in Blended E-Studies for Adults: A Holistic Fractal Model

ERIC Educational Resources Information Center

Bojare, Inara; Skrinda, Astrida

2016-01-01

The present study is aimed at creating a holistic fractal model (HFM) of autonomous learning for English acquisition in a blended environment of e-studies in adult non-formal education on the basis of the theories and paradigms of philosophy, psychology and education for sustainable development to promote the development of adult learners'…

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.

Interfacial contact stiffness of fractal rough surfaces.

PubMed

Zhang, Dayi; Xia, Ying; Scarpa, Fabrizio; Hong, Jie; Ma, Yanhong

2017-10-09

In this work we describe a theoretical model that predicts the interfacial contact stiffness of fractal rough surfaces by considering the effects of elastic and plastic deformations of the fractal asperities. We also develop an original test rig that simulates dovetail joints for turbo machinery blades, which can fine tune the normal contact load existing between the contacting surfaces of the blade root. The interfacial contact stiffness is obtained through an inverse identification method in which finite element simulations are fitted to the experimental results. Excellent agreement is observed between the contact stiffness predicted by the theoretical model and by the analogous experimental results. We demonstrate that the contact stiffness is a power law function of the normal contact load with an exponent α within the whole range of fractal dimension D(1 < D < 2). We also show that for 1 < D < 1.5 the Pohrt-Popov behavior (α = 1/(3 - D)) is valid, however for 1.5 < D < 2, the exponent α is different and equal to 2(D - 1)/D. The diversity between the model developed in the work and the Pohrt-Popov one is explained in detail.

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.

Fractal interrelationships in field and seismic data. Quarterly report, September 21 - December 31, 1995

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

Wilson, T.H.; Dominic, J.; Halverson, J.

1995-12-31

Under task 1 contour irregularities traced over both study areas in the previous quarter were scanned into the computer and digitized at a 30 meter interval. Patters mapped in both the Granny Creek and Middle Mountain field areas are presented in Figures 1 and 2 respectively. One of the hypotheses of this research project is that contour irregularities must be controlled by a combination of sedimentation features, lithologic variation, and local structure and fracture distribution. The most promising result obtained thus far in this study are those reported under Tasks 4 and 5, seismic analysis. If further tests continue tomore » support the observation that increased fractal dimension reflects the presence of detached structure, the analytical techniques employed here may be of use in the routine evaluation of seismic data to locate subtle traps. The observations may allow one to predict the variation of fractal dimension within a subsurface fracture network based on seismic observation of resolvable structural parameters. Such predictions would provide a working hypothesis, which could be modified within the context of available subsurface data.« less

Circular Microstrip Antenna with Fractal Slots for Multiband Applications

NASA Astrophysics Data System (ADS)

Singh, Sivia Jagtar; Singh, Gurpreet; Bharti, Gurpreet

2017-10-01

In this paper, a multiband, fractal, slotted, Circular Microstrip Patch Antenna for GSM, WiMAX, C and X bands (satellite communication applications) is presented. A cantor set theory is used to make fractal slots for obtaining the desired multiband. The projected antenna is simulated using Ansys HFSS v13.0 software. Simulation test of this antenna has been carried out for a frequency range of 1 GHz-10 GHz and a peak gain of 9.19 dB at a resonance frequency of 1.9 GHz is obtained. The antenna also resonates at 3.7 GHz, 6.06 GHz and 7.9 GHz with gains of 3.04 dB, 5.19 dB and 5.39 dB respectively. Parameters like voltage standing wave ratio, return loss, and gain are used to compare the results of the projected antenna with conventional CMPA's of same dimensions with full and defective grounds. The projected antenna is fabricated on a glass epoxy material and is tested using Vector Network Analyzer. The performance parameters of the antenna are found to in good agreement with each both using simulated and measured data.

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.

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 dimension and nonlinear dynamical processes

NASA Astrophysics Data System (ADS)

McCarty, Robert C.; Lindley, John P.

1993-11-01

Mandelbrot, Falconer and others have demonstrated the existence of dimensionally invariant geometrical properties of non-linear dynamical processes known as fractals. Barnsley defines fractal geometry as an extension of classical geometry. Such an extension, however, is not mathematically trivial Of specific interest to those engaged in signal processing is the potential use of fractal geometry to facilitate the analysis of non-linear signal processes often referred to as non-linear time series. Fractal geometry has been used in the modeling of non- linear time series represented by radar signals in the presence of ground clutter or interference generated by spatially distributed reflections around the target or a radar system. It was recognized by Mandelbrot that the fractal geometries represented by man-made objects had different dimensions than the geometries of the familiar objects that abound in nature such as leaves, clouds, ferns, trees, etc. The invariant dimensional property of non-linear processes suggests that in the case of acoustic signals (active or passive) generated within a dispersive medium such as the ocean environment, there exists much rich structure that will aid in the detection and classification of various objects, man-made or natural, within the medium.

Fractal hierarchies of magma transport in Hawaii and critical self-organization of tremor

NASA Astrophysics Data System (ADS)

Shaw, Herbert R.; Chouet, Bernard

1991-06-01

A hierarchical model of magma transport in Hawaii is developed from the seismic records of deep (30-60 km) and intermediate-depth (5-15 km) harmonic tremor between January 1, 1962, and December 31, 1983. We find two kinds of spatial distributions of magma fractions at depths below 5 km, defined by the fractal dimension D3, where the subscript is the embedding dimension. The first is a focused distribution with D3 = 0.28, and the second is a dispersed distribution with D3 = 1.52. The former dimension reflects conduitlike structures where the magma flow converges toward a summit magma chamber and the fractal dimension tends to zero. The latter dimension reflects multifractal clustering of dendritic fractures where hypocentral domains represent subsets of fractures within spherical domains with an average radius of about 1 km. These geometries constitute a percolation network of clustered intermittent fracture and magma transport. The magma volume of the average fracture is about 2 × 104 m3. A tremor model of magma transport is developed from mass balances of percolation that are proportional to tremor durations. It gives reasonable magma fractions and residence times for a vertical drift velocity of 4 km yr-1 and yields patterns of intermittency that are in accord with singularity analyses of the 22-year time series record. According to the model, sustained tremor is generated by the relaxation oscillations of the percolation network with a dominant frequency of about 1 Hz to obtain internally consistent values of fracture geometry, fracture opening force, and magma supply rate. Calculated tremor frequencies are higher in fracture networks of small volume in harmony with the observed relation between seismic amplitude and dominant frequency of tremor. Tectonic relaxation times of rock stresses versus magma pressures are in fair agreement with the average length of tremor episodes and average period of tremor intermittencies. These observations suggest that a high degree of self-organization is characteristic of the nonlinear dynamics of fracture percolation and coupled tremor processes. Logarithms of frequencies (in hertz) of high-amplitude tremor (1-s period), mean tremor duration (28-min period), and mean onset interval (14-day period) are 0, -3.2, and -6.1, implying broadband maxima in the frequency spectrum of transport at intervals of 103. The next longer period of this sequence, which corresponds to eruptions and shallow intrusions, is about 32 years (10 -9 Hz), comparable to the average eruption intermission of Mauna Loa during the last 150 years (about 20 years). This and other evidence suggest that spatiotemporal universality extends from small to large scales in Hawaiian and other magmatic systems. The apparent universal scaling of frequencies may be more than 15 decades in time (1 s to about 60 m.y.) and 10 decades in length (0.1 mm to 103 km).

Comparative analysis of seismic persistence of Hindu Kush nests (Afghanistan) and Los Santos (Colombia) using fractal dimension

NASA Astrophysics Data System (ADS)

Prada, D. A.; Sanabria, M. P.; Torres, A. F.; Álvarez, M. A.; Gómez, J.

2018-04-01

The study of persistence in time series in seismic events in two of the most important nets such as Hindu Kush in Afghanistan and Los Santos Santander in Colombia generate great interest due to its high presence of telluric activity. The data were taken from the global seismological network. Using the Jarque-Bera test the presence of gaussian distribution was analyzed, and because the distribution in the series was asymmetric, without presence of mesocurtisity, the Hurst coefficient was calculated using the rescaled range method, with which it was found the fractal dimension associated to these time series and under what is possible to determine the persistence, antipersistence and volatility in these phenomena.

Analysis of fluid flow and solute transport through a single fracture with variable apertures intersecting a canister: Comparison between fractal and Gaussian fractures

NASA Astrophysics Data System (ADS)

Liu, L.; Neretnieks, I.

Canisters with spent nuclear fuel will be deposited in fractured crystalline rock in the Swedish concept for a final repository. The fractures intersect the canister holes at different angles and they have variable apertures and therefore locally varying flowrates. Our previous model with fractures with a constant aperture and a 90° intersection angle is now extended to arbitrary intersection angles and stochastically variable apertures. It is shown that the previous basic model can be simply amended to account for these effects. More importantly, it has been found that the distributions of the volumetric and the equivalent flow rates are all close to the Normal for both fractal and Gaussian fractures, with the mean of the distribution of the volumetric flow rate being determined solely by the hydraulic aperture, and that of the equivalent flow rate being determined by the mechanical aperture. Moreover, the standard deviation of the volumetric flow rates of the many realizations increases with increasing roughness and spatial correlation length of the aperture field, and so does that of the equivalent flow rates. Thus, two simple statistical relations can be developed to describe the stochastic properties of fluid flow and solute transport through a single fracture with spatially variable apertures. This obviates, then, the need to simulate each fracture that intersects a canister in great detail, and allows the use of complex fractures also in very large fracture network models used in performance assessment.

A contact angle hysteresis model based on the fractal structure of contact line.

PubMed

Wu, Shuai; Ma, Ming

2017-11-01

Contact angle is one of the most popular concept used in fields such as wetting, transport and microfludics. In practice, different contact angles such as equilibrium, receding and advancing contact angles are observed due to hysteresis. The connection among these contact angles is important in revealing the chemical and physical properties of surfaces related to wetting. Inspired by the fractal structure of contact line, we propose a single parameter model depicting the connection of the three angles. This parameter is decided by the fractal structure of the contact line. The results of this model agree with experimental observations. In certain cases, it can be reduced to other existing models. It also provides a new point of view in understanding the physical nature of the contact angle hysteresis. Interestingly, some counter-intuitive phenomena, such as the binary receding angles, are indicated in this model, which are waited to be validated by experiments. Copyright © 2017 Elsevier Inc. All rights reserved.

Towards thermomechanics of fractal media

NASA Astrophysics Data System (ADS)

Ostoja-Starzewski, Martin

2007-11-01

Hans Ziegler’s thermomechanics [1,2,3], established half a century ago, is extended to fractal media on the basis of a recently introduced continuum mechanics due to Tarasov [14,15]. Employing the concept of internal (kinematic) variables and internal stresses, as well as the quasiconservative and dissipative stresses, a field form of the second law of thermodynamics is derived. In contradistinction to the conventional Clausius Duhem inequality, it involves generalized rates of strain and internal variables. Upon introducing a dissipation function and postulating the thermodynamic orthogonality on any lengthscale, constitutive laws of elastic-dissipative fractal media naturally involving generalized derivatives of strain and stress can then be derived. This is illustrated on a model viscoelastic material. Also generalized to fractal bodies is the Hill condition necessary for homogenization of their constitutive responses.

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.

Discrete mathematical model of wave diffraction on pre-fractal impedance strips. TM mode case

NASA Astrophysics Data System (ADS)

Nesvit, K. V.

2013-10-01

In this paper a transverse magnetic (TM) wave diffraction problem on pre-fractal impedance strips is considered. The overall aim of this work is to develop a discrete mathematical model of the boundary integral equations (IEs) with the help of special quadrature formulas with the nodes in the zeros of Chebyshev polynomials and to perform a numerical experiments with the help of an efficient discrete singularities method (DSM).

Fractals, malware, and data models

NASA Astrophysics Data System (ADS)

Jaenisch, Holger M.; Potter, Andrew N.; Williams, Deborah; Handley, James W.

2012-06-01

We examine the hypothesis that the decision boundary between malware and non-malware is fractal. We introduce a novel encoding method derived from text mining for converting disassembled programs first into opstrings and then filter these into a reduced opcode alphabet. These opcodes are enumerated and encoded into real floating point number format and used for characterizing frequency of occurrence and distribution properties of malware functions to compare with non-malware functions. We use the concept of invariant moments to characterize the highly non-Gaussian structure of the opcode distributions. We then derive Data Model based classifiers from identified features and interpolate and extrapolate the parameter sample space for the derived Data Models. This is done to examine the nature of the parameter space classification boundary between families of malware and the general non-malware category. Preliminary results strongly support the fractal boundary hypothesis, and a summary of our methods and results are presented here.

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.

Protein surface roughness accounts for binding free energy of Plasmepsin II-ligand complexes.

