Synthesis of the advances in and application of fractal characteristic of traffic flow.

DOT National Transportation Integrated Search

2013-07-01

Fractals are irregular geometric objects that exhibit finite details at all scales, and once magnified, their basic structures remain the same regardless of the scale of magnification. Fractal theory has been successfully applied in different fields ...

Synthesis of the advance in and application of fractal characteristics of traffic flow.

DOT National Transportation Integrated Search

2013-07-01

Fractals are irregular geometric objects that exhibit finite details at all scales, and once magnified, their basic structures remain the same regardless of the scale of magnification. Fractal theory has been successfully applied in different fields ...

Synthesis of the advances in and application of fractal characteristic of traffic flow : [summary].

DOT National Transportation Integrated Search

2013-07-01

Fractals are geometric objects that are self-similar, meaning that their basic structure remains the same regardless of the scale of magnification. Self-similarity is readily seen in nature, for example, in trees, coastlines, clouds, etc. fractal...

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.

Processes of conversion of a hot metal particle into aerogel through clusters

NASA Astrophysics Data System (ADS)

Smirnov, B. M.

2015-10-01

Processes are considered for conversion into a fractal structure of a hot metal micron-size particle that is located in a buffer gas or a gas flow and is heated by an external electric or electromagnetic source or by a plasma. The parameter of this heating is the particle temperature, which is the same in the entire particle volume because of its small size and high conductivity. Three processes determine the particle heat balance: particle radiation, evaporation of metal atoms from the particle surface, and heat transport to the surrounding gas due to its thermal conductivity. The particle heat balance is analyzed based on these processes, which are analogous to those for bulk metals with the small particle size, and its high temperature taken into account. Outside the particle, where the gas temperature is lower than on its surface, the formed metal vapor in a buffer gas flow is converted into clusters. Clusters grow as a result of coagulation until they become liquid, and then clusters form fractal aggregates if they are removed form the gas flow. Subsequently, associations of fractal aggregates join into a fractal structure. The rate of this process increases in medium electric fields, and the formed fractal structure has features of aerogels and fractal fibers. As a result of a chain of the above processes, a porous metal film may be manufactured for use as a filter or catalyst for gas flows.

Turbulence Enhancement by Fractal Square Grids: Effects of the Number of Fractal Scales

NASA Astrophysics Data System (ADS)

Omilion, Alexis; Ibrahim, Mounir; Zhang, Wei

2017-11-01

Fractal square grids offer a unique solution for passive flow control as they can produce wakes with a distinct turbulence intensity peak and a prolonged turbulence decay region at the expense of only minimal pressure drop. While previous studies have solidified this characteristic of fractal square grids, how the number of scales (or fractal iterations N) affect turbulence production and decay of the induced wake is still not well understood. The focus of this research is to determine the relationship between the fractal iteration N and the turbulence produced in the wake flow using well-controlled water-tunnel experiments. Particle Image Velocimetry (PIV) is used to measure the instantaneous velocity fields downstream of four different fractal grids with increasing number of scales (N = 1, 2, 3, and 4) and a conventional single-scale grid. By comparing the turbulent scales and statistics of the wake, we are able to determine how each iteration affects the peak turbulence intensity and the production/decay of turbulence from the grid. In light of the ability of these fractal grids to increase turbulence intensity with low pressure drop, this work can potentially benefit a wide variety of applications where energy efficient mixing or convective heat transfer is a key process.

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 structure of sequential behaviour patterns: an indicator of stress

USGS Publications Warehouse

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

1996-01-01

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

Lava Flow Dynamics

NASA Technical Reports Server (NTRS)

Taylor, G. Jeffrey

1996-01-01

This grant originally had four major tasks, all of which were addressed to varying extents during the course of the research: (1) Measure the fractal dimensions of lava flows as a function of topography, substrate, and rheology; (2) The nature of lava tube systems and their relation to flow fields; (3) A quantitative assessment of lava flow dynamics in light of the fractal nature of lava flow margins; and (4) Development and application of a new remote sensing tool based on fractal properties. During the course of the research, the project expanded to include the following projects: (1) A comparison of what we can-learn from remote sensing studies of lava flow morphology and from studies of samples of lava flows; (2) Study of a terrestrial analog of the nakhlites, one of the groups of meteorites from Mars; and (3) Study of the textures of Hawaiian basalts as an aid in understanding the dynamics (flow rates, inflation rates, thermal history) of flow interiors. In addition, during the first year an educational task (development and writing of a teacher's guide and activity set to accompany the lunar sample disk when it is sent to schools) was included.

Gas flow through rough microchannels in the transition flow regime.

PubMed

Deng, Zilong; Chen, Yongping; Shao, Chenxi

2016-01-01

A multiple-relaxation-time lattice Boltzmann model of Couette flow is developed to investigate the rarified gas flow through microchannels with roughness characterized by fractal geometry, especially to elucidate the coupled effects of roughness and rarefaction on microscale gas flow in the transition flow regime. The results indicate that the surface roughness effect on gas flow behavior becomes more significant in rarefied gas flow with the increase of Knudsen number. We find the gas flow behavior in the transition flow regime is more sensitive to roughness height than that in the slip flow regime. In particular, the influence of fractal dimension on rarefied gas flow behavior is less significant than roughness height.

Interaction of side-by-side fluidic harvesters in fractal grid-generated turbulence

NASA Astrophysics Data System (ADS)

Ferko, Kevin; Lachendro, David; Chiappazzi, Nick; Danesh-Yazdi, Amir H.

2018-03-01

While the vast majority of the literature in energy harvesting is dedicated to resonant harvesters, non-resonant harvesters, especially those that use turbulence-induced vibration to generate energy, have not been studied in as much detail. This is especially true for grid-generated turbulence. In this paper, the interaction of two side-by-side fluidic harvesters from a passive fractal grid-generated turbulent flow is considered. The fractal grid has been shown to significantly increase the turbulence generated in the flow which is the source of the vibration of the piezoelectric beams. In this experimental study, the influence of four parameters has been investigated: Beam lengths and configurations, mean flow velocity, distance from the grid and gap between the two beams. Experimental results show that the piezoelectric harvesters in fractal grid turbulence are capable of producing at least the same amount of power as those placed in passive rectangular grids with a larger pressure loss, allowing for a potentially significant increase in the efficiency of the energy conversion process, even though more experiments are required to study the behavior of the beams in homogeneous, fractal grid-generated turbulence.

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

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

Dynamical and fractal properties in periodically forced stretch-twist-fold (STF) flow

NASA Astrophysics Data System (ADS)

Aqeel, Muhammad; Ahmad, Salman; Azam, Anam; Ahmed, Faizan

2017-05-01

The periodically forced stretch-twist-fold (STF) flow is introduced in this article. The nonlinear behavior of the STF flow with periodic force along the y -axis is investigated analytically and numerically. The STF flow is a prototype of the dynamo theory that proposes a mechanism of magnetic field generation continuously. The stability analysis is done by Routh Huwritz criteria and Cardano method. Chasing chaos through numerical simulation is determined to demonstrate the chaotic behavior of the forced STF flow. With the help of fractal processes based on the forced STF flow, a multi-wing forced STF flow is obtained that gives a n -wing forced STF flow system.