PubMed

Valdés-Tresanco, Mario E; Valdés-Tresanco, Mario S; Valiente, Pedro A; Cocho, Germinal; Mansilla, Ricardo; Nieto-Villar, J M

2018-01-01

The calculation of absolute binding affinities for protein-inhibitor complexes remains as one of the main challenges in computational structure-based ligand design. The present work explored the calculations of surface fractal dimension (as a measure of surface roughness) and the relationship with experimental binding free energies of Plasmepsin II complexes. Plasmepsin II is an attractive target for novel therapeutic compounds to treat malaria. However, the structural flexibility of this enzyme is a drawback when searching for specific inhibitors. Concerning that, we performed separate explicitly solvated molecular dynamics simulations using the available high-resolution crystal structures of different Plasmepsin II complexes. Molecular dynamics simulations allowed a better approximation to systems dynamics and, therefore, a more reliable estimation of surface roughness. This constitutes a novel approximation in order to obtain more realistic values of fractal dimension, because previous works considered only x-ray structures. Binding site fractal dimension was calculated considering the ensemble of structures generated at different simulation times. A linear relationship between binding site fractal dimension and experimental binding free energies of the complexes was observed within 20 ns. Previous studies of the subject did not uncover this relationship. Regression model, coined FD model, was built to estimate binding free energies from binding site fractal dimension values. Leave-one-out cross-validation showed that our model reproduced accurately the absolute binding free energies for our training set (R 2  = 0.76; <|error|> =0.55 kcal/mol; SD error  = 0.19 kcal/mol). The fact that such a simple model may be applied raises some questions that are addressed in the article. Copyright © 2017 John Wiley & Sons, Ltd.

Complexity, Chaos, and Nonlinear Dynamics: A New Perspective on Career Development Theory

ERIC Educational Resources Information Center

Bloch, Deborah P.

2005-01-01

The author presents a theory of career development drawing on nonlinear dynamics and chaos and complexity theories. Career is presented as a complex adaptive entity, a fractal of the human entity. Characteristics of complex adaptive entities, including (a) autopiesis, or self-regeneration; (b) open exchange; (c) participation in networks; (d)…

[Network structures in biological systems].

PubMed

Oleskin, A V

2013-01-01

Network structures (networks) that have been extensively studied in the humanities are characterized by cohesion, a lack of a central control unit, and predominantly fractal properties. They are contrasted with structures that contain a single centre (hierarchies) as well as with those whose elements predominantly compete with one another (market-type structures). As far as biological systems are concerned, their network structures can be subdivided into a number of types involving different organizational mechanisms. Network organization is characteristic of various structural levels of biological systems ranging from single cells to integrated societies. These networks can be classified into two main subgroups: (i) flat (leaderless) network structures typical of systems that are composed of uniform elements and represent modular organisms or at least possess manifest integral properties and (ii) three-dimensional, partly hierarchical structures characterized by significant individual and/or intergroup (intercaste) differences between their elements. All network structures include an element that performs structural, protective, and communication-promoting functions. By analogy to cell structures, this element is denoted as the matrix of a network structure. The matrix includes a material and an immaterial component. The material component comprises various structures that belong to the whole structure and not to any of its elements per se. The immaterial (ideal) component of the matrix includes social norms and rules regulating network elements' behavior. These behavioral rules can be described in terms of algorithms. Algorithmization enables modeling the behavior of various network structures, particularly of neuron networks and their artificial analogs.

Nonlinear dynamical model of human gait

NASA Astrophysics Data System (ADS)

West, Bruce J.; Scafetta, Nicola

2003-05-01

We present a nonlinear dynamical model of the human gait control system in a variety of gait regimes. The stride-interval time series in normal human gait is characterized by slightly multifractal fluctuations. The fractal nature of the fluctuations becomes more pronounced under both an increase and decrease in the average gait. Moreover, the long-range memory in these fluctuations is lost when the gait is keyed on a metronome. Human locomotion is controlled by a network of neurons capable of producing a correlated syncopated output. The central nervous system is coupled to the motocontrol system, and together they control the locomotion of the gait cycle itself. The metronomic gait is simulated by a forced nonlinear oscillator with a periodic external force associated with the conscious act of walking in a particular way.

Higgs field and cosmological parameters in the fractal quantum system

NASA Astrophysics Data System (ADS)

Abramov, Valeriy

2017-10-01

For the fractal model of the Universe the relations of cosmological parameters and the Higgs field are established. Estimates of the critical density, the expansion and speed-up parameters of the Universe (the Hubble constant and the cosmological redshift); temperature and anisotropy of the cosmic microwave background radiation were performed.

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.

A physically based connection between fractional calculus and fractal geometry

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

Butera, Salvatore, E-mail: sg.butera@gmail.com; Di Paola, Mario, E-mail: mario.dipaola@unipa.it

2014-11-15

We show a relation between fractional calculus and fractals, based only on physical and geometrical considerations. The link has been found in the physical origins of the power-laws, ruling the evolution of many natural phenomena, whose long memory and hereditary properties are mathematically modelled by differential operators of non integer order. Dealing with the relevant example of a viscous fluid seeping through a fractal shaped porous medium, we show that, once a physical phenomenon or process takes place on an underlying fractal geometry, then a power-law naturally comes up in ruling its evolution, whose order is related to the anomalousmore » dimension of such geometry, as well as to the model used to describe the physics involved. By linearizing the non linear dependence of the response of the system at hand to a proper forcing action then, exploiting the Boltzmann superposition principle, a fractional differential equation is found, describing the dynamics of the system itself. The order of such equation is again related to the anomalous dimension of the underlying geometry.« less

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.

Objective Auscultation of TCM Based on Wavelet Packet Fractal Dimension and Support Vector Machine.

PubMed

Yan, Jian-Jun; Guo, Rui; Wang, Yi-Qin; Liu, Guo-Ping; Yan, Hai-Xia; Xia, Chun-Ming; Shen, Xiaojing

2014-01-01

This study was conducted to illustrate that auscultation features based on the fractal dimension combined with wavelet packet transform (WPT) were conducive to the identification the pattern of syndromes of Traditional Chinese Medicine (TCM). The WPT and the fractal dimension were employed to extract features of auscultation signals of 137 patients with lung Qi-deficient pattern, 49 patients with lung Yin-deficient pattern, and 43 healthy subjects. With these features, the classification model was constructed based on multiclass support vector machine (SVM). When all auscultation signals were trained by SVM to decide the patterns of TCM syndromes, the overall recognition rate of model was 79.49%; when male and female auscultation signals were trained, respectively, to decide the patterns, the overall recognition rate of model reached 86.05%. The results showed that the methods proposed in this paper were effective to analyze auscultation signals, and the performance of model can be greatly improved when the distinction of gender was considered.

Objective Auscultation of TCM Based on Wavelet Packet Fractal Dimension and Support Vector Machine

PubMed Central

Yan, Jian-Jun; Wang, Yi-Qin; Liu, Guo-Ping; Yan, Hai-Xia; Xia, Chun-Ming; Shen, Xiaojing

2014-01-01

This study was conducted to illustrate that auscultation features based on the fractal dimension combined with wavelet packet transform (WPT) were conducive to the identification the pattern of syndromes of Traditional Chinese Medicine (TCM). The WPT and the fractal dimension were employed to extract features of auscultation signals of 137 patients with lung Qi-deficient pattern, 49 patients with lung Yin-deficient pattern, and 43 healthy subjects. With these features, the classification model was constructed based on multiclass support vector machine (SVM). When all auscultation signals were trained by SVM to decide the patterns of TCM syndromes, the overall recognition rate of model was 79.49%; when male and female auscultation signals were trained, respectively, to decide the patterns, the overall recognition rate of model reached 86.05%. The results showed that the methods proposed in this paper were effective to analyze auscultation signals, and the performance of model can be greatly improved when the distinction of gender was considered. PMID:24883068

A Fractal Study on the Effective Thermal Conductivity of Porous Media

NASA Astrophysics Data System (ADS)

Qin, X.; Cai, J.; Wei, W.

2017-12-01

Thermal conduction in porous media has steadily received attention in science and engineering, for instance, exploiting and utilizing the geothermal energy, developing the oil-gas resource, ground water flow in hydrothermal systems and investigating the potential host nuclear wastes, etc. The thermal conductivity is strongly influenced by the microstructure features of porous media. In this work, based on the fractal characteristics of the grains, a theoretical model of effective thermal conductivity is proposed for saturated and unsaturated porous media. It is found that the proposed effective thermal conductivity solution is a function of geometrical parameters of porous media, such as the porosity, fractal dimension of granular matrix and the thermal conductivity of the grains and pore fluid. The model predictions are compared with existing experimental data and the results show that they are in good agreement with existing experimental data. The proposed model may provide a better understanding of the physical mechanisms of thermal transfer in porous media than conventional models.

Evaluation of statistical methods for quantifying fractal scaling in water-quality time series with irregular sampling

NASA Astrophysics Data System (ADS)

Zhang, Qian; Harman, Ciaran J.; Kirchner, James W.

2018-02-01

River water-quality time series often exhibit fractal scaling, which here refers to autocorrelation that decays as a power law over some range of scales. Fractal scaling presents challenges to the identification of deterministic trends because (1) fractal scaling has the potential to lead to false inference about the statistical significance of trends and (2) the abundance of irregularly spaced data in water-quality monitoring networks complicates efforts to quantify fractal scaling. Traditional methods for estimating fractal scaling - in the form of spectral slope (β) or other equivalent scaling parameters (e.g., Hurst exponent) - are generally inapplicable to irregularly sampled data. Here we consider two types of estimation approaches for irregularly sampled data and evaluate their performance using synthetic time series. These time series were generated such that (1) they exhibit a wide range of prescribed fractal scaling behaviors, ranging from white noise (β = 0) to Brown noise (β = 2) and (2) their sampling gap intervals mimic the sampling irregularity (as quantified by both the skewness and mean of gap-interval lengths) in real water-quality data. The results suggest that none of the existing methods fully account for the effects of sampling irregularity on β estimation. First, the results illustrate the danger of using interpolation for gap filling when examining autocorrelation, as the interpolation methods consistently underestimate or overestimate β under a wide range of prescribed β values and gap distributions. Second, the widely used Lomb-Scargle spectral method also consistently underestimates β. A previously published modified form, using only the lowest 5 % of the frequencies for spectral slope estimation, has very poor precision, although the overall bias is small. Third, a recent wavelet-based method, coupled with an aliasing filter, generally has the smallest bias and root-mean-squared error among all methods for a wide range of prescribed β values and gap distributions. The aliasing method, however, does not itself account for sampling irregularity, and this introduces some bias in the result. Nonetheless, the wavelet method is recommended for estimating β in irregular time series until improved methods are developed. Finally, all methods' performances depend strongly on the sampling irregularity, highlighting that the accuracy and precision of each method are data specific. Accurately quantifying the strength of fractal scaling in irregular water-quality time series remains an unresolved challenge for the hydrologic community and for other disciplines that must grapple with irregular sampling.

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.

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

Empirical Relationships Between Optical Properties and Equivalent Diameters of Fractal Soot Aggregates at 550 Nm Wavelength.

NASA Technical Reports Server (NTRS)

Pandey, Apoorva; Chakrabarty, Rajan K.; Liu, Li; Mishchenko, Michael I.

2015-01-01

Soot aggregates (SAs)-fractal clusters of small, spherical carbonaceous monomers-modulate the incoming visible solar radiation and contribute significantly to climate forcing. Experimentalists and climate modelers typically assume a spherical morphology for SAs when computing their optical properties, causing significant errors. Here, we calculate the optical properties of freshly-generated (fractal dimension Df = 1.8) and aged (Df = 2.6) SAs at 550 nm wavelength using the numericallyexact superposition T-Matrix method. These properties were expressed as functions of equivalent aerosol diameters as measured by contemporary aerosol instruments. This work improves upon previous efforts wherein SA optical properties were computed as a function of monomer number, rendering them unusable in practical applications. Future research will address the sensitivity of variation in refractive index, fractal prefactor, and monomer overlap of SAs on the reported empirical relationships.

Human development I: twenty fundamental problems of biology, medicine, and neuro-psychology related to biological information.

PubMed

Hermansen, Tyge Dahl; Ventegodt, Søren; Rald, Erik; Clausen, Birgitte; Nielsen, Maj Lyck; Merrick, Joav

2006-07-06

In a new series of papers, we address a number of unsolved problems in biology today. First of all, the unsolved enigma concerning how the differentiation from a single zygote to an adult individual happens has been object for severe research for decades. By uncovering a new holistic biological paradigm that introduces an energetic-informational interpretation of reality as a new way to experience biology, these papers will try to solve the problems connected with the events of biological ontogenesis involving a fractal hierarchy, from a single cell to the function of the human brain. The problems discussed are interpreted within the frames of a universe of roomy fractal structures containing energetic patterns that are able to deliver biological information. We think biological organization is guided by energetic changes on the level of quantum mechanics, interacting with the intention that again guides the energetic conformation of the fractal structures to gain disorders or healthiness. Furthermore, we introduce two new concepts: "metamorphous top down" evolution and "adult human metamorphosis". The first is a new evolutionary theory involving metamorphosis as a main concept of evolution. The last is tightly linked to the evolutionary principle and explains how human self-recovery is governed. Other subjects of special interest that we shall look deeper into are the immunological self-nonself discrimination, the structure and function of the human brain, the etiology and salutogenesis of mental and somatic diseases, and the structure of the consciousness of a human being. We shall criticize Szentagothai's model for the modulated structure of the human cerebral cortex and Jerne's theory of the immunological regulatory anti-idiotypic network.

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

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.

Analysis of the moisture diffusion transfer through fibrous porous membrane used for waterproof breathable fabrics

NASA Astrophysics Data System (ADS)

Zhu, Fanglong; Zhou, Yu; Liu, Suyan

2013-10-01

In this paper, we propose a new fractal model to determine the moisture effective diffusivity of porous membrane such as expanded polytetrafluorethylene membrane, by taking account of both parallel and perpendicular channels to diffusion flow direction. With the consideration of both the Knudsen and bulk diffusion effect, a relationship between micro-structural parameters and effective moisture diffusivity is deduced. The effective moisture diffusivities predicted by the present fractal model are compared with moisture diffusion experiment data and calculated values obtained from other theoretical models.

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

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.

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.

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.

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.

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

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.

Fractal Analysis of Air Pollutant Concentrations

NASA Astrophysics Data System (ADS)

Cortina-Januchs, M. G.; Barrón-Adame, J. M.; Vega-Corona, A.; Andina, D.

2010-05-01

Air pollution poses significant threats to human health and the environment throughout the developed and developing countries. This work focuses on fractal analysis of pollutant concentration in Salamanca, Mexico. The city of Salamanca has been catalogued as one of the most polluted cities in Mexico. The main causes of pollution in this city are fixed emission sources, such as chemical industry and electricity generation. Sulphur Dioxide (SO2) and Particulate Matter less than 10 micrometer in diameter (PM10) are the most important pollutants in this region. Air pollutant concentrations were investigated by applying the box counting method in time series obtained of the Automatic Environmental Monitoring Network (AEMN). One year of time series of hourly average concentrations were analyzed in order to characterize the temporal structures of SO2 and PM10.

Application of fractal dimension method of functional MRI time-series to limbic dysregulation in anxiety study.

PubMed

Olejarczyk, Elzbieta

2007-01-01

Functional magnetic resonance imaging (fMRI) allows to investigate the amplitude of activation in neural networks of brain. In this work we present the results of fMRI time-series analysis performed to identify the process of dysregulation of dynamic interaction between different limbic system regions in healthy adults in state of increased anxiety. The results obtain for 65 healthy adults using nonlinear dynamics methods like fractal dimension confirm the key roles of the bilateral amygdala, bilateral hippocampus, BA9 (dorsolateral prefrontal cortex), and BA45 (ventromedial prefrontal cortex) in modulating emotional response in healthy adults. For different regions of interest (ROIs) significant correlations were found not only for the neutral respective rest but also for fear and angry contrasts.

A NEW LOG EVALUATION METHOD TO APPRAISE MESAVERDE RE-COMPLETION OPPORTUNITIES

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

Albert Greer

2003-09-11

Artificial intelligence tools, fuzzy logic and neural networks were used to evaluate the potential of the behind pipe Mesaverde formation in BMG's Mancos formation wells. A fractal geostatistical mapping algorithm was also used to predict Mesaverde production. Additionally, a conventional geological study was conducted. To date one Mesaverde completion has been performed. The Janet No.3 Mesaverde completion was non-economic. Both the AI method and the geostatistical methods predicted the failure of the Janet No.3. The Gavilan No.1 in the Mesaverde was completed during the course of the study and was an extremely good well. This well was not included inmore » the statistical dataset. The AI method predicted very good production while the fractal map predicted a poor producer.« less

Do-It-Yourself Fractal Functions

ERIC Educational Resources Information Center

Shriver, Janet; Willard, Teri; McDaniel, Mandy

2017-01-01

In the set of fractal activities described in this article, students will accomplish much more than just creating a fun set of cards that simply resemble an art project. Goals of this activity, designed for an algebra 1 class, are to encourage students to generate data, look for and analyze patterns, and create their own models--all from a set of…

Fine-granularity inference and estimations to network traffic for SDN.

PubMed

Jiang, Dingde; Huo, Liuwei; Li, Ya

2018-01-01

An end-to-end network traffic matrix is significantly helpful for network management and for Software Defined Networks (SDN). However, the end-to-end network traffic matrix's inferences and estimations are a challenging problem. Moreover, attaining the traffic matrix in high-speed networks for SDN is a prohibitive challenge. This paper investigates how to estimate and recover the end-to-end network traffic matrix in fine time granularity from the sampled traffic traces, which is a hard inverse problem. Different from previous methods, the fractal interpolation is used to reconstruct the finer-granularity network traffic. Then, the cubic spline interpolation method is used to obtain the smooth reconstruction values. To attain an accurate the end-to-end network traffic in fine time granularity, we perform a weighted-geometric-average process for two interpolation results that are obtained. The simulation results show that our approaches are feasible and effective.

Fine-granularity inference and estimations to network traffic for SDN

PubMed Central

Huo, Liuwei; Li, Ya

2018-01-01

An end-to-end network traffic matrix is significantly helpful for network management and for Software Defined Networks (SDN). However, the end-to-end network traffic matrix's inferences and estimations are a challenging problem. Moreover, attaining the traffic matrix in high-speed networks for SDN is a prohibitive challenge. This paper investigates how to estimate and recover the end-to-end network traffic matrix in fine time granularity from the sampled traffic traces, which is a hard inverse problem. Different from previous methods, the fractal interpolation is used to reconstruct the finer-granularity network traffic. Then, the cubic spline interpolation method is used to obtain the smooth reconstruction values. To attain an accurate the end-to-end network traffic in fine time granularity, we perform a weighted-geometric-average process for two interpolation results that are obtained. The simulation results show that our approaches are feasible and effective. PMID:29718913

Fractional Gaussian model in global optimization

NASA Astrophysics Data System (ADS)

Dimri, V. P.; Srivastava, R. P.

2009-12-01

Earth system is inherently non-linear and it can be characterized well if we incorporate no-linearity in the formulation and solution of the problem. General tool often used for characterization of the earth system is inversion. Traditionally inverse problems are solved using least-square based inversion by linearizing the formulation. The initial model in such inversion schemes is often assumed to follow posterior Gaussian probability distribution. It is now well established that most of the physical properties of the earth follow power law (fractal distribution). Thus, the selection of initial model based on power law probability distribution will provide more realistic solution. We present a new method which can draw samples of posterior probability density function very efficiently using fractal based statistics. The application of the method has been demonstrated to invert band limited seismic data with well control. We used fractal based probability density function which uses mean, variance and Hurst coefficient of the model space to draw initial model. Further this initial model is used in global optimization inversion scheme. Inversion results using initial models generated by our method gives high resolution estimates of the model parameters than the hitherto used gradient based liner inversion method.

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)

Analytic study of small scale structure on cosmic strings

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

Polchinski, Joseph; Rocha, Jorge V.; Department of Physics, University of California, Santa Barbara, California 93106

2006-10-15

The properties of string networks at scales well below the horizon are poorly understood, but they enter critically into many observables. We argue that in some regimes, stretching will be the only relevant process governing the evolution. In this case, the string two-point function is determined up to normalization: the fractal dimension approaches one at short distance, but the rate of approach is characterized by an exponent that plays an essential role in network properties. The smoothness at short distance implies, for example, that cosmic string lensing images are almost undistorted. We then add in loop production as a perturbationmore » and find that it diverges at small scales. This need not invalidate the stretching model, since the loop production occurs in localized regions, but it implies a complicated fragmentation process. Our ability to model this process is limited, but we argue that loop production peaks a few orders of magnitude below the horizon scale, without the inclusion of gravitational radiation. We find agreement with some features of simulations, and interesting discrepancies that must be resolved by future work.« less

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

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.

Relativistic corrections to fractal analyses of the galaxy distribution

NASA Astrophysics Data System (ADS)

Célérier, M.-N.; Thieberger, R.

2001-02-01

The effect of curvature on the results of fractal analyses of the galaxy distribution is investigated. We show that, if the universe satisfies the criteria of a wide class of parabolic homogeneous models, the observers measuring the fractal index with the integrated conditional density procedure may use the Hubble formula, without having to allow for curvature, out to distances of 600 Mpc, and possibly far beyond. This contradicts a previous claim by Ribeiro (\\cite{r33}) that, in the Einstein-de Sitter case, relativistic corrections should be taken into account at much smaller scales. We state for the class of cosmological models under study, and give grounds for conjecture for others, that the averaging procedure has a smoothing effect and that, therefore, the redshift-distance relation provides an upper limit to the relativistic corrections involved in such analyses.

Designing for Learning: Online Social Networks as a Classroom Environment

ERIC Educational Resources Information Center

Casey, Gail; Evans, Terry

2011-01-01

This paper deploys notions of emergence, connections, and designs for learning to conceptualize high school students' interactions when using online social media as a learning environment. It makes links to chaos and complexity theories and to fractal patterns as it reports on a part of the first author's action research study, conducted while she…

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.

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.

A Comparison of Local Variance, Fractal Dimension, and Moran's I as Aids to Multispectral Image Classification

NASA Technical Reports Server (NTRS)

Emerson, Charles W.; Sig-NganLam, Nina; Quattrochi, Dale A.

2004-01-01

The accuracy of traditional multispectral maximum-likelihood image classification is limited by the skewed statistical distributions of reflectances from the complex heterogenous mixture of land cover types in urban areas. This work examines the utility of local variance, fractal dimension and Moran's I index of spatial autocorrelation in segmenting multispectral satellite imagery. Tools available in the Image Characterization and Modeling System (ICAMS) were used to analyze Landsat 7 imagery of Atlanta, Georgia. Although segmentation of panchromatic images is possible using indicators of spatial complexity, different land covers often yield similar values of these indices. Better results are obtained when a surface of local fractal dimension or spatial autocorrelation is combined as an additional layer in a supervised maximum-likelihood multispectral classification. The addition of fractal dimension measures is particularly effective at resolving land cover classes within urbanized areas, as compared to per-pixel spectral classification techniques.

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.

Chimera states in complex networks: interplay of fractal topology and delay

NASA Astrophysics Data System (ADS)

Sawicki, Jakub; Omelchenko, Iryna; Zakharova, Anna; Schöll, Eckehard

2017-06-01

Chimera states are an example of intriguing partial synchronization patterns emerging in networks of identical oscillators. They consist of spatially coexisting domains of coherent (synchronized) and incoherent (desynchronized) dynamics. We analyze chimera states in networks of Van der Pol oscillators with hierarchical connectivities, and elaborate the role of time delay introduced in the coupling term. In the parameter plane of coupling strength and delay time we find tongue-like regions of existence of chimera states alternating with regions of existence of coherent travelling waves. We demonstrate that by varying the time delay one can deliberately stabilize desired spatio-temporal patterns in the system.

Interactive Effects of Dorsomedial Hypothalamic Nucleus and Time-Restricted Feeding on Fractal Motor Activity Regulation.

PubMed

Lo, Men-Tzung; Chiang, Wei-Yin; Hsieh, Wan-Hsin; Escobar, Carolina; Buijs, Ruud M; Hu, Kun

2016-01-01

One evolutionary adaptation in motor activity control of animals is the anticipation of food that drives foraging under natural conditions and is mimicked in laboratory with daily scheduled food availability. Food anticipation is characterized by increased activity a few hours before the feeding period. Here we report that 2-h food availability during the normal inactive phase of rats not only increases activity levels before the feeding period but also alters the temporal organization of motor activity fluctuations over a wide range of time scales from minutes up to 24 h. We demonstrate this multiscale alteration by assessing fractal patterns in motor activity fluctuations-similar fluctuation structure at different time scales-that are robust in intact animals with ad libitum food access but are disrupted under food restriction. In addition, we show that fractal activity patterns in rats with ad libitum food access are also perturbed by lesion of the dorsomedial hypothalamic (DMH)-a neural node that is involved in food anticipatory behavior. Instead of further disrupting fractal regulation, food restriction restores the disrupted fractal patterns in these animals after the DMH lesion despite the persistence of the 24-h rhythms. This compensatory effect of food restriction is more clearly pronounced in the same animals after the additional lesion of the suprachiasmatic nucleus (SCN)-the central master clock in the circadian system that generates and orchestrates circadian rhythms in behavior and physiological functions in synchrony with day-night cycles. Moreover, all observed influences of food restriction persist even when data during the food anticipatory and feeding period are excluded. These results indicate that food restriction impacts dynamics of motor activity at different time scales across the entire circadian/daily cycle, which is likely caused by the competition between the food-induced time cue and the light-entrained circadian rhythm of the SCN. The differential impacts of food restriction on fractal activity control in intact and DMH-lesioned animals suggest that the DMH plays a crucial role in integrating these different time cues to the circadian network for multiscale regulation of motor activity.

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

Transepithelial ultrafiltration and fractal power diffusion of D-glucose in the perfused rat intestine.