Exterior dimension of fat fractals

NASA Technical Reports Server (NTRS)

Grebogi, C.; Mcdonald, S. W.; Ott, E.; Yorke, J. A.

1985-01-01

Geometric scaling properties of fat fractal sets (fractals with finite volume) are discussed and characterized via the introduction of a new dimension-like quantity which is called the exterior dimension. In addition, it is shown that the exterior dimension is related to the 'uncertainty exponent' previously used in studies of fractal basin boundaries, and it is shown how this connection can be exploited to determine the exterior dimension. Three illustrative applications are described, two in nonlinear dynamics and one dealing with blood flow in the body. Possible relevance to porous materials and ballistic driven aggregation is also noted.

An examination of coherent structures in a lobed mixer using multifractal measures in conjunction with the proper orthogonal decomposition

NASA Technical Reports Server (NTRS)

Ukeiley, L.; Varghese, M.; Glauser, M.; Valentine, D.

1991-01-01

A 'lobed mixer' device that enhances mixing through secondary flows and streamwise vorticity is presently studied within the framework of multifractal-measures theory, in order to deepen understanding of velocity time trace data gathered on its operation. Proper orthogonal decomposition-based knowledge of coherent structures has been applied to obtain the generalized fractal dimensions and multifractal spectrum of several proper eigenmodes for data samples of the velocity time traces; this constitutes a marked departure from previous multifractal theory applications to self-similar cascades. In certain cases, a single dimension may suffice to capture the entire spectrum of scaling exponents for the velocity time trace.

Multifractal characterization of Vesuvio lava-flow margins and its implications

NASA Astrophysics Data System (ADS)

Luongo, G.; Mazzarella, A.; Di Donna, G.

2000-09-01

The digitized lava-flow margins of well-defined extended eruptions occurring at Vesuvio in 1760, 1794, 1861, 1906, 1929 and 1944 are found to follow fractal behaviours inside a scaling region enclosed between 50 and 400 m. Although the invariance region is well respected, the fractal dimension D varies from one lava flow to another: the more irregular the lava-flow margin, the larger the value of D. The ascertained dependence of D on the duration of premonitory activity, preceding the emission of lavas, might provide some insight into the inner volcanic processes before the eruption and into the dynamical processes operating during flow emplacement.

An efective fractal-tree closure model for simulating blood flow in large arterial networks

PubMed Central

Perdikaris, Paris; Grinberg, Leopold; Karniadakis, George Em.

2014-01-01

The aim of the present work is to address the closure problem for hemodynamic simulations by developing a exible and effective model that accurately distributes flow in the downstream vasculature and can stably provide a physiological pressure out flow boundary condition. To achieve this goal, we model blood flow in the sub-pixel vasculature by using a non-linear 1D model in self-similar networks of compliant arteries that mimic the structure and hierarchy of vessels in the meso-vascular regime (radii 500 μm – 10 μm). We introduce a variable vessel length-to-radius ratio for small arteries and arterioles, while also addressing non-Newtonian blood rheology and arterial wall viscoelasticity effects in small arteries and arterioles. This methodology aims to overcome substantial cut-off radius sensitivities, typically arising in structured tree and linearized impedance models. The proposed model is not sensitive to out flow boundary conditions applied at the end points of the fractal network, and thus does not require calibration of resistance/capacitance parameters typically required for out flow conditions. The proposed model convergences to a periodic state in two cardiac cycles even when started from zero-flow initial conditions. The resulting fractal-trees typically consist of thousands to millions of arteries, posing the need for efficient parallel algorithms. To this end, we have scaled up a Discontinuous Galerkin solver that utilizes the MPI/OpenMP hybrid programming paradigm to thousands of computer cores, and can simulate blood flow in networks of millions of arterial segments at the rate of one cycle per 5 minutes. The proposed model has been extensively tested on a large and complex cranial network with 50 parent, patient-specific arteries and 21 outlets to which fractal trees where attached, resulting to a network of up to 4,392,484 vessels in total, and a detailed network of the arm with 276 parent arteries and 103 outlets (a total of 702,188 vessels after attaching the fractal trees), returning physiological flow and pressure wave predictions without requiring any parameter estimation or calibration procedures. We present a novel methodology to overcome substantial cut-off radius sensitivities PMID:25510364

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.

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.

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.

Factors Affecting the Changes of Ice Crystal Form in Ice Cream

NASA Astrophysics Data System (ADS)

Wang, Xin; Watanabe, Manabu; Suzuki, Toru

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

Synthesis of the advance in and application of fractal characteristics of traffic flow : summary.

DOT National Transportation Integrated Search

2013-07-01

Fractals are geometric objects that are selfsimilar, meaning that their basic structure : remains the same regardless of the scale of : magnification. Self-similarity is readily seen in : nature, for example, in trees, coastlines, clouds, : etc. ...

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

Fractal aspects of the flow and shear behaviour of free-flowable particle size fractions of pharmaceutical directly compressible excipient sorbitol.

PubMed

Hurychová, Hana; Lebedová, Václava; Šklubalová, Zdenka; Dzámová, Pavlína; Svěrák, Tomáš; Stoniš, Jan

Flowability of powder excipients is directly influenced by their size and shape although the granulometric influence of the flow and shear behaviour of particulate matter is not studied frequently. In this work, the influence of particle size on the mass flow rate through the orifice of a conical hopper, and the cohesion and flow function was studied for four free-flowable size fractions of sorbitol for direct compression in the range of 0.080-0.400 mm. The particles were granulometricaly characterized using an optical microscopy; a boundary fractal dimension of 1.066 was estimated for regular sorbitol particles. In the particle size range studied, a non-linear relationship between the mean particle size and the mass flow rate Q10 (g/s) was detected having amaximum at the 0.245mm fraction. The best flow properties of this fraction were verified with aJenike shear tester due to the highest value of flow function and the lowest value of the cohesion. The results of this work show the importance of the right choice of the excipient particle size to achieve the best flow behaviour of particulate material.Key words: flowability size fraction sorbitol for direct compaction Jenike shear tester fractal dimension.

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.

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.

Visualization of the structural response of a hypersonic turbulent boundary layer to convex curvature

NASA Astrophysics Data System (ADS)

Humble, R. A.; Peltier, S. J.; Bowersox, R. D. W.

2012-10-01

The effects of convex curvature on the outer structure of a Mach 4.9 turbulent boundary layer (Reθ = 4.7 × 104) are investigated using condensate Rayleigh scattering and analyzed using spatial correlations, intermittency, and fractal theory. It is found that the post-expansion boundary layer structure morphology appears subtle, but certain features exhibit a more obvious response. The large-scale flow structures survive the initial expansion, appearing to maintain the same physical size. However, due to the nature of the expansion fan, a differential acceleration effect takes place across the flow structures, causing them to be reoriented, leaning farther away from the wall. The onset of intermittency moves closer towards the boundary layer edge and the region of intermittent flow decreases. It is likely that this reflects the less frequent penetration of outer irrotational fluid into the boundary layer, consistent with a boundary layer that is losing its ability to entrain freestream fluid. The fractal dimension of the turbulent/nonturbulent interface decreases with increasing favorable pressure gradient, indicating that the interface's irregularity decreases. Because fractal scale similarity does not encompass the largest scales, this suggests that the change in fractal dimension is due to the action of the smaller-scales, consistent with the idea that the small-scale flow structures are quenched during the expansion in response to bulk dilatation.