PubMed

Kochak, Gregory M; Mangat, Surinder

2002-12-23

Despite an enormous body of research investigating the mass transfer of D-glucose through biological membranes, carrier-mediated and first-order models have remained the prevalent models describing glucose's quantitative behavior even though they have proven to be inadequate over extended concentration ranges. Recent evidence from GLUT2 knockout studies further questions our understanding of molecular models, especially those employing Michaelis-Menten (MM)-type kinetic models. In this report, evidence is provided that D-glucose is absorbed by rat intestinal epithelium by a combination of convective ultrafiltration and nonlinear diffusion. The diffusive component of mass transfer is described by a concentration-dependent permeability coefficient, modeled as a fractal power function. Glucose and sodium chloride-dependent-induced aqueous convection currents are the result of prevailing oncotic and osmotic pressure effects, and a direct effect of glucose and sodium chloride on intestinal epithelium resulting in enhanced glucose, sodium ion, and water mobility. The fractal power model of glucose diffusion was superior to the conventional MM description. A convection-diffusion model of mass transfer adequately characterized glucose mass transfer over a 105-fold glucose concentration range in the presence and absence of sodium ion.

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.

[Advances in studies on the structure of farmland shelterbelt ecosystem].

PubMed

Li, Chunping; Guan, Wenbin; Fan, Zhiping; Su, Fanxin; Wang, Xilin

2003-11-01

The ecological function of farmland shelterbelt system is determined by its structure. The spatio-temporal structure is a key aspect in related researches, which is very necessary to study the integrity, stability and durability of shelterbelt modules. In this article, the researches on the structure of farmland shelterbelt ecosystem were reviewed from the four scales of tree structure, shelterbelt structure, shelterbelts network and landscape structure. The principles, methods and productions of each scale were summarized, and the prospects were also discussed. Dynamic simulation of tree growth process in shelterbelts could be conducted by the theory of form and quality structure of tree and by fractal graphics, which were helpful to study the mechanism of individual trees and belts based on photosynthetic and transpiration mechanism of individual trees. The mechanism model of shelterbelt porosity should be conducted, so that, the sustainable yield model of shelterbelt management could be established, and the optimized model of shelterbelt networks with multi-special and multi-hierarchical structure could also be formed. Evaluating the reasonability, stability and durability of shelterbelt landscape based on the theories and methods of landscape ecology was an important task in the future studies.

Stochastic geometry in disordered systems, applications to quantum Hall transitions

NASA Astrophysics Data System (ADS)

Gruzberg, Ilya

2012-02-01

A spectacular success in the study of random fractal clusters and their boundaries in statistical mechanics systems at or near criticality using Schramm-Loewner Evolutions (SLE) naturally calls for extensions in various directions. Can this success be repeated for disordered and/or non-equilibrium systems? Naively, when one thinks about disordered systems and their average correlation functions one of the very basic assumptions of SLE, the so called domain Markov property, is lost. Also, in some lattice models of Anderson transitions (the network models) there are no natural clusters to consider. Nevertheless, in this talk I will argue that one can apply the so called conformal restriction, a notion of stochastic conformal geometry closely related to SLE, to study the integer quantum Hall transition and its variants. I will focus on the Chalker-Coddington network model and will demonstrate that its average transport properties can be mapped to a classical problem where the basic objects are geometric shapes (loosely speaking, the current paths) that obey an important restriction property. At the transition point this allows to use the theory of conformal restriction to derive exact expressions for point contact conductances in the presence of various non-trivial boundary conditions.

Fractality of profit landscapes and validation of time series models for stock prices

NASA Astrophysics Data System (ADS)

Yi, Il Gu; Oh, Gabjin; Kim, Beom Jun

2013-08-01

We apply a simple trading strategy for various time series of real and artificial stock prices to understand the origin of fractality observed in the resulting profit landscapes. The strategy contains only two parameters p and q, and the sell (buy) decision is made when the log return is larger (smaller) than p (-q). We discretize the unit square (p,q) ∈ [0,1] × [0,1] into the N × N square grid and the profit Π(p,q) is calculated at the center of each cell. We confirm the previous finding that local maxima in profit landscapes are scattered in a fractal-like fashion: the number M of local maxima follows the power-law form M ˜ Na, but the scaling exponent a is found to differ for different time series. From comparisons of real and artificial stock prices, we find that the fat-tailed return distribution is closely related to the exponent a ≈ 1.6 observed for real stock markets. We suggest that the fractality of profit landscape characterized by a ≈ 1.6 can be a useful measure to validate time series model for stock prices.

Stochastic Erosion of Fractal Structure in Nonlinear Dynamical Systems

NASA Astrophysics Data System (ADS)

Agarwal, S.; Wettlaufer, J. S.

2014-12-01

We analyze the effects of stochastic noise on the Lorenz-63 model in the chaotic regime to demonstrate a set of general issues arising in the interpretation of data from nonlinear dynamical systems typical in geophysics. The model is forced using both additive and multiplicative, white and colored noise and it is shown that, through a suitable choice of the noise intensity, both additive and multiplicative noise can produce similar dynamics. We use a recently developed measure, histogram distance, to show the similarity between the dynamics produced by additive and multiplicative forcing. This phenomenon, in a nonlinear fractal structure with chaotic dynamics can be explained by understanding how noise affects the Unstable Periodic Orbits (UPOs) of the system. For delta-correlated noise, the UPOs erode the fractal structure. In the presence of memory in the noise forcing, the time scale of the noise starts to interact with the period of some UPO and, depending on the noise intensity, stochastic resonance may be observed. This also explains the mixing in dissipative dynamical systems in presence of white noise; as the fractal structure is smoothed, the decay of correlations is enhanced, and hence the rate of mixing increases with noise intensity.

The effects of intermolecular interactions on the physical properties of organogels in edible oils.

PubMed

Lupi, Francesca R; Greco, Valeria; Baldino, Noemi; de Cindio, Bruno; Fischer, Peter; Gabriele, Domenico

2016-12-01

The microstructure of organogels based on monoglycerides of fatty acids (MAGs) and policosanol and on different edible oils was investigated by using different techniques (calorimetry, nuclear magnetic resonance, infrared spectroscopy, rheology, polarized light microscopy) towards a better understanding and control of the oil gelation phenomena. Dynamic moduli were related via a fractal model to microstructural information such as solid content and fractal dimension. Infrared spectroscopy evidenced that network structure in MAGs gel is mainly due to hydrogen bonding, whereas in policosanol system is mainly given by van der Waals interactions. Because of the different relative contribution of molecular interactions, the investigated organogelators exhibit a distinguished macroscopic behavior. MAGs are sensitive to the utilized oil and structuration occurs quickly, even though at a temperature lower than policosanol. Policosanol organogels exhibit a behavior independent of the used oil and a slower gelation rate, as a result of the weaker van der Waals interactions. Nevertheless, at lower concentration a stronger final gel is obtained, probably due to of the large number of interactions arising among the long alkyl chains of the fatty alcohols. Obtained results evidenced that policosanol is very effective in gelation of different oils and seems promising for potential commercial uses. Copyright © 2016 Elsevier Inc. All rights reserved.

Influence of refractive condition on retinal vasculature complexity in younger subjects.

PubMed

Azemin, Mohd Zulfaezal Che; Daud, Norsyazwani Mohamad; Ab Hamid, Fadilah; Zahari, Ilyanoon; Sapuan, Abdul Halim

2014-01-01

The aim of this study was to compare the retinal vasculature complexity between emmetropia, and myopia in younger subjects. A total of 82 patients (24.12 ± 1.25 years) with two types of refractive conditions, myopia and emmetropia were enrolled in this study. Refraction data were converted to spherical equivalent refraction. These retinal images (right eyes) were obtained from NAVIS Lite Image Filing System and the vasculature complexity was measured by fractal dimension (D f ), quantified using a computer software following a standardized protocol. There was a significant difference (P < 0.05) in the value of D f between emmetropic (1.5666 ± 0.0160) and myopic (1.5588 ± 0.0142) groups. A positive correlation (rho = 0.260, P < 0.05) between the D f and the spherical equivalent refraction was detected in this study. Using a linear model, it was estimated that 6.7% of the variation in D f could be explained by spherical equivalent refraction. This study provides valuable findings about the effect of moderate to high myopia on the fractal dimension of the retinal vasculature network. These results show that myopic refraction in younger subjects was associated with a decrease in D f , suggesting a loss of retinal vessel density with moderate to high myopia.

Complexity and multifractality of neuronal noise in mouse and human hippocampal epileptiform dynamics

NASA Astrophysics Data System (ADS)

Serletis, Demitre; Bardakjian, Berj L.; Valiante, Taufik A.; Carlen, Peter L.

2012-10-01

Fractal methods offer an invaluable means of investigating turbulent nonlinearity in non-stationary biomedical recordings from the brain. Here, we investigate properties of complexity (i.e. the correlation dimension, maximum Lyapunov exponent, 1/fγ noise and approximate entropy) and multifractality in background neuronal noise-like activity underlying epileptiform transitions recorded at the intracellular and local network scales from two in vitro models: the whole-intact mouse hippocampus and lesional human hippocampal slices. Our results show evidence for reduced dynamical complexity and multifractal signal features following transition to the ictal epileptiform state. These findings suggest that pathological breakdown in multifractal complexity coincides with loss of signal variability or heterogeneity, consistent with an unhealthy ictal state that is far from the equilibrium of turbulent yet healthy fractal dynamics in the brain. Thus, it appears that background noise-like activity successfully captures complex and multifractal signal features that may, at least in part, be used to classify and identify brain state transitions in the healthy and epileptic brain, offering potential promise for therapeutic neuromodulatory strategies for afflicted patients suffering from epilepsy and other related neurological disorders. This paper is based on chapter 5 of Serletis (2010 PhD Dissertation Department of Physiology, Institute of Biomaterials and Biomedical Engineering, University of Toronto).

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.

Spontaneous Imbibition Process in Micro-Nano Fractal Capillaries Considering Slip Flow

NASA Astrophysics Data System (ADS)

Shen, Yinghao; Li, Caoxiong; Ge, Hongkui; Guo, Xuejing; Wang, Shaojun

An imbibition process of water into a matrix is required to investigate the influences of large-volume fracturing fluids on gas production of unconventional formations. Slip flow has been recognized by recent studies as a major mechanism of fluid transport in nanotubes. For nanopores in shale, a slip boundary is nonnegligible in the imbibition process. In this study, we established an analytic equation of spontaneous imbibition considering slip effects in capillaries. A spontaneous imbibition model that couples the analytic equation considering the slip effect was constructed based on fractal theory. We then used a model for various conditions, such as slip boundary, pore structure, and fractal dimension of pore tortuosity, to capture the imbibition characteristics considering the slip effect. A dynamic contact angle was integrated into the modeling. Results of our study verify that the slip boundary influences water imbibition significantly. The imbibition speed is significantly improved when slip length reaches the equivalent diameter of a tube. Therefore, disregarding the slip effect will underestimate the imbibition speed in shale samples.

Growing surfaces with anomalous diffusion: Results for the fractal Kardar-Parisi-Zhang equation

NASA Astrophysics Data System (ADS)

Katzav, Eytan

2003-09-01

In this paper I study a model for a growing surface in the presence of anomalous diffusion, also known as the fractal Kardar-Parisi-Zhang equation (FKPZ). This equation includes a fractional Laplacian that accounts for the possibility that surface transport is caused by a hopping mechanism of a Levy flight. It is shown that for a specific choice of parameters of the FKPZ equation, the equation can be solved exactly in one dimension, so that all the critical exponents, which describe the surface that grows under FKPZ, can be derived for that case. Afterwards, the self-consistent expansion (SCE) is used to predict the critical exponents for the FKPZ model for any choice of the parameters and any spatial dimension. It is then verified that the results obtained using SCE recover the exact result in one dimension. At the end a simple picture for the behavior of the fractal KPZ equation is suggested and the upper critical dimension of this model is discussed.

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.

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

On the Mass Fractal Character of Si-Based Structural Networks in Amorphous Polymer Derived Ceramics

PubMed Central

Sen, Sabyasachi; Widgeon, Scarlett

2015-01-01

The intermediate-range packing of SiNxC4−x (0 ≤ x ≤ 4) tetrahedra in polysilycarbodiimide and polysilazane-derived amorphous SiCN ceramics is investigated using 29Si spin-lattice relaxation nuclear magnetic resonance (SLR NMR) spectroscopy. The SiCN network in the polysilylcarbodiimide-derived ceramic consists predominantly of SiN4 tetrahedra that are characterized by a 3-dimensional spatial distribution signifying compact packing of such units to form amorphous Si3N4 clusters. On the other hand, the SiCN network of the polysilazane-derived ceramic is characterized by mixed bonded SiNxC4−x tetrahedra that are inefficiently packed with a mass fractal dimension of Df ~2.5 that is significantly lower than the embedding Euclidean dimension (D = 3). This result unequivocally confirms the hypothesis that the presence of dissimilar atoms, namely, 4-coordinated C and 3-coordinated N, in the nearest neighbor environment of Si along with some exclusion in connectivity between SiCxN4−x tetrahedra with widely different N:C ratios and the absence of bonding between C and N result in steric hindrance to an efficient packing of these structural units. It is noted that similar inefficiencies in packing are observed in polymer-derived amorphous SiOC ceramics as well as in proteins and binary hard sphere systems. PMID:28347016

Evaluation of Yogurt Microstructure Using Confocal Laser Scanning Microscopy and Image Analysis.