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.

Vortex structure and breakup mechanism of gaseous jet in supersonic crossflow with laminar boundary layer

NASA Astrophysics Data System (ADS)

Zhao, Yanhui; Liang, Jianhan; Zhao, Yuxin

2016-11-01

Employing nano-particle planar laser scattering and particle image velocimetry technology, underexpanded jet in supersonic crossflow with laminar boundary layer is experimental investigated in a low noise wind tunnel. Instantaneous flow structures and average velocity distribution of jet plume are captured in experimental images. Horseshoe vortex system is dominated by oscillating and coalescing regime, contributing to vortex generation of jet shear layer. The "tilting-stretching-tearing" mechanism dominating in near field raises average fractal dimension. But vortex structures generated on the windward side of jet plume scatter in jet plume and dissipate gradually, which makes the vortexes break up from outside in near field and break down into small turbulence completely in far field.

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.

Monitoring the soil degradation by Metastatistical Analysis

NASA Astrophysics Data System (ADS)

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

2009-04-01

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

Fractal regional myocardial blood flows pattern according to metabolism, not vascular anatomy

PubMed Central

Yipintsoi, Tada; Kroll, Keith

2015-01-01

Regional myocardial blood flows are markedly heterogeneous. Fractal analysis shows strong near-neighbor correlation. In experiments to distinguish control by vascular anatomy vs. local vasomotion, coronary flows were increased in open-chest dogs by stimulating myocardial metabolism (catecholamines + atropine) with and without adenosine. During control states mean left ventricular (LV) myocardial blood flows (microspheres) were 0.5–1 ml·g−1·min−1 and increased to 2–3 ml·g−1·min−1 with catecholamine infusion and to ∼4 ml·g−1·min−1 with adenosine (Ado). Flow heterogeneity was similar in all states: relative dispersion (RD = SD/mean) was ∼25%, using LV pieces 0.1–0.2% of total. During catecholamine infusion local flows increased in proportion to the mean flows in 45% of the LV, “tracking” closely (increased proportionately to mean flow), while ∼40% trended toward the mean. Near-neighbor regional flows remained strongly spatially correlated, with fractal dimension D near 1.2 (Hurst coefficient 0.8). The spatial patterns remain similar at varied levels of metabolic stimulation inferring metabolic dominance. In contrast, adenosine vasodilation increased flows eightfold times control while destroying correlation with the control state. The Ado-induced spatial patterns differed from control but were self-consistent, inferring that with full vasodilation the relaxed arterial anatomy dominates the distribution. We conclude that vascular anatomy governs flow distributions during adenosine vasodilation but that metabolic vasoregulation dominates in normal physiological states. PMID:26589329

Fractal regional myocardial blood flows pattern according to metabolism, not vascular anatomy.

PubMed

Yipintsoi, Tada; Kroll, Keith; Bassingthwaighte, James B

2016-02-01

Regional myocardial blood flows are markedly heterogeneous. Fractal analysis shows strong near-neighbor correlation. In experiments to distinguish control by vascular anatomy vs. local vasomotion, coronary flows were increased in open-chest dogs by stimulating myocardial metabolism (catecholamines + atropine) with and without adenosine. During control states mean left ventricular (LV) myocardial blood flows (microspheres) were 0.5-1 ml·g(-1)·min(-1) and increased to 2-3 ml·g(-1)·min(-1) with catecholamine infusion and to ∼4 ml·g(-1)·min(-1) with adenosine (Ado). Flow heterogeneity was similar in all states: relative dispersion (RD = SD/mean) was ∼25%, using LV pieces 0.1-0.2% of total. During catecholamine infusion local flows increased in proportion to the mean flows in 45% of the LV, "tracking" closely (increased proportionately to mean flow), while ∼40% trended toward the mean. Near-neighbor regional flows remained strongly spatially correlated, with fractal dimension D near 1.2 (Hurst coefficient 0.8). The spatial patterns remain similar at varied levels of metabolic stimulation inferring metabolic dominance. In contrast, adenosine vasodilation increased flows eightfold times control while destroying correlation with the control state. The Ado-induced spatial patterns differed from control but were self-consistent, inferring that with full vasodilation the relaxed arterial anatomy dominates the distribution. We conclude that vascular anatomy governs flow distributions during adenosine vasodilation but that metabolic vasoregulation dominates in normal physiological states. Copyright © 2016 the American Physiological Society.

An effective fractal-tree closure model for simulating blood flow in large arterial networks.

PubMed

Perdikaris, Paris; Grinberg, Leopold; Karniadakis, George Em

2015-06-01

The aim of the present work is to address the closure problem for hemodynamic simulations by developing a flexible and effective model that accurately distributes flow in the downstream vasculature and can stably provide a physiological pressure outflow boundary condition. To achieve this goal, we model blood flow in the sub-pixel vasculature by using a non-linear 1D model in self-similar networks of compliant arteries that mimic the structure and hierarchy of vessels in the meso-vascular regime (radii [Formula: see text]). We introduce a variable vessel length-to-radius ratio for small arteries and arterioles, while also addressing non-Newtonian blood rheology and arterial wall viscoelasticity effects in small arteries and arterioles. This methodology aims to overcome substantial cut-off radius sensitivities, typically arising in structured tree and linearized impedance models. The proposed model is not sensitive to outflow boundary conditions applied at the end points of the fractal network, and thus does not require calibration of resistance/capacitance parameters typically required for outflow conditions. The proposed model convergences to a periodic state in two cardiac cycles even when started from zero-flow initial conditions. The resulting fractal-trees typically consist of thousands to millions of arteries, posing the need for efficient parallel algorithms. To this end, we have scaled up a Discontinuous Galerkin solver that utilizes the MPI/OpenMP hybrid programming paradigm to thousands of computer cores, and can simulate blood flow in networks of millions of arterial segments at the rate of one cycle per 5 min. The proposed model has been extensively tested on a large and complex cranial network with 50 parent, patient-specific arteries and 21 outlets to which fractal trees where attached, resulting to a network of up to 4,392,484 vessels in total, and a detailed network of the arm with 276 parent arteries and 103 outlets (a total of 702,188 vessels after attaching the fractal trees), returning physiological flow and pressure wave predictions without requiring any parameter estimation or calibration procedures. We present a novel methodology to overcome substantial cut-off radius sensitivities.

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.

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.

The art and science of hyperbolic tessellations.

PubMed

Van Dusen, B; Taylor, R P

2013-04-01

The visual impact of hyperbolic tessellations has captured artists' imaginations ever since M.C. Escher generated his Circle Limit series in the 1950s. The scaling properties generated by hyperbolic geometry are different to the fractal scaling properties found in nature's scenery. Consequently, prevalent interpretations of Escher's art emphasize the lack of connection with nature's patterns. However, a recent collaboration between the two authors proposed that Escher's motivation for using hyperbolic geometry was as a method to deliberately distort nature's rules. Inspired by this hypothesis, this year's cover artist, Ben Van Dusen, embeds natural fractals such as trees, clouds and lightning into a hyperbolic scaling grid. The resulting interplay of visual structure at multiple size scales suggests that hybridizations of fractal and hyperbolic geometries provide a rich compositional tool for artists.