PubMed

Skytte, Jacob L; Ghita, Ovidiu; Whelan, Paul F; Andersen, Ulf; Møller, Flemming; Dahl, Anders B; Larsen, Rasmus

2015-06-01

The microstructure of protein networks in yogurts defines important physical properties of the yogurt and hereby partly its quality. Imaging this protein network using confocal scanning laser microscopy (CSLM) has shown good results, and CSLM has become a standard measuring technique for fermented dairy products. When studying such networks, hundreds of images can be obtained, and here image analysis methods are essential for using the images in statistical analysis. Previously, methods including gray level co-occurrence matrix analysis and fractal analysis have been used with success. However, a range of other image texture characterization methods exists. These methods describe an image by a frequency distribution of predefined image features (denoted textons). Our contribution is an investigation of the choice of image analysis methods by performing a comparative study of 7 major approaches to image texture description. Here, CSLM images from a yogurt fermentation study are investigated, where production factors including fat content, protein content, heat treatment, and incubation temperature are varied. The descriptors are evaluated through nearest neighbor classification, variance analysis, and cluster analysis. Our investigation suggests that the texton-based descriptors provide a fuller description of the images compared to gray-level co-occurrence matrix descriptors and fractal analysis, while still being as applicable and in some cases as easy to tune. © 2015 Institute of Food Technologists®

Concept of Fractal Dimension use of Multifractal Cloud Liquid Models Based on Real Data as Input to Monte Carlo Radiation Models

NASA Technical Reports Server (NTRS)

Wiscombe, W.

1999-01-01

The purpose of this paper is discuss the concept of fractal dimension; multifractal statistics as an extension of this; the use of simple multifractal statistics (power spectrum, structure function) to characterize cloud liquid water data; and to understand the use of multifractal cloud liquid water models based on real data as input to Monte Carlo radiation models of shortwave radiation transfer in 3D clouds, and the consequences of this in two areas: the design of aircraft field programs to measure cloud absorptance; and the explanation of the famous "Landsat scale break" in measured radiance.

Singular structure of Mueller matrices images of biological crystal networks for diagnostic human tissues pathological changes

NASA Astrophysics Data System (ADS)

Sakhnovskiy, M. Y.; Ushenko, V. A.

2013-09-01

The process of converting of laser radiation by optically anisotropic crystals of biological networks are singular in the sense of total (simultaneous) of mechanisms of orientation and phase (birefringence) anisotropy the formation of polarization-inhomogeneous field of scattered radiation. This work is aimed at developing a method of polarization selection mechanisms of blood plasma polycrystalline networks anisotropy. The relationship between statistics, correlation and fractal parameters of polarization-inhomogeneous images of blood plasma and by linear dichroism and linear birefringence of polycrystalline networks albumin and globulin was found. The criteria of differentiation and diagnostic images of polarization-inhomogeneous plasma samples of the control group (donor) and a group of patients with malignant changes of breast tissue was identified.

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...

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.

Determination of the relationship between major fault and zinc mineralization using fractal modeling in the Behabad fault zone, central Iran

NASA Astrophysics Data System (ADS)

Adib, Ahmad; Afzal, Peyman; Mirzaei Ilani, Shapour; Aliyari, Farhang

2017-10-01

The aim of this study is to determine a relationship between zinc mineralization and a major fault in the Behabad area, central Iran, using the Concentration-Distance to Major Fault (C-DMF), Area of Mineralized Zone-Distance to Major Fault (AMZ-DMF), and Concentration-Area (C-A) fractal models for Zn deposit/mine classification according to their distance from the Behabad fault. Application of the C-DMF and the AMZ-DMF models for Zn mineralization classification in the Behabad fault zone reveals that the main Zn deposits have a good correlation with the major fault in the area. The distance from the known zinc deposits/mines with Zn values higher than 29% and the area of the mineralized zone of more than 900 m2 to the major fault is lower than 1 km, which shows a positive correlation between Zn mineralization and the structural zone. As a result, the AMZ-DMF and C-DMF fractal models can be utilized for the delineation and the recognition of different mineralized zones in different types of magmatic and hydrothermal deposits.

Effective degrees of freedom of a random walk on a fractal

NASA Astrophysics Data System (ADS)

Balankin, Alexander S.

2015-12-01

We argue that a non-Markovian random walk on a fractal can be treated as a Markovian process in a fractional dimensional space with a suitable metric. This allows us to define the fractional dimensional space allied to the fractal as the ν -dimensional space Fν equipped with the metric induced by the fractal topology. The relation between the number of effective spatial degrees of freedom of walkers on the fractal (ν ) and fractal dimensionalities is deduced. The intrinsic time of random walk in Fν is inferred. The Laplacian operator in Fν is constructed. This allows us to map physical problems on fractals into the corresponding problems in Fν. In this way, essential features of physics on fractals are revealed. Particularly, subdiffusion on path-connected fractals is elucidated. The Coulomb potential of a point charge on a fractal embedded in the Euclidean space is derived. Intriguing attributes of some types of fractals are highlighted.

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.

Size Effect on Specific Energy Distribution in Particle Comminution

NASA Astrophysics Data System (ADS)

Xu, Yongfu; Wang, Yidong

A theoretical study is made to derive an energy distribution equation for the size reduction process from the fractal model for the particle comminution. Fractal model is employed as a valid measure of the self-similar size distribution of comminution daughter products. The tensile strength of particles varies with particle size in the manner of a power function law. The energy consumption for comminuting single particle is found to be proportional to the 5(D-3)/3rd order of the particle size, D being the fractal dimension of particle comminution daughter. The Weibull statistics is applied to describe the relationship between the breakage probability and specific energy of particle comminution. A simple equation is derived for the breakage probability of particles in view of the dependence of fracture energy on particle size. The calculated exponents and Weibull coefficients are generally in conformity with published data for fracture of particles.

Comparison of U-spatial statistics and C-A fractal models for delineating anomaly patterns of porphyry-type Cu geochemical signatures in the Varzaghan district, NW Iran

NASA Astrophysics Data System (ADS)

Ghezelbash, Reza; Maghsoudi, Abbas

2018-05-01

The delineation of populations of stream sediment geochemical data is a crucial task in regional exploration surveys. In this contribution, uni-element stream sediment geochemical data of Cu, Au, Mo, and Bi have been subjected to two reliable anomaly-background separation methods, namely, the concentration-area (C-A) fractal and the U-spatial statistics methods to separate geochemical anomalies related to porphyry-type Cu mineralization in northwest Iran. The quantitative comparison of the delineated geochemical populations using the modified success-rate curves revealed the superiority of the U-spatial statistics method over the fractal model. Moreover, geochemical maps of investigated elements revealed strongly positive correlations between strong anomalies and Oligocene-Miocene intrusions in the study area. Therefore, follow-up exploration programs should focus on these areas.

A fractal comparison of real and Austrian business cycle models

NASA Astrophysics Data System (ADS)

Mulligan, Robert F.

2010-06-01

Rescaled range and power spectral density analysis are applied to examine a diverse set of macromonetary data for fractal character and stochastic dependence. Fractal statistics are used to evaluate two competing models of the business cycle, Austrian business cycle theory and real business cycle theory. Strong evidence is found for antipersistent stochastic dependence in transactions money (M1) and components of the monetary aggregates most directly concerned with transactions, which suggests an activist monetary policy. Savings assets exhibit persistent long memory, as do those monetary aggregates which include savings assets, such as savings money (M2), M2 minus small time deposits, and money of zero maturity (MZM). Virtually all measures of economic activity display antipersistence, and this finding is invariant to whether the measures are adjusted for inflation, including real gross domestic product, real consumption expenditures, real fixed private investment, and labor productivity. This strongly disconfirms real business cycle theory.

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.

Modeling of Fibrin Gels Based on Confocal Microscopy and Light-Scattering Data

PubMed Central

Magatti, Davide; Molteni, Matteo; Cardinali, Barbara; Rocco, Mattia; Ferri, Fabio

2013-01-01

Fibrin gels are biological networks that play a fundamental role in blood coagulation and other patho/physiological processes, such as thrombosis and cancer. Electron and confocal microscopies show a collection of fibers that are relatively monodisperse in diameter, not uniformly distributed, and connected at nodal points with a branching order of ∼3–4. Although in the confocal images the hydrated fibers appear to be quite straight (mass fractal dimension Dm = 1), for the overall system 1

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.

Is volcanic phenomena of fractal nature?

NASA Astrophysics Data System (ADS)

Quevedo, R.; Lopez, D. A. L.; Alparone, S.; Hernandez Perez, P. A.; Sagiya, T.; Barrancos, J.; Rodriguez-Santana, A. A.; Ramos, A.; Calvari, S.; Perez, N. M.

2016-12-01

A particular resonance waveform pattern has been detected beneath different physical volcano manifestations from recent 2011-2012 period of volcanic unrest at El Hierro Island, Canary Islands, and also from other worldwide volcanoes with different volcanic typology. This mentioned pattern appears to be a fractal time dependent waveform repeated in different time scales (periods of time). This time dependent feature suggests this resonance as a new approach to volcano phenomena for predicting such interesting matters as earthquakes, gas emission, deformation etc. as this fractal signal has been discovered hidden in a wide typical volcanic parameters measurements. It is known that the resonance phenomenon occurring in nature usually denote a structure, symmetry or a subjacent law (Fermi et al., 1952; and later -about enhanced cross-sections symmetry in protons collisions), which, in this particular case, may be indicative of some physical interactions showing a sequence not completely chaotic but cyclic provided with symmetries. The resonance and fractal model mentioned allowed the authors to make predictions in cycles from a few weeks to months. In this work an equation for this waveform has been described and also correlations with volcanic parameters and fractal behavior demonstration have been performed, including also some suggestive possible explanations of this signal origin.

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.

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.

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.

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.

Use of wavelet-packet transforms to develop an engineering model for multifractal characterization of mutation dynamics in pathological and nonpathological gene sequences

NASA Astrophysics Data System (ADS)

Walker, David Lee

1999-12-01

This study uses dynamical analysis to examine in a quantitative fashion the information coding mechanism in DNA sequences. This exceeds the simple dichotomy of either modeling the mechanism by comparing DNA sequence walks as Fractal Brownian Motion (fbm) processes. The 2-D mappings of the DNA sequences for this research are from Iterated Function System (IFS) (Also known as the ``Chaos Game Representation'' (CGR)) mappings of the DNA sequences. This technique converts a 1-D sequence into a 2-D representation that preserves subsequence structure and provides a visual representation. The second step of this analysis involves the application of Wavelet Packet Transforms, a recently developed technique from the field of signal processing. A multi-fractal model is built by using wavelet transforms to estimate the Hurst exponent, H. The Hurst exponent is a non-parametric measurement of the dynamism of a system. This procedure is used to evaluate gene- coding events in the DNA sequence of cystic fibrosis mutations. The H exponent is calculated for various mutation sites in this gene. The results of this study indicate the presence of anti-persistent, random walks and persistent ``sub-periods'' in the sequence. This indicates the hypothesis of a multi-fractal model of DNA information encoding warrants further consideration. This work examines the model's behavior in both pathological (mutations) and non-pathological (healthy) base pair sequences of the cystic fibrosis gene. These mutations both natural and synthetic were introduced by computer manipulation of the original base pair text files. The results show that disease severity and system ``information dynamics'' correlate. These results have implications for genetic engineering as well as in mathematical biology. They suggest that there is scope for more multi-fractal models to be developed.

The correlation of fractal structures in the photospheric and the coronal magnetic field

NASA Astrophysics Data System (ADS)

Dimitropoulou, M.; Georgoulis, M.; Isliker, H.; Vlahos, L.; Anastasiadis, A.; Strintzi, D.; Moussas, X.