Absorption and scattering by fractal aggregates and by their equivalent coated spheres

NASA Astrophysics Data System (ADS)

Kandilian, Razmig; Heng, Ri-Liang; Pilon, Laurent

2015-01-01

This paper demonstrates that the absorption and scattering cross-sections and the asymmetry factor of randomly oriented fractal aggregates of spherical monomers can be rapidly estimated as those of coated spheres with equivalent volume and average projected area. This was established for fractal aggregates with fractal dimension ranging from 2.0 to 3.0 and composed of up to 1000 monodisperse or polydisperse monomers with a wide range of size parameter and relative complex index of refraction. This equivalent coated sphere approximation was able to capture the effects of both multiple scattering and shading among constituent monomers on the integral radiation characteristics of the aggregates. It was shown to be superior to the Rayleigh-Debye-Gans approximation and to the equivalent coated sphere approximation proposed by Latimer. However, the scattering matrix element ratios of equivalent coated spheres featured large angular oscillations caused by internal reflection in the coating which were not observed in those of the corresponding fractal aggregates. Finally, the scattering phase function and the scattering matrix elements of aggregates with large monomer size parameter were found to have unique features that could be used in remote sensing applications.

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

Fractal universe and quantum gravity.

PubMed

Calcagni, Gianluca

2010-06-25

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

Fractal and multifractal analyses of bipartite networks

NASA Astrophysics Data System (ADS)

Liu, Jin-Long; Wang, Jian; Yu, Zu-Guo; Xie, Xian-Hua

2017-03-01

Bipartite networks have attracted considerable interest in various fields. Fractality and multifractality of unipartite (classical) networks have been studied in recent years, but there is no work to study these properties of bipartite networks. In this paper, we try to unfold the self-similarity structure of bipartite networks by performing the fractal and multifractal analyses for a variety of real-world bipartite network data sets and models. First, we find the fractality in some bipartite networks, including the CiteULike, Netflix, MovieLens (ml-20m), Delicious data sets and (u, v)-flower model. Meanwhile, we observe the shifted power-law or exponential behavior in other several networks. We then focus on the multifractal properties of bipartite networks. Our results indicate that the multifractality exists in those bipartite networks possessing fractality. To capture the inherent attribute of bipartite network with two types different nodes, we give the different weights for the nodes of different classes, and show the existence of multifractality in these node-weighted bipartite networks. In addition, for the data sets with ratings, we modify the two existing algorithms for fractal and multifractal analyses of edge-weighted unipartite networks to study the self-similarity of the corresponding edge-weighted bipartite networks. The results show that our modified algorithms are feasible and can effectively uncover the self-similarity structure of these edge-weighted bipartite networks and their corresponding node-weighted versions.

Fractal and multifractal analyses of bipartite networks.

PubMed

Liu, Jin-Long; Wang, Jian; Yu, Zu-Guo; Xie, Xian-Hua

2017-03-31

Bipartite networks have attracted considerable interest in various fields. Fractality and multifractality of unipartite (classical) networks have been studied in recent years, but there is no work to study these properties of bipartite networks. In this paper, we try to unfold the self-similarity structure of bipartite networks by performing the fractal and multifractal analyses for a variety of real-world bipartite network data sets and models. First, we find the fractality in some bipartite networks, including the CiteULike, Netflix, MovieLens (ml-20m), Delicious data sets and (u, v)-flower model. Meanwhile, we observe the shifted power-law or exponential behavior in other several networks. We then focus on the multifractal properties of bipartite networks. Our results indicate that the multifractality exists in those bipartite networks possessing fractality. To capture the inherent attribute of bipartite network with two types different nodes, we give the different weights for the nodes of different classes, and show the existence of multifractality in these node-weighted bipartite networks. In addition, for the data sets with ratings, we modify the two existing algorithms for fractal and multifractal analyses of edge-weighted unipartite networks to study the self-similarity of the corresponding edge-weighted bipartite networks. The results show that our modified algorithms are feasible and can effectively uncover the self-similarity structure of these edge-weighted bipartite networks and their corresponding node-weighted versions.

Fractal and multifractal analyses of bipartite networks

PubMed Central

Liu, Jin-Long; Wang, Jian; Yu, Zu-Guo; Xie, Xian-Hua

2017-01-01

Bipartite networks have attracted considerable interest in various fields. Fractality and multifractality of unipartite (classical) networks have been studied in recent years, but there is no work to study these properties of bipartite networks. In this paper, we try to unfold the self-similarity structure of bipartite networks by performing the fractal and multifractal analyses for a variety of real-world bipartite network data sets and models. First, we find the fractality in some bipartite networks, including the CiteULike, Netflix, MovieLens (ml-20m), Delicious data sets and (u, v)-flower model. Meanwhile, we observe the shifted power-law or exponential behavior in other several networks. We then focus on the multifractal properties of bipartite networks. Our results indicate that the multifractality exists in those bipartite networks possessing fractality. To capture the inherent attribute of bipartite network with two types different nodes, we give the different weights for the nodes of different classes, and show the existence of multifractality in these node-weighted bipartite networks. In addition, for the data sets with ratings, we modify the two existing algorithms for fractal and multifractal analyses of edge-weighted unipartite networks to study the self-similarity of the corresponding edge-weighted bipartite networks. The results show that our modified algorithms are feasible and can effectively uncover the self-similarity structure of these edge-weighted bipartite networks and their corresponding node-weighted versions. PMID:28361962

Structural features of biomass in a hybrid MBBR reactor.

PubMed

Xiao, G Y; Ganczarczyk, J

2006-03-01

The structural features of biomass present in the hybrid MBBR (Moving Bed Biofilm Reactor) aeration tank were studied in two subsequent periods, which differed in hydraulic and substrate loads. The physical characteristics of attached-growth biomass, such as, biofilm thickness, density, porosity, inner and surface fractal dimensions, and those of suspended-growth biomass, such as, floc size distribution, density, porosity, inner and surface fractal dimensions, were investigated in each study period and then compared. The results indicated that biofilm always had a higher density, geometric porosity, and a larger boundary fractal dimension than flocs. Both types of biomass were found to exhibit at least two distinct Sierpinski fractal dimensions, indicating two major different pore space populations. With the increasing wastewater flow, both types of biomass were found to shift their structural properties to larger values, except porosity and surface roughness, which decreased. Floc density and biomass Sierpinski fractals were not affected much by the system loadings.

Lobate impact melt flows within the extended ejecta blanket of Pierazzo crater

NASA Astrophysics Data System (ADS)

Bray, Veronica J.; Atwood-Stone, Corwin; Neish, Catherine D.; Artemieva, Natalia A.; McEwen, Alfred S.; McElwaine, Jim N.

2018-02-01

Impact melt flows are observed within the continuous and discontinuous ejecta blanket of the 9 km lunar crater Pierazzo, from the crater rim to more than 40 km away from the center of the crater. Our mapping, fractal analysis, and thermal modeling suggest that melt can be emplaced ballistically and, upon landing, can become separated from solid ejecta to form the observed flow features. Our analysis is based on the identification of established melt morphology for these in-ejecta flows and supported by fractal analysis and thermal modeling. We computed the fractal dimension for the flow boundaries and found values of D = 1.05-1.17. These are consistent with terrestrial basaltic lava flows (D = 1.06-1.2) and established lunar impact melt flows (D = 1.06-1.18), but inconsistent with lunar dry granular flows (D = 1.31-1.34). Melt flows within discontinuous ejecta deposits are noted within just 1.5% of the mapping area, suggesting that the surface expression of impact melt in the extended ejecta around craters of this size is rare, most likely due to the efficient mixing of melts with solid ejecta and local target rocks. However, if the ejected fragments (both, molten and solid) are large enough, segregation of melt and its consequent flow is possible. As most of the flows mapped in this work occur on crater-facing slopes, the development of defined melt flows within ejecta deposits might be facilitated by high crater-facing topography restricting the flow of ejecta soon after it makes ground contact, limiting the quenching of molten ejecta through turbulent mixing with solid debris. Our study confirms the idea that impact melt can travel far beyond the continuous ejecta blanket, adding to the lunar regolith over an extensive area.

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).

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.

Temporal scaling of hydraulic head and river base flow and its implication for groundwater recharge

USGS Publications Warehouse

Zhang, You‐Kuan; Schilling, Keith

2004-01-01

Spectral analyses were conducted for hourly hydraulic head (h) data observed over a 4‐year period at seven monitoring wells in the Walnut Creek watershed, Iowa. The log power spectral density of the hydraulic head fluctuations versus log frequency (f) at all seven wells is shown to have a distinct slope or fractal dimension (D), indicating temporal scaling in the time series of water level fluctuations. The fractal dimension of the time series varies from well to well, and the spectrum for the average h over all seven wells has a fractal dimension of 1.46 and Hurst coefficient of 0.54. The log power spectral density of estimated base flow in the Walnut Creek and four other watersheds versus log f is shown to have two distinct slopes with a break in scaling at about 30 days. It is shown that the groundwater recharge process in a basin can be estimated from a head spectrum based on existing theoretical results. Hydraulic head in an aquifer may fluctuate as a fractal in time in response to either a white noise or fractal recharge process, depending on physical parameters (i.e., transmissivity and specific yield) of the aquifer. The recharge process at the Walnut Creek watershed is shown to have a white noise spectrum based on the observed head spectrum.

Fractality and the law of the wall

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Can fractal objects operate as efficient inline mixers?

NASA Astrophysics Data System (ADS)

Laizet, Sylvain; Vassilicos, John; Turbulence, Mixing; Flow Control Group Team

2011-11-01

Recently, Hurst & Vassilicos, PoF 2007, Seoud & Vassilicos, PoF 2007, Mazellier & Vassilicos, PoF, 2010 used different multiscale grids to generate turbulence in a wind tunnel and have shown that complex multiscale boundary/initial conditions can drastically influence the behaviour of a turbulent flow, but that the detailled specific nature of the multiscale geometry matters too. Multiscale (fractal) objects can be designed to be immersed in any fluid flow where there is a need to control and design the turbulence generated by the object. Different types of multiscale objects can be designed as different types of energy-efficient mixers with varying degrees of high turbulent intensities, small pressure drop and downstream distance from the grid where the turbulence is most vigorous. Here, we present a 3D DNS study of the stirring and mixing of a passive scalar by turbulence generated with either a fractal square grid or a regular grid in the presence of a mean scalar gradient. The results show that: (1) there is a linear increase for the passive scalar variance for both grids, (2) the passive scalar variance is ten times bigger for the fractal grid, (3) the passive scalar flux is constant after the production region for both grids, (4) the passive scalar flux is enhanced by an order of magnitude for the fractal grid. We acknowledge support from EPSRC, UK.

Self-Similar Random Process and Chaotic Behavior In Serrated Flow of High Entropy Alloys

PubMed Central

Chen, Shuying; Yu, Liping; Ren, Jingli; Xie, Xie; Li, Xueping; Xu, Ying; Zhao, Guangfeng; Li, Peizhen; Yang, Fuqian; Ren, Yang; Liaw, Peter K.

2016-01-01

The statistical and dynamic analyses of the serrated-flow behavior in the nanoindentation of a high-entropy alloy, Al0.5CoCrCuFeNi, at various holding times and temperatures, are performed to reveal the hidden order associated with the seemingly-irregular intermittent flow. Two distinct types of dynamics are identified in the high-entropy alloy, which are based on the chaotic time-series, approximate entropy, fractal dimension, and Hurst exponent. The dynamic plastic behavior at both room temperature and 200 °C exhibits a positive Lyapunov exponent, suggesting that the underlying dynamics is chaotic. The fractal dimension of the indentation depth increases with the increase of temperature, and there is an inflection at the holding time of 10 s at the same temperature. A large fractal dimension suggests the concurrent nucleation of a large number of slip bands. In particular, for the indentation with the holding time of 10 s at room temperature, the slip process evolves as a self-similar random process with a weak negative correlation similar to a random walk. PMID:27435922

Self-similar random process and chaotic behavior in serrated flow of high entropy alloys

DOE PAGES

Chen, Shuying; Yu, Liping; Ren, Jingli; ...

2016-07-20

Here, the statistical and dynamic analyses of the serrated-flow behavior in the nanoindentation of a high-entropy alloy, Al 0.5CoCrCuFeNi, at various holding times and temperatures, are performed to reveal the hidden order associated with the seemingly-irregular intermittent flow. Two distinct types of dynamics are identified in the high-entropy alloy, which are based on the chaotic time-series, approximate entropy, fractal dimension, and Hurst exponent. The dynamic plastic behavior at both room temperature and 200 °C exhibits a positive Lyapunov exponent, suggesting that the underlying dynamics is chaotic. The fractal dimension of the indentation depth increases with the increase of temperature, andmore » there is an inflection at the holding time of 10 s at the same temperature. A large fractal dimension suggests the concurrent nucleation of a large number of slip bands. In particular, for the indentation with the holding time of 10 s at room temperature, the slip process evolves as a self-similar random process with a weak negative correlation similar to a random walk.« less

Self-Similar Random Process and Chaotic Behavior In Serrated Flow of High Entropy Alloys.

PubMed

Chen, Shuying; Yu, Liping; Ren, Jingli; Xie, Xie; Li, Xueping; Xu, Ying; Zhao, Guangfeng; Li, Peizhen; Yang, Fuqian; Ren, Yang; Liaw, Peter K

2016-07-20

The statistical and dynamic analyses of the serrated-flow behavior in the nanoindentation of a high-entropy alloy, Al0.5CoCrCuFeNi, at various holding times and temperatures, are performed to reveal the hidden order associated with the seemingly-irregular intermittent flow. Two distinct types of dynamics are identified in the high-entropy alloy, which are based on the chaotic time-series, approximate entropy, fractal dimension, and Hurst exponent. The dynamic plastic behavior at both room temperature and 200 °C exhibits a positive Lyapunov exponent, suggesting that the underlying dynamics is chaotic. The fractal dimension of the indentation depth increases with the increase of temperature, and there is an inflection at the holding time of 10 s at the same temperature. A large fractal dimension suggests the concurrent nucleation of a large number of slip bands. In particular, for the indentation with the holding time of 10 s at room temperature, the slip process evolves as a self-similar random process with a weak negative correlation similar to a random walk.