2009-10-01

Context: This work examines the relation between the fractal properties of the photospheric magnetic patterns and those of the coronal magnetic fields in solar active regions. Aims: We investigate whether there is any correlation between the fractal dimensions of the photospheric structures and the magnetic discontinuities formed in the corona. Methods: To investigate the connection between the photospheric and coronal complexity, we used a nonlinear force-free extrapolation method that reconstructs the 3d magnetic fields using 2d observed vector magnetograms as boundary conditions. We then located the magnetic discontinuities, which are considered as spatial proxies of reconnection-related instabilities. These discontinuities form well-defined volumes, called here unstable volumes. We calculated the fractal dimensions of these unstable volumes and compared them to the fractal dimensions of the boundary vector magnetograms. Results: Our results show no correlation between the fractal dimensions of the observed 2d photospheric structures and the extrapolated unstable volumes in the corona, when nonlinear force-free extrapolation is used. This result is independent of efforts to (1) bring the photospheric magnetic fields closer to a nonlinear force-free equilibrium and (2) omit the lower part of the modeled magnetic field volume that is almost completely filled by unstable volumes. A significant correlation between the fractal dimensions of the photospheric and coronal magnetic features is only observed at the zero level (lower limit) of approximation of a current-free (potential) magnetic field extrapolation. Conclusions: We conclude that the complicated transition from photospheric non-force-free fields to coronal force-free ones hampers any direct correlation between the fractal dimensions of the 2d photospheric patterns and their 3d counterparts in the corona at the nonlinear force-free limit, which can be considered as a second level of approximation in this study. Correspondingly, in the zero and first levels of approximation, namely, the potential and linear force-free extrapolation, respectively, we reveal a significant correlation between the fractal dimensions of the photospheric and coronal structures, which can be attributed to the lack of electric currents or to their purely field-aligned orientation.

Continuous Time Random Walk and Migration-Proliferation Dichotomy of Brain Cancer

NASA Astrophysics Data System (ADS)

Iomin, A.

A theory of fractional kinetics of glial cancer cells is presented. A role of the migration-proliferation dichotomy in the fractional cancer cell dynamics in the outer-invasive zone is discussed and explained in the framework of a continuous time random walk. The main suggested model is based on a construction of a 3D comb model, where the migration-proliferation dichotomy becomes naturally apparent and the outer-invasive zone of glioma cancer is considered as a fractal composite with a fractal dimension Dfr < 3.

Demonstration of fundamental statistics by studying timing of electronics signals in a physics-based laboratory

NASA Astrophysics Data System (ADS)

Beach, Shaun E.; Semkow, Thomas M.; Remling, David J.; Bradt, Clayton J.

2017-07-01

We have developed accessible methods to demonstrate fundamental statistics in several phenomena, in the context of teaching electronic signal processing in a physics-based college-level curriculum. A relationship between the exponential time-interval distribution and Poisson counting distribution for a Markov process with constant rate is derived in a novel way and demonstrated using nuclear counting. Negative binomial statistics is demonstrated as a model for overdispersion and justified by the effect of electronic noise in nuclear counting. The statistics of digital packets on a computer network are shown to be compatible with the fractal-point stochastic process leading to a power-law as well as generalized inverse Gaussian density distributions of time intervals between packets.

Correlation processing of polarization inhomogenous images in laser diagnostics of biological tissues

NASA Astrophysics Data System (ADS)

Trifonyuk, L.

2012-10-01

The model of interaction of laser radiation with biological tissue as a two-component amorphous-crystalline matrix was proposed. The processes of formation of polarization of laser radiation are considered, taking into account birefringence network protein fibrils. Measurement of the coordinate distribution of polarization states in the location of the laser micropolarimetr was conducted .The results of investigating the interrelation between the values of correlation (correlation area, asymmetry coefficient and autocorrelation function excess) and fractal (dispersion of logarithmic dependencies of power spectra) parameters are presented. They characterize the coordinate distributions of polarization azimuth of laser images of histological sections of women's reproductive sphere tissues and pathological changes in human organism. The diagnostic criteria of the prolapse of the vaginal tissue arising are determined.

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.

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.

Effective degrees of freedom of a random walk on a fractal.

PubMed

Balankin, Alexander S

2015-12-01

We argue that a non-Markovian random walk on a fractal can be treated as a Markovian process in a fractional dimensional space with a suitable metric. This allows us to define the fractional dimensional space allied to the fractal as the ν-dimensional space F(ν) equipped with the metric induced by the fractal topology. The relation between the number of effective spatial degrees of freedom of walkers on the fractal (ν) and fractal dimensionalities is deduced. The intrinsic time of random walk in F(ν) is inferred. The Laplacian operator in F(ν) is constructed. This allows us to map physical problems on fractals into the corresponding problems in F(ν). In this way, essential features of physics on fractals are revealed. Particularly, subdiffusion on path-connected fractals is elucidated. The Coulomb potential of a point charge on a fractal embedded in the Euclidean space is derived. Intriguing attributes of some types of fractals are highlighted.

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

Generalized Cauchy model of sea level fluctuations with long-range dependence

NASA Astrophysics Data System (ADS)

Li, Ming; Li, Jia-Yue

2017-10-01

This article suggests the contributions with two highlights. One is to propose a novel model of sea level fluctuations (sea level for short), which is called the generalized Cauchy (GC) process. It provides a new outlook for the description of local and global behaviors of sea level from a view of fractal in that the fractal dimension D that measures the local behavior of sea level and the Hurst parameter H which characterizes the global behavior of sea level are independent of each other. The other is to show that sea level appears multi-fractal in both spatial and time. Such a meaning of multi-fractal is new in the sense that a pair of fractal parameters (D, H) of sea level is varying with measurement sites and time. This research exhibits that the ranges of D and H of sea level, in general, are 1 ≤ D < 2 and 0 . 5 < H < 1, respectively but D is independent of H. With respect to the global behavior of sea level, we shall show that H > 0 . 96 for all data records at all measurement sites, implying that strong LRD may be a general phenomenon of sea level. On the other side, regarding with the local behavior, we will reveal that there appears D = 1 or D ≈ 1 for data records at a few stations and at some time, but D > 0 . 96 at most stations and at most time, meaning that sea level may appear highly local irregularity more frequently than weak local one.

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

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.

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.

Modeling Reality - How Computers Mirror Life

NASA Astrophysics Data System (ADS)

Bialynicki-Birula, Iwo; Bialynicka-Birula, Iwona

2005-01-01

The bookModeling Reality covers a wide range of fascinating subjects, accessible to anyone who wants to learn about the use of computer modeling to solve a diverse range of problems, but who does not possess a specialized training in mathematics or computer science. The material presented is pitched at the level of high-school graduates, even though it covers some advanced topics (cellular automata, Shannon's measure of information, deterministic chaos, fractals, game theory, neural networks, genetic algorithms, and Turing machines). These advanced topics are explained in terms of well known simple concepts: Cellular automata - Game of Life, Shannon's formula - Game of twenty questions, Game theory - Television quiz, etc. The book is unique in explaining in a straightforward, yet complete, fashion many important ideas, related to various models of reality and their applications. Twenty-five programs, written especially for this book, are provided on an accompanying CD. They greatly enhance its pedagogical value and make learning of even the more complex topics an enjoyable pleasure.

Stochastic Models for Precipitable Water in Convection

NASA Astrophysics Data System (ADS)

Leung, Kimberly

Atmospheric precipitable water vapor (PWV) is the amount of water vapor in the atmosphere within a vertical column of unit cross-sectional area and is a critically important parameter of precipitation processes. However, accurate high-frequency and long-term observations of PWV in the sky were impossible until the availability of modern instruments such as radar. The United States Department of Energy (DOE)'s Atmospheric Radiation Measurement (ARM) Program facility made the first systematic and high-resolution observations of PWV at Darwin, Australia since 2002. At a resolution of 20 seconds, this time series allowed us to examine the volatility of PWV, including fractal behavior with dimension equal to 1.9, higher than the Brownian motion dimension of 1.5. Such strong fractal behavior calls for stochastic differential equation modeling in an attempt to address some of the difficulties of convective parameterization in various kinds of climate models, ranging from general circulation models (GCM) to weather research forecasting (WRF) models. This important observed data at high resolution can capture the fractal behavior of PWV and enables stochastic exploration into the next generation of climate models which considers scales from micrometers to thousands of kilometers. As a first step, this thesis explores a simple stochastic differential equation model of water mass balance for PWV and assesses accuracy, robustness, and sensitivity of the stochastic model. A 1000-day simulation allows for the determination of the best-fitting 25-day period as compared to data from the TWP-ICE field campaign conducted out of Darwin, Australia in early 2006. The observed data and this portion of the simulation had a correlation coefficient of 0.6513 and followed similar statistics and low-resolution temporal trends. Building on the point model foundation, a similar algorithm was applied to the National Center for Atmospheric Research (NCAR)'s existing single-column model as a test-of-concept for eventual inclusion in a general circulation model. The stochastic scheme was designed to be coupled with the deterministic single-column simulation by modifying results of the existing convective scheme (Zhang-McFarlane) and was able to produce a 20-second resolution time series that effectively simulated observed PWV, as measured by correlation coefficient (0.5510), fractal dimension (1.9), statistics, and visual examination of temporal trends. Results indicate that simulation of a highly volatile time series of observed PWV is certainly achievable and has potential to improve prediction capabilities in climate modeling. Further, this study demonstrates the feasibility of adding a mathematics- and statistics-based stochastic scheme to an existing deterministic parameterization to simulate observed fractal behavior.

Lidar cross-sections of soot fractal aggregates: Assessment of equivalent-sphere models

NASA Astrophysics Data System (ADS)

Ceolato, Romain; Gaudfrin, Florian; Pujol, Olivier; Riviere, Nicolas; Berg, Matthew J.; Sorensen, Christopher M.

2018-06-01

This work assesses the ability of equivalent-sphere models to reproduce the optical properties of soot aggregates relevant for lidar remote sensing, i.e. the backscattering and extinction cross sections. Lidar cross-sections are computed with a spectral discrete dipole approximation model over the visible-to-infrared (400-5000 nm) spectrum and compared with equivalent-sphere approximations. It is shown that the equivalent-sphere approximation, applied to fractal aggregates, has a limited ability to calculate such cross-sections well. The approximation should thus be used with caution for the computation of broadband lidar cross-sections, especially backscattering, at small and intermediate wavelengths (e.g. UV to visible).

Modeling Complex Phenomena Using Multiscale Time Sequences

DTIC Science & Technology

2009-08-24

measures based on Hurst and Holder exponents , auto-regressive methods and Fourier and wavelet decomposition methods. The applications for this technology...relate to each other. This can be done by combining a set statistical fractal measures based on Hurst and Holder exponents , auto-regressive...different scales and how these scales relate to each other. This can be done by combining a set statistical fractal measures based on Hurst and

Human development VII: a spiral fractal model of fine structure of physical energy could explain central aspects of biological information, biological organization and biological creativity.

PubMed

Ventegodt, Søren; Hermansen, Tyge Dahl; Flensborg-Madsen, Trine; Rald, Erik; Nielsen, Maj Lyck; Merrick, Joav

2006-11-14

In this paper we have made a draft of a physical fractal essence of the universe, a sketch of a new cosmology, which we believe to lay at the root of our new holistic biological paradigm. We present the fractal roomy spiraled structures and the energy-rich dancing "infinite strings" or lines of the universe that our hypothesis is based upon. The geometric language of this cosmology is symbolic and both pre-mathematical and pre-philosophical. The symbols are both text and figures, and using these we step by step explain the new model that at least to some extent is able to explain the complex informational system behind morphogenesis, ontogenesis, regeneration and healing. We suggest that it is from this highly dynamic spiraled structure that organization of cells, organs, and the wholeness of the human being including consciousness emerge. The model of "dancing fractal spirals" carries many similarities to premodern cultures descriptions of the energy of the life and universe. Examples are the Native American shamanistic descriptions of their perception of energy and the old Indian Yogis descriptions of the life-energy within the body and outside. Similar ideas of energy and matter are found in the modern superstring theories. The model of the informational system of the organism gives new meaning to Bateson's definition of information: "A difference that makes a difference", and indicates how information-directed self-organization can exist on high structural levels in living organisms, giving birth to their subjectivity and consciousness.

Digital video technologies and their network requirements

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

R. P. Tsang; H. Y. Chen; J. M. Brandt

1999-11-01

Coded digital video signals are considered to be one of the most difficult data types to transport due to their real-time requirements and high bit rate variability. In this study, the authors discuss the coding mechanisms incorporated by the major compression standards bodies, i.e., JPEG and MPEG, as well as more advanced coding mechanisms such as wavelet and fractal techniques. The relationship between the applications which use these coding schemes and their network requirements are the major focus of this study. Specifically, the authors relate network latency, channel transmission reliability, random access speed, buffering and network bandwidth with the variousmore » coding techniques as a function of the applications which use them. Such applications include High-Definition Television, Video Conferencing, Computer-Supported Collaborative Work (CSCW), and Medical Imaging.« less

Use of space-filling curves to select sample locations in natural resource monitoring studies

Treesearch

Andrew Lister; Charles T. Scott

2009-01-01

The establishment of several large area monitoring networks over the past few decades has led to increased research into ways to spatially balance sample locations across the landscape. Many of these methods are well documented and have been used in the past with great success. In this paper, we present a method using geographic information systems (GIS) and fractals...

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

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.

An improved method of continuous LOD based on fractal theory in terrain rendering

NASA Astrophysics Data System (ADS)

Lin, Lan; Li, Lijun

2007-11-01

With the improvement of computer graphic hardware capability, the algorithm of 3D terrain rendering is going into the hot topic of real-time visualization. In order to solve conflict between the rendering speed and reality of rendering, this paper gives an improved method of terrain rendering which improves the traditional continuous level of detail technique based on fractal theory. This method proposes that the program needn't to operate the memory repeatedly to obtain different resolution terrain model, instead, obtains the fractal characteristic parameters of different region according to the movement of the viewpoint. Experimental results show that the method guarantees the authenticity of landscape, and increases the real-time 3D terrain rendering speed.