Modeling preferential water flow and solute transport in unsaturated soil using the active region model

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

Sheng, F.; Wang, K.; Zhang, R.

2009-03-15

Preferential flow and solute transport are common processes in the unsaturated soil, in which distributions of soil water content and solute concentrations are often characterized as fractal patterns. An active region model (ARM) was recently proposed to describe the preferential flow and transport patterns. In this study, ARM governing equations were derived to model the preferential soil water flow and solute transport processes. To evaluate the ARM equations, dye infiltration experiments were conducted, in which distributions of soil water content and Cl{sup -} concentration were measured. Predicted results using the ARM and the mobile-immobile region model (MIM) were compared withmore » the measured distributions of soil water content and Cl{sup -} concentration. Although both the ARM and the MIM are two-region models, they are fundamental different in terms of treatments of the flow region. The models were evaluated based on the modeling efficiency (ME). The MIM provided relatively poor prediction results of the preferential flow and transport with negative ME values or positive ME values less than 0.4. On the contrary, predicted distributions of soil water content and Cl- concentration using the ARM agreed reasonably well with the experimental data with ME values higher than 0.8. The results indicated that the ARM successfully captured the macroscopic behavior of preferential flow and solute transport in the unsaturated soil.« less

Percolation characteristics of solvent invasion in rough fractures under miscible conditions

NASA Astrophysics Data System (ADS)

Korfanta, M.; Babadagli, T.; Develi, K.

2017-10-01

Surface roughness and flow rate effects on the solvent transport under miscible conditions in a single fracture are studied. Surface replicas of seven different rocks (marble, granite, and limestone) are used to represent different surface roughness characteristics each described by different mathematical models including three fractal dimensions. Distribution of dyed solvent is investigated at various flow rate conditions to clarify the effect of roughness on convective and diffusive mixing. After a qualitative analysis using comparative images of different rocks, the area covered by solvent with respect to time is determined to conduct a semi-quantitative analysis. In this exercise, two distinct zones are identified, namely the straight lines obtained for convective (early times) and diffusive (late times) flow. The bending point between these two lines is used to point the transition between the two zones. Finally, the slopes of the straight lines and the bending points are correlated to five different roughness parameters and the rate (Peclet number). It is observed that both surface roughness and flow rate have significant effect on solvent spatial distribution. The largest area covered is obtained at moderate flow rates and hence not only the average surface roughness characteristic is important, but coessentially total fracture surface area needs to be considered when evaluating fluid distribution. It is also noted that the rate effect is critically different for the fracture samples of large grain size (marbles and granite) compared to smaller grain sizes (limestones). Variogram fractal dimension exhibits the strongest correlation with the maximum area covered by solvent, and display increasing trend at the moderate flow rates. Equations with variogram surface fractal dimension in combination with any other surface fractal parameter coupled with Peclet number can be used to predict maximum area covered by solvent in a single fracture, which in turn can be utilized to model oil recovery, waste disposal, and groundwater contamination processes in the presence of fractures.

Multiscale plant wakes, turbulence and non linear scaling flexible effects

NASA Astrophysics Data System (ADS)

Vila, Teresa; Redondo, Jose M.; Velasco, David

2010-05-01

We present velocity ADV measurements and flow visualization of the turbulent wakes behind plant arrays, as these are often fractal in nature, we compare the multifractal spectra and the turbulence structure behind the wakes. Both statistical measures allowing to calculate integral lengthscales and their profiles modified by the plant cannopies [1,2] as well as intermittency and spectral behaviour are also measured [3,4]. We distinguish several momentum transfer mechanisms between the cannopy and the flow, an internal one where lateral turbulent tensions are dominant, and another one just above the plant average height dominated by vertical Reynolds stresses. Visualization of flow over individual plant models show the role of coherent vortices triggered by plant elasticity. The deformation rate of the plants and their Youngs modulus may be correlated with overal plant drag and geometry. This is modified strongly in fractal canopies. Large turbulent integral scales are linked to rugosity and the scaling of the waves.[5,6] Pearlescence experiments where local shear is visualized and numerical simulations of Fractal grids are compared following [7]. [1] Nepf,H.M. Drag, turbulence and diffusion in flow through emergent vegetation. Water Resources Res. 35(2)(1999) [2] Ben Mahjoub,O., Redondo J.M. and Babiano A. Jour.Structure functions in complex flows. Flow Turbulence and Combustion 59, 299-313. [3] El-Hakim, O. Salama, M. Velocity distribution inside and above branched flexible roughness. ASCE Journal of Irrigation and Drainage Engineering, Vol. 118, No 6, (November/December 1992) 914-927. [4] Finnigan,J. Turbulence in plant canopies. Annu. Rev. Fluid Mech. 2000 , Vol. 32: 519-571. [5] Ikeda, S., Kanazawa, M. Three- dimensional organized vortices above flexible water plants. ASCE Journal of Hydraulic Engineering, Vol. 122, No 11, (1996) 634-640. [6] Velasco, D.,Bateman A.,Redondo J.M and Medina V. An open channel flow experimental and theorical study of resistance and turbulent characterization over flexible vegetated linnings. Flow, Turbulence and Combustion. 70, 69-88. [7] Layzet S. Vassilicos C. Vila T and Redondo J.M. I.O.P Fractal grids and wakes, Proceedings on Earth sciences (2009)

Role of rough surface topography on gas slip flow in microchannels.

PubMed

Zhang, Chengbin; Chen, Yongping; Deng, Zilong; Shi, Mingheng

2012-07-01

We conduct a lattice Boltzmann simulation of gas slip flow in microchannels incorporating rough surface effects as characterized by fractal geometry with a focus on gas-solid interaction. The gas slip flow in rough microchannels, which is characterized by Poiseuille number and mass flow rate, is evaluated and compared with smooth microchannels. The effects of roughness height, surface fractal dimension, and Knudsen number on slip behavior of gas flow in microchannels are all investigated and discussed. The results indicate that the presence of surface roughness reduces boundary slip for gas flow in microchannels with respect to a smooth surface. The gas flows at the valleys of rough walls are no-slip while velocity slips are observed over the top of rough walls. We find that the gas flow behavior in rough microchannels is insensitive to the surface topography irregularity (unlike the liquid flow in rough microchannels) but is influenced by the statistical height of rough surface and rarefaction effects. In particular, decrease in roughness height or increase in Knudsen number can lead to large wall slip for gas flow in microchannels.

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

Organization of complex networks

NASA Astrophysics Data System (ADS)

Kitsak, Maksim

Many large complex systems can be successfully analyzed using the language of graphs and networks. Interactions between the objects in a network are treated as links connecting nodes. This approach to understanding the structure of networks is an important step toward understanding the way corresponding complex systems function. Using the tools of statistical physics, we analyze the structure of networks as they are found in complex systems such as the Internet, the World Wide Web, and numerous industrial and social networks. In the first chapter we apply the concept of self-similarity to the study of transport properties in complex networks. Self-similar or fractal networks, unlike non-fractal networks, exhibit similarity on a range of scales. We find that these fractal networks have transport properties that differ from those of non-fractal networks. In non-fractal networks, transport flows primarily through the hubs. In fractal networks, the self-similar structure requires any transport to also flow through nodes that have only a few connections. We also study, in models and in real networks, the crossover from fractal to non-fractal networks that occurs when a small number of random interactions are added by means of scaling techniques. In the second chapter we use k-core techniques to study dynamic processes in networks. The k-core of a network is the network's largest component that, within itself, exhibits all nodes with at least k connections. We use this k-core analysis to estimate the relative leadership positions of firms in the Life Science (LS) and Information and Communication Technology (ICT) sectors of industry. We study the differences in the k-core structure between the LS and the ICT sectors. We find that the lead segment (highest k-core) of the LS sector, unlike that of the ICT sector, is remarkably stable over time: once a particular firm enters the lead segment, it is likely to remain there for many years. In the third chapter we study how epidemics spread though networks. Our results indicate that a virus is more likely to infect a large area of a network if it originates at a node contained within k-core of high index k.

Study of the fractal dimension of the wind and its relationships with turbulent and stability parameters

NASA Astrophysics Data System (ADS)

Tijera, Manuel; Maqueda, Gregorio; Cano, José L.; López, Pilar; Yagüe, Carlos

2010-05-01

The wind velocity series of the atmospheric turbulent flow in the planetary boundary layer (PBL), in spite of being highly erratic, present a self-similarity structure (Frisch, 1995; Peitgen et., 2004; Falkovich et., 2006). So, the wind velocity can be seen as a fractal magnitude. We calculate the fractal dimension (Komolgorov capacity or box-counting dimension) of the wind perturbation series (u' = u- ) in the physical spaces (namely velocity-time). It has been studied the time evolution of the fractal dimension along different days and at three levels above the ground (5.8 m, 13.5 m, 32 m). The data analysed was recorded in the experimental campaign SABLES-98 (Cuxart et al., 2000) at the Research Centre for the Lower Atmosphere (CIBA) located in Valladolid (Spain). In this work the u, v and w components of wind velocity series have been measured by sonic anemometers (20 Hz sampling rate). The fractal dimension versus the integral length scales of the mean wind series have been studied, as well as the influence of different turbulent parameters. A method for estimating these integral scales is developed using the normalized autocorrelation function and a Gaussian fit. Finally, it will be analysed the variation of the fractal dimension versus stability parameters (as Richardson number) in order to explain some of the dominant features which are likely immersed in the fractal nature of these turbulent flows. References - Cuxart J, Yagüe C, Morales G, Terradellas E, Orbe J, Calvo J, Fernández A, Soler MR, Infante C, Buenestado P, Espinalt A, Joergensen HE, Rees JM, Vilá J, Redondo JM, Cantalapiedra IR and Conangla L (2000) Stable atmospheric boundary-layer experiment in Spain (SABLES98): a report. Boundary- Layer Meteorol 96:337-370 - Falkovich G and Kattepalli R. Sreenivasan (2006) Lessons from Hidrodynamic Turbulence. Physics Today 59: 43-49 - Frisch U (1995) Turbulence the legacy of A.N. Kolmogorov Cambridge University Press 269pp - Peitgen H, Jürgens H and Saupe D (2004) Chaos and Fractals Springer-Verlag 971pp

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.

Depth to Curie temperature across the central Red Sea from magnetic data using the de-fractal method

NASA Astrophysics Data System (ADS)

Salem, Ahmed; Green, Chris; Ravat, Dhananjay; Singh, Kumar Hemant; East, Paul; Fairhead, J. Derek; Mogren, Saad; Biegert, Ed

2014-06-01

The central Red Sea rift is considered to be an embryonic ocean. It is characterised by high heat flow, with more than 90% of the heat flow measurements exceeding the world mean and high values extending to the coasts - providing good prospects for geothermal energy resources. In this study, we aim to map the depth to the Curie isotherm (580 °C) in the central Red Sea based on magnetic data. A modified spectral analysis technique, the “de-fractal spectral depth method” is developed and used to estimate the top and bottom boundaries of the magnetised layer. We use a mathematical relationship between the observed power spectrum due to fractal magnetisation and an equivalent random magnetisation power spectrum. The de-fractal approach removes the effect of fractal magnetisation from the observed power spectrum and estimates the parameters of depth to top and depth to bottom of the magnetised layer using iterative forward modelling of the power spectrum. We applied the de-fractal approach to 12 windows of magnetic data along a profile across the central Red Sea from onshore Sudan to onshore Saudi Arabia. The results indicate variable magnetic bottom depths ranging from 8.4 km in the rift axis to about 18.9 km in the marginal areas. Comparison of these depths with published Moho depths, based on seismic refraction constrained 3D inversion of gravity data, showed that the magnetic bottom in the rift area corresponds closely to the Moho, whereas in the margins it is considerably shallower than the Moho. Forward modelling of heat flow data suggests that depth to the Curie isotherm in the centre of the rift is also close to the Moho depth. Thus Curie isotherm depths estimated from magnetic data may well be imaging the depth to the Curie temperature along the whole profile. Geotherms constrained by the interpreted Curie isotherm depths have subsequently been calculated at three points across the rift - indicating the variation in the likely temperature profile with depth.

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.

The breakup mechanism of biomolecular and colloidal aggregates in a shear flow

NASA Astrophysics Data System (ADS)

Ó Conchúir, Breanndán; Zaccone, Alessio

2014-03-01

The theory of self-assembly of colloidal particles in shear flow is incomplete. Previous analytical approaches have failed to capture the microscopic interplay between diffusion, shear and intermolecular interactions which controls the aggregates fate in shear. In this work we analytically solved the drift-diffusion equation for the breakup rate of a dimer in flow. Then applying rigidity percolation theory, we found that the lifetime of a generic cluster formed under shear is controlled by the typical lifetime of a single bond in its interior, which in turn depends on the efficiency of the stress transmitted from other bonds in the cluster. We showed that aggregate breakup is a thermally-activated process where the activation energy is controlled by the interplay between intermolecular forces and the shear drift, and where structural parameters determine whether cluster fragmentation or surface erosion prevails. In our latest work, we analyzed floppy modes and nonaffine deformations to derive a lower bound on the fractal dimension df below which aggregates are mechanically unstable, ie. for large aggregates df ~= 2.4. This theoretical framework is in quantitative agreement with experiments and can be used for population balance modeling of colloidal and protein aggregation.

Fractal structure of low-temperature plasma of arc discharge as a consequence of the interaction of current sheets

NASA Astrophysics Data System (ADS)

Smolanov, N. A.

2016-01-01

The structure of the particles deposited from the plasma arc discharge were studied. The flow of plasma spreading from the cathode spot to the walls of the vacuum chamber. Electric and magnetic fields to influence the plasma flow. The fractal nature of the particles from the plasma identified by small-angle X-ray scattering. Possible cause of their formation is due to the instability of the growth front and nonequilibrium conditions for their production - a high speed transition of the vapor-liquid-solid or vapor - crystal. The hypothesis of a plasma arc containing dust particles current sheets was proposed.