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.

Multi-year encoding of daily rainfall and streamflow via the fractal-multifractal method

NASA Astrophysics Data System (ADS)

Puente, C. E.; Maskey, M.; Sivakumar, B.

2017-12-01

A deterministic geometric approach, the fractal-multifractal (FM) method, which has been proven to be faithful in encoding daily geophysical sets over a year, is used to describe records over multiple years at a time. Looking for FM parameter trends over longer periods, the present study shows FM descriptions of daily rainfall and streamflow gathered over five consecutive years optimizing deviations on accumulated sets. The results for 100 and 60 sets of five years for rainfall streamflow, respectively, near Sacramento, California illustrate that: (a) encoding of both types of data sets may be accomplished with relatively small errors; and (b) predicting the geometry of both variables appears to be possible, even five years ahead, training neural networks on the respective FM parameters. It is emphasized that the FM approach not only captures the accumulated sets over successive pentades but also preserves other statistical attributes including the overall "texture" of the records.

On the holistic approach in cellular and cancer biology: nonlinearity, complexity, and quasi-determinism of the dynamic cellular network.

PubMed

Waliszewski, P; Molski, M; Konarski, J

1998-06-01

A keystone of the molecular reductionist approach to cellular biology is a specific deductive strategy relating genotype to phenotype-two distinct categories. This relationship is based on the assumption that the intermediary cellular network of actively transcribed genes and their regulatory elements is deterministic (i.e., a link between expression of a gene and a phenotypic trait can always be identified, and evolution of the network in time is predetermined). However, experimental data suggest that the relationship between genotype and phenotype is nonbijective (i.e., a gene can contribute to the emergence of more than just one phenotypic trait or a phenotypic trait can be determined by expression of several genes). This implies nonlinearity (i.e., lack of the proportional relationship between input and the outcome), complexity (i.e. emergence of the hierarchical network of multiple cross-interacting elements that is sensitive to initial conditions, possesses multiple equilibria, organizes spontaneously into different morphological patterns, and is controlled in dispersed rather than centralized manner), and quasi-determinism (i.e., coexistence of deterministic and nondeterministic events) of the network. Nonlinearity within the space of the cellular molecular events underlies the existence of a fractal structure within a number of metabolic processes, and patterns of tissue growth, which is measured experimentally as a fractal dimension. Because of its complexity, the same phenotype can be associated with a number of alternative sequences of cellular events. Moreover, the primary cause initiating phenotypic evolution of cells such as malignant transformation can be favored probabilistically, but not identified unequivocally. Thermodynamic fluctuations of energy rather than gene mutations, the material traits of the fluctuations alter both the molecular and informational structure of the network. Then, the interplay between deterministic chaos, complexity, self-organization, and natural selection drives formation of malignant phenotype. This concept offers a novel perspective for investigation of tumorigenesis without invalidating current molecular findings. The essay integrates the ideas of the sciences of complexity in a biological context.

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

PIV Measurements of the Near-Wake behind a Fractal Tree

NASA Astrophysics Data System (ADS)

Bai, Kunlun; Meneveau, Charles; Katz, Joseph

2010-11-01

An experimental study of turbulent flow in the wake of a fractal-like tree has been carried out. Fractals provide the opportunity to study the interactions of flow with complicated, multiple-scale objects, yet whose geometric construction rules are simple. We consider a pre-fractal tree with five generations, with three branches and scale- reduction factor 1/2 at each generation. Its similarity fractal dimension is Ds˜1.585. Experiments are carried out in a water tunnel with the ability of index- matching, although current measurements do not utilize this capability yet. The incoming velocity profile is designed to mimic the velocity profile in a forest canopy. PIV measurements are carried out on 14 horizontal planes parallel to the bottom surface. Drag forces are measured using a load cell. Mean velocity and turbulence quantities are reported at various heights in the wake. Mean vorticity contours on the upper planes show signatures of the smaller branches, although the wakes from the smallest two branches are not visible in the data possibly due to rapid mixing. Interestingly, their signatures can be observed from the elevated spectra at small scales. Momentum deficit in the wake profiles and drag forces are compared. The results from this experiment also serve as database against which to compare computer simulations and models.

Archean Earth Atmosphere Fractal Haze Aggregates: Light Scattering Calculations and the Faint Young Sun Paradox

NASA Astrophysics Data System (ADS)

Boness, D. A.; Terrell-Martinez, B.

2010-12-01

As part of an ongoing undergraduate research project of light scattering calculations involving fractal carbonaceous soot aggregates relevant to current anthropogenic and natural sources in Earth's atmosphere, we have read with interest a recent paper [E.T. Wolf and O.B Toon,Science 328, 1266 (2010)] claiming that the Faint Young Sun paradox discussed four decades ago by Carl Sagan and others can be resolved without invoking heavy CO2 concentrations as a greenhouse gas warming the early Earth enough to sustain liquid water and hence allow the origin of life. Wolf and Toon report that a Titan-like Archean Earth haze, with a fractal haze aggregate nature due to nitrogen-methane photochemistry at high altitudes, should block enough UV light to protect the warming greenhouse gas NH3 while allowing enough visible light to reach the surface of the Earth. To test this hypothesis, we have employed a rigorous T-Matrix arbitrary-particle light scattering technique, to avoid the simplifications inherent in Mie-sphere scattering, on haze fractal aggregates at UV and visible wavelenths of incident light. We generate these model aggregates using diffusion-limited cluster aggregation (DLCA) algorithms, which much more closely fit actual haze fractal aggregates than do diffusion-limited aggregation (DLA) algorithms.

Ocean manganese nodules as stromatolite with a fractal like-signature

NASA Astrophysics Data System (ADS)

Akai, Junji; Akiyama, Shigeki; Tsuchiyama, Akira; Akai, Kurumi

Deep-sea manganese (Mn) nodules are problematic in terms of factors such as their characteristic form and genesis. There are many reports of bacterial species from manganese nodules. However, the genesis of these nodules has not been fully confirmed. Samples, mainly from the Clarion Clipperton Fracture zone in the Pacific Ocean, were examined by mineralogical methods and X-ray CT. Thin sections of these samples showed columnar stromatolite structures with rhythmic bands. Mineralized bacteria were observed by SEM and TEM. Surface morphology could be described as having a fractal-like nature. The fractal characteristics of spherical to dome-like forms were fundamentally composed of at least four ranks. The 4th order form corresponds to the stromatolite dome top shapes. Similar granular domain units and porous characteristics in manganese nodules were clearly observed by X-ray CT sections. Mathematical simulation based on fractal models reproduced similar morphological characteristics to the natural samples. So, we arrived at the concluding hypothesis that manganese nodules are aggregated stromatolite with fractal-like characteristics. Furthermore, we discussed the possibility that the nature of the layer manganese oxide minerals as the major component of the nodule and associated Fe-oxyhydroxide minerals may become an absorber/scavenger of strategic heavy metals and also toxic metals in the environments.

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

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.

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…

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.

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.

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.

Distinctive fingerprints of erosional regimes in terrestrial channel networks

NASA Astrophysics Data System (ADS)

Grau Galofre, A.; Jellinek, M.

2017-12-01

Satellite imagery and digital elevation maps capture the large scale morphology of channel networks attributed to long term erosional processes, such as fluvial, glacial, groundwater sapping and subglacial erosion. Characteristic morphologies associated with each of these styles of erosion have been studied in detail, but there exists a knowledge gap related to their parameterization and quantification. This knowledge gap prevents a rigorous analysis of the dominant processes that shaped a particular landscape, and a comparison across styles of erosion. To address this gap, we use previous morphological descriptions of glaciers, rivers, sapping valleys and tunnel valleys to identify and measure quantitative metrics diagnostic of these distinctive styles of erosion. From digital elevation models, we identify four geometric metrics: The minimum channel width, channel aspect ratio (longest length to channel width at the outlet), presence of undulating longitudinal profiles, and tributary junction angle. We also parameterize channel network complexity in terms of its stream order and fractal dimension. We then perform a statistical classification of the channel networks using a Principal Component Analysis on measurements of these six metrics on a dataset of 70 channelized systems. We show that rivers, glaciers, groundwater seepage and subglacial meltwater erode the landscape in rigorously distinguishable ways. Our methodology can more generally be applied to identify the contributions of different processes involved in carving a channel network. In particular, we are able to identify transitions from fluvial to glaciated landscapes or vice-versa.

OBSIFRAC: database-supported software for 3D modeling of rock mass fragmentation

NASA Astrophysics Data System (ADS)

Empereur-Mot, Luc; Villemin, Thierry

2003-03-01

Under stress, fractures in rock masses tend to form fully connected networks. The mass can thus be thought of as a 3D series of blocks produced by fragmentation processes. A numerical model has been developed that uses a relational database to describe such a mass. The model, which assumes the fractures to be plane, allows data from natural networks to test theories concerning fragmentation processes. In the model, blocks are bordered by faces that are composed of edges and vertices. A fracture can originate from a seed point, its orientation being controlled by the stress field specified by an orientation matrix. Alternatively, it can be generated from a discrete set of given orientations and positions. Both kinds of fracture can occur together in a model. From an original simple block, a given fracture produces two simple polyhedral blocks, and the original block becomes compound. Compound and simple blocks created throughout fragmentation are stored in the database. Several fragmentation processes have been studied. In one scenario, a constant proportion of blocks is fragmented at each step of the process. The resulting distribution appears to be fractal, although seed points are random in each fragmented block. In a second scenario, division affects only one random block at each stage of the process, and gives a Weibull volume distribution law. This software can be used for a large number of other applications.

Fractal attractors and singular invariant measures in two-sector growth models with random factor shares

NASA Astrophysics Data System (ADS)

La Torre, Davide; Marsiglio, Simone; Mendivil, Franklin; Privileggi, Fabio

2018-05-01

We analyze a multi-sector growth model subject to random shocks affecting the two sector-specific production functions twofold: the evolution of both productivity and factor shares is the result of such exogenous shocks. We determine the optimal dynamics via Euler-Lagrange equations, and show how these dynamics can be described in terms of an iterated function system with probability. We also provide conditions that imply the singularity of the invariant measure associated with the fractal attractor. Numerical examples show how specific parameter configurations might generate distorted copies of the Barnsley's fern attractor.

Is fractal 1/f scaling in stream chemistry universal?

NASA Astrophysics Data System (ADS)

Hrachowitz, Markus

2016-04-01

Stream water chemistry data from catchments worldwide suggest that catchments act as filters that transform white noise, i.e. random, input signals such as in precipitation, into 1/f^α noise whose slope in a power spectrum typically ranges between -0.5>α>-1.5. This previously lead to the hypothesis that catchments act as fractal filters. In other words, it was posed that considering uncertainty, a slope of α=-1 may be a universal and intrinsic property of catchments. Such fractal scaling characteristics would have considerable implications on the predictability of stream water chemistry, as both, temporal short- and long-range interdependence and memory control the system response. While short memories and thus flatter slopes with α closer to 0 indicate poor short term but good long-term predictability, steeper slopes with values of α <<-1 indicate the opposite. In fractal systems, i.e. where α=-1, this therefore leads to inherent problems of robustly predicting both, short and long-term response patterns. The hypothesis of catchments acting as fractal filters (α=-1), however, remains to be tested more profoundly. It is, for example, not yet clear, if the observed inter-catchment variations in α indeed need to be interpreted as uncertainty and noise in the signal or if the variations underlie a systematic pattern and can be explained by some characteristic of catchment function, as was recently suggested in a modelling study based two experimental catchments (Hrachowitz et al., 2015). Here we will therefore further test the hypothesis that the spectral slope of stream water chemistry is not necessarily α=-1 and that catchments therefore do not inherently act as fractal filters. Further, it will be tested if closer links between the variations in spectral slope and hydrological function of catchments can be identified. The combined data-analysis and modelling study uses hydrochemical data (i.e. Cl- and O-18) from a wide range of catchments worldwide to allow a robust inter-comparison of response characteristics. The high number of study catchments is chosen to represent physically contrasting catchments in distinct climate zones, distinct landscape types and with distinct vegetation patterns. To identify potential patterns in the variations of α, firstly the power spectra of the observed stream chemistry in the study catchments are compared with physical catchment characteristics using statistical methods such as cluster analysis. In a subsequent step, the stream water dynamics of the study catchments are modeled using integrated catchment-scale conceptual models. Catchments for which the observed spectral signature can be meaningfully reproduced by the model, are used for further analysis, relating the model-internal flux and state dynamics to variations in α, to explore if systematic links between different flow processes and a can be established.

Mapping Curie temperature depth in the western United States with a fractal model for crustal magnetization

USGS Publications Warehouse

Bouligand, C.; Glen, J.M.G.; Blakely, R.J.

2009-01-01

We have revisited the problem of mapping depth to the Curie temperature isotherm from magnetic anomalies in an attempt to provide a measure of crustal temperatures in the western United States. Such methods are based on the estimation of the depth to the bottom of magnetic sources, which is assumed to correspond to the temperature at which rocks lose their spontaneous magnetization. In this study, we test and apply a method based on the spectral analysis of magnetic anomalies. Early spectral analysis methods assumed that crustal magnetization is a completely uncorrelated function of position. Our method incorporates a more realistic representation where magnetization has a fractal distribution defined by three independent parameters: the depths to the top and bottom of magnetic sources and a fractal parameter related to the geology. The predictions of this model are compatible with radial power spectra obtained from aeromagnetic data in the western United States. Model parameters are mapped by estimating their value within a sliding window swept over the study area. The method works well on synthetic data sets when one of the three parameters is specified in advance. The application of this method to western United States magnetic compilations, assuming a constant fractal parameter, allowed us to detect robust long-wavelength variations in the depth to the bottom of magnetic sources. Depending on the geologic and geophysical context, these features may result from variations in depth to the Curie temperature isotherm, depth to the mantle, depth to the base of volcanic rocks, or geologic settings that affect the value of the fractal parameter. Depth to the bottom of magnetic sources shows several features correlated with prominent heat flow anomalies. It also shows some features absent in the map of heat flow. Independent geophysical and geologic data sets are examined to determine their origin, thereby providing new insights on the thermal and geologic crustal structure of the western United States.

The Sun-Earth connect 2: Modelling patterns of a fractal Sun in time and space using the fine structure constant

NASA Astrophysics Data System (ADS)

Baker, Robert G. V.

2017-02-01

Self-similar matrices of the fine structure constant of solar electromagnetic force and its inverse, multiplied by the Carrington synodic rotation, have been previously shown to account for at least 98% of the top one hundred significant frequencies and periodicities observed in the ACRIM composite irradiance satellite measurement and the terrestrial 10.7cm Penticton Adjusted Daily Flux data sets. This self-similarity allows for the development of a time-space differential equation (DE) where the solutions define a solar model for transmissions through the core, radiative, tachocline, convective and coronal zones with some encouraging empirical and theoretical results. The DE assumes a fundamental complex oscillation in the solar core and that time at the tachocline is smeared with real and imaginary constructs. The resulting solutions simulate for tachocline transmission, the solar cycle where time-line trajectories either 'loop' as Hermite polynomials for an active Sun or 'tail' as complementary error functions for a passive Sun. Further, a mechanism that allows for the stable energy transmission through the tachocline is explored and the model predicts the initial exponential coronal heating from nanoflare supercharging. The twisting of the field at the tachocline is then described as a quaternion within which neutrinos can oscillate. The resulting fractal bubbles are simulated as a Julia Set which can then aggregate from nanoflares into solar flares and prominences. Empirical examples demonstrate that time and space fractals are important constructs in understanding the behaviour of the Sun, from the impact on climate and biological histories on Earth, to the fractal influence on the spatial distributions of the solar system. The research suggests that there is a fractal clock underpinning solar frequencies in packages defined by the fine structure constant, where magnetic flipping and irradiance fluctuations at phase changes, have periodically impacted on the Earth and the rest of the solar system since time immemorial.

Critical phenomena at a first-order phase transition in a lattice of glow lamps: Experimental findings and analogy to neural activity

NASA Astrophysics Data System (ADS)

Minati, Ludovico; de Candia, Antonio; Scarpetta, Silvia

2016-07-01

Networks of non-linear electronic oscillators have shown potential as physical models of neural dynamics. However, two properties of brain activity, namely, criticality and metastability, remain under-investigated with this approach. Here, we present a simple circuit that exhibits both phenomena. The apparatus consists of a two-dimensional square lattice of capacitively coupled glow (neon) lamps. The dynamics of lamp breakdown (flash) events are controlled by a DC voltage globally connected to all nodes via fixed resistors. Depending on this parameter, two phases having distinct event rate and degree of spatiotemporal order are observed. The transition between them is hysteretic, thus a first-order one, and it is possible to enter a metastability region, wherein, approaching a spinodal point, critical phenomena emerge. Avalanches of events occur according to power-law distributions having exponents ≈3/2 for size and ≈2 for duration, and fractal structure is evident as power-law scaling of the Fano factor. These critical exponents overlap observations in biological neural networks; hence, this circuit may have value as building block to realize corresponding physical models.

Fuzzy set methods for object recognition in space applications

NASA Technical Reports Server (NTRS)

Keller, James M.

1991-01-01

Progress on the following tasks is reported: (1) fuzzy set-based decision making methodologies; (2) feature calculation; (3) clustering for curve and surface fitting; and (4) acquisition of images. The general structure for networks based on fuzzy set connectives which are being used for information fusion and decision making in space applications is described. The structure and training techniques for such networks consisting of generalized means and gamma-operators are described. The use of other hybrid operators in multicriteria decision making is currently being examined. Numerous classical features on image regions such as gray level statistics, edge and curve primitives, texture measures from cooccurrance matrix, and size and shape parameters were implemented. Several fractal geometric features which may have a considerable impact on characterizing cluttered background, such as clouds, dense star patterns, or some planetary surfaces, were used. A new approach to a fuzzy C-shell algorithm is addressed. NASA personnel are in the process of acquiring suitable simulation data and hopefully videotaped actual shuttle imagery. Photographs have been digitized to use in the algorithms. Also, a model of the shuttle was assembled and a mechanism to orient this model in 3-D to digitize for experiments on pose estimation is being constructed.

Critical phenomena at a first-order phase transition in a lattice of glow lamps: Experimental findings and analogy to neural activity

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

Minati, Ludovico, E-mail: lminati@ieee.org, E-mail: ludovico.minati@unitn.it, E-mail: ludovico.minati@ifj.edu; Complex Systems Theory Department, Institute of Nuclear Physics, Polish Academy of Sciences, Kraków; Candia, Antonio de

2016-07-15

Networks of non-linear electronic oscillators have shown potential as physical models of neural dynamics. However, two properties of brain activity, namely, criticality and metastability, remain under-investigated with this approach. Here, we present a simple circuit that exhibits both phenomena. The apparatus consists of a two-dimensional square lattice of capacitively coupled glow (neon) lamps. The dynamics of lamp breakdown (flash) events are controlled by a DC voltage globally connected to all nodes via fixed resistors. Depending on this parameter, two phases having distinct event rate and degree of spatiotemporal order are observed. The transition between them is hysteretic, thus a first-ordermore » one, and it is possible to enter a metastability region, wherein, approaching a spinodal point, critical phenomena emerge. Avalanches of events occur according to power-law distributions having exponents ≈3/2 for size and ≈2 for duration, and fractal structure is evident as power-law scaling of the Fano factor. These critical exponents overlap observations in biological neural networks; hence, this circuit may have value as building block to realize corresponding physical models.« less

Multifractality of cerebral blood flow

NASA Astrophysics Data System (ADS)

West, Bruce J.; Latka, Miroslaw; Glaubic-Latka, Marta; Latka, Dariusz

2003-02-01

Scale invariance, the property relating time series across multiple scales, has provided a new perspective of physiological phenomena and their underlying control systems. The traditional “signal plus noise” paradigm of the engineer was first replaced with a model in which biological time series have a fractal structure in time (Fractal Physiology, Oxford University Press, Oxford, 1994). This new paradigm was subsequently shown to be overly restrictive when certain physiological signals were found to be characterized by more than one scaling parameter and therefore to belong to a class of more complex processes known as multifractals (Fractals, Plenum Press, New York, 1988). Here we demonstrate that in addition to heart rate (Nature 399 (1999) 461) and human gait (Phys. Rev. E, submitted for publication), the nonlinear control system for cerebral blood flow (CBF) (Phys. Rev. Lett., submitted for publication; Phys. Rev. E 59 (1999) 3492) is multifractal. We also find that this multifractality is greatly reduced for subjects with “serious” migraine and we present a simple model for the underlying control process to describe this effect.

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

T-matrix modeling of linear depolarization by morphologically complex soot and soot-containing aerosols

NASA Astrophysics Data System (ADS)

Mishchenko, Michael I.; Liu, Li; Mackowski, Daniel W.

2013-07-01

We use state-of-the-art public-domain Fortran codes based on the T-matrix method to calculate orientation and ensemble averaged scattering matrix elements for a variety of morphologically complex black carbon (BC) and BC-containing aerosol particles, with a special emphasis on the linear depolarization ratio (LDR). We explain theoretically the quasi-Rayleigh LDR peak at side-scattering angles typical of low-density soot fractals and conclude that the measurement of this feature enables one to evaluate the compactness state of BC clusters and trace the evolution of low-density fluffy fractals into densely packed aggregates. We show that small backscattering LDRs measured with ground-based, airborne, and spaceborne lidars for fresh smoke generally agree with the values predicted theoretically for fluffy BC fractals and densely packed near-spheroidal BC aggregates. To reproduce higher lidar LDRs observed for aged smoke, one needs alternative particle models such as shape mixtures of BC spheroids or cylinders.

T-Matrix Modeling of Linear Depolarization by Morphologically Complex Soot and Soot-Containing Aerosols

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Liu, Li; Mackowski, Daniel W.

2013-01-01

We use state-of-the-art public-domain Fortran codes based on the T-matrix method to calculate orientation and ensemble averaged scattering matrix elements for a variety of morphologically complex black carbon (BC) and BC-containing aerosol particles, with a special emphasis on the linear depolarization ratio (LDR). We explain theoretically the quasi-Rayleigh LDR peak at side-scattering angles typical of low-density soot fractals and conclude that the measurement of this feature enables one to evaluate the compactness state of BC clusters and trace the evolution of low-density fluffy fractals into densely packed aggregates. We show that small backscattering LDRs measured with groundbased, airborne, and spaceborne lidars for fresh smoke generally agree with the values predicted theoretically for fluffy BC fractals and densely packed near-spheroidal BC aggregates. To reproduce higher lidar LDRs observed for aged smoke, one needs alternative particle models such as shape mixtures of BC spheroids or cylinders.

Cerebral Microcirculation and Oxygen Tension in the Human Secondary Cortex

PubMed Central

Linninger, A. A.; Gould, I. G.; Marinnan, T.; Hsu, C.-Y.; Chojecki, M.; Alaraj, A.

2013-01-01

The three-dimensional spatial arrangement of the cortical microcirculatory system is critical for understanding oxygen exchange between blood vessels and brain cells. A three-dimensional computer model of a 3 × 3 × 3 mm3 subsection of the human secondary cortex was constructed to quantify oxygen advection in the microcirculation, tissue oxygen perfusion, and consumption in the human cortex. This computer model accounts for all arterial, capillary and venous blood vessels of the cerebral microvascular bed as well as brain tissue occupying the extravascular space. Microvessels were assembled with optimization algorithms emulating angiogenic growth; a realistic capillary bed was built with space filling procedures. The extravascular tissue was modeled as a porous medium supplied with oxygen by advection–diffusion to match normal metabolic oxygen demand. The resulting synthetic computer generated network matches prior measured morphometrics and fractal patterns of the cortical microvasculature. This morphologically accurate, physiologically consistent, multi-scale computer network of the cerebral microcirculation predicts the oxygen exchange of cortical blood vessels with the surrounding gray matter. Oxygen tension subject to blood pressure and flow conditions were computed and validated for the blood as well as brain tissue. Oxygen gradients along arterioles, capillaries and veins agreed with in vivo trends observed recently in imaging studies within experimental tolerances and uncertainty. PMID:23842693

Viscoelasticity and structure of blood clots generated in-vitro by rheometry: A comparison between human, horse, rat, and camel.

PubMed

Dibiasi, Christoph; Plewka, Jacek; Ploszczanski, Leon; Glanz, Veronika; Lichtenegger, Helga; Windberger, Ursula

2018-04-14

Although the coagulation system is evolutionary well preserved, profound species differences exist in viscoelastic as well as in common laboratory tests of coagulation. Evaluating differences in clot formation and material characterisation of clots of four mammalian species on macro-, micro- and nanoscales by the means of rheometry, scanning electron microscopy (SEM) and small angle x-ray scattering (SAXS). Blood samples were collected from healthy human volunteers, laboratory rats (HL/LE inbred strain), warmblood horses and dromedary camels. Clot formation was observed by oscillating shear rheometry until plateau formation of the shear storage modulus G', at which point selected clots were prepared for scanning electron microscopy. SEM images were analysed for fibre diameter and fractal dimension. Additionally, scattering profiles for plasma and whole blood samples were obtained with SAXS. Viscoelasticity of clots showed great interspecies variation: clots of rats and horses exhibited shorter clotting times and higher G' plateau values, when compared to human clots. Camel clots showed unique clotting characteristics with no G' plateau formation in the timeframe observed. Less differentiating features were found with SEM and SAXS, although the rat fibre network appears to be more convoluted and dense, which resulted in a higher fractal dimension. Clotting kinetic differs between the species, which is not only of clinical interest, but could also be an important finding for animal models of blood coagulation.

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.