Microstructure evolution, thermal stability and fractal behavior of water vapor flow assisted in situ growth poly(vinylcarbazole)-titania quantum dots nanocomposites

NASA Astrophysics Data System (ADS)

Mombrú, Dominique; Romero, Mariano; Faccio, Ricardo; Mombrú, Alvaro W.

2017-12-01

Here, we report a novel strategy for the preparation of TiO2 quantum dots fillers prepared from alkoxide precursor via in situ water vapor flow diffusion into poly(N-vinylcarbazole) host. A detailed characterization by means of infrared and Raman spectroscopy, X-ray powder diffraction, small angle X-ray scattering and differential scanning calorimetry is reported. The growth mechanism of both crystallites and particles was mostly governed by the classical coarsening reaction limited growth and the polymer host showed no detectable chemical modifications at the interface or active participation in the growing process. The main relevance of our strategy respect to the typical sol-gel growth in solution is the possibility of the interruption of the reaction by simple stopping the water vapor flow diffusion into the polymer host thus achieving good control in the nanoparticles size. The thermal stability and fractal behavior of our nanocomposites were also studied by differential scanning calorimetry and in situ small angle X-ray scattering versus temperature. Strong correlations between modifications in the fractal behavior and glass transition or fusion processes were observed for these nanocomposites.

3D numerical modeling of hyporheic exchange processes in fractal riverbed

NASA Astrophysics Data System (ADS)

Lee, A.; Aubeneau, A.

2017-12-01

The subsurface region receiving stream water is known as the hyporheic zone and the flow of water in and out of this zone is called hyporheic exchange. The hyporheic zone is populated by biofilms and is a hotspot for nutrient uptake and contaminant transformation. Traditionally, pumping models predicting the head distribution over the riverbed boundary are used to obtain the velocity field in the subsurface. However, past research has largely overlooked the nonlinearity of the turbulent flow above the bumpy riverbed. The main objective of this research is to investigate the effect of spatial and temporal heterogeneity created by turbulent flow on hyporheic exchange and residence time distribution in fractal channel beds. The 3-D fractal riverbed is created from the power spectrum. Large-Eddy Simulation is used to provide the pressure field over the benthic boundary. Finally, Darcian fluxes in the sub-surface are calculated and hyporheic travel times computed using random walks. Surface and subsurface transport processes are represented explicitly and can be studied in detail. Our results suggest that (1) Eddies and wakes around the dunes force the exchange (2) The bigger the dunes, the greater the influence of turbulence (3) Turbulence induces more exchange than pumping predicts.

Fractal Physiology and the Fractional Calculus: A Perspective

PubMed Central

West, Bruce J.

2010-01-01

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

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.

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.

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.

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

Multi-fractality in aeroelastic response as a precursor to flutter

NASA Astrophysics Data System (ADS)

Venkatramani, J.; Nair, Vineeth; Sujith, R. I.; Gupta, Sayan; Sarkar, Sunetra

2017-01-01

Wind tunnel tests on a NACA 0012 airfoil have been carried out to study the transition in aeroelastic response from an initial state characterised by low-amplitude aperiodic fluctuations to aeroelastic flutter when the system exhibits limit cycle oscillations. An analysis of the aeroelastic measurements reveals multi-fractal characteristics in the pre-flutter regime. This has not been studied in the literature. As the flow velocity approaches the flutter velocity from below, a gradual loss in multi-fractality is observed. Measures based on the generalised Hurst exponents are developed and are shown to have the potential to warn against impending aeroelastic flutter. The results of this study could be useful for health monitoring of aeroelastic structures.

Experimental investigation of the flow field and power consumption characteristics of regular and fractal blade impellers in a dynamic mixer

NASA Astrophysics Data System (ADS)

Steiros, K.; Bruce, P. J. K.; Buxton, O. R. H.; Vassilicos, J. C.

2015-11-01

Experiments have been performed in an octagonal un-baffled water tank, stirred by three radial turbines with different geometry impellers: (1) regular rectangular blades; (2) single-iteration fractal blades; (3) two-iteration fractal blades. Shaft torque was monitored and the power number calculated for each case. Both impellers with fractal geometry blades exhibited a decrease of turbine power number compared to the regular one (15% decrease for single-iteration and 19% for two iterations). Phase locked PIV in the discharge region of the blades revealed that the vortices emanating from the regular blades are more coherent, have higher kinetic energy, and advect faster towards the tank's walls where they are dissipated, compared to their fractal counterparts. This suggests a strong link between vortex production and behaviour and the energy input for the different impellers. Planar PIV measurements in the bulk of the tank showed an increase of turbulence intensity of over 20% for the fractal geometry blades, suggesting higher mixing efficiency. Experiments with pressure measurements on the different geometry blade surfaces are ongoing to investigate the distribution of forces, and calculate hydrodynamic centres of pressure. The authors would like to acknowledge the financial support given by European Union FP7 Marie Curie MULTISOLVE project (Grant Agreement No. 317269).

Contact Kinetics in Fractal Macromolecules.

PubMed

Dolgushev, Maxim; Guérin, Thomas; Blumen, Alexander; Bénichou, Olivier; Voituriez, Raphaël

2015-11-13

We consider the kinetics of first contact between two monomers of the same macromolecule. Relying on a fractal description of the macromolecule, we develop an analytical method to compute the mean first contact time for various molecular sizes. In our theoretical description, the non-Markovian feature of monomer motion, arising from the interactions with the other monomers, is captured by accounting for the nonequilibrium conformations of the macromolecule at the very instant of first contact. This analysis reveals a simple scaling relation for the mean first contact time between two monomers, which involves only their equilibrium distance and the spectral dimension of the macromolecule, independently of its microscopic details. Our theoretical predictions are in excellent agreement with numerical stochastic simulations.

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

PubMed Central

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

2015-01-01

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

Performance of an attention-demanding task during treadmill walking shifts the noise qualities of step-to-step variation in step width.

PubMed

Grabiner, Mark D; Marone, Jane R; Wyatt, Marilynn; Sessoms, Pinata; Kaufman, Kenton R

2018-06-01

The fractal scaling evident in the step-to-step fluctuations of stepping-related time series reflects, to some degree, neuromotor noise. The primary purpose of this study was to determine the extent to which the fractal scaling of step width, step width and step width variability are affected by performance of an attention-demanding task. We hypothesized that the attention-demanding task would shift the structure of the step width time series toward white, uncorrelated noise. Subjects performed two 10-min treadmill walking trials, a control trial of undisturbed walking and a trial during which they performed a mental arithmetic/texting task. Motion capture data was converted to step width time series, the fractal scaling of which were determined from their power spectra. Fractal scaling decreased by 22% during the texting condition (p < 0.001) supporting the hypothesized shift toward white uncorrelated noise. Step width and step width variability increased 19% and five percent, respectively (p < 0.001). However, a stepwise discriminant analysis to which all three variables were input revealed that the control and dual task conditions were discriminated only by step width fractal scaling. The change of the fractal scaling of step width is consistent with increased cognitive demand and suggests a transition in the characteristics of the signal noise. This may reflect an important advance toward the understanding of the manner in which neuromotor noise contributes to some types of falls. However, further investigation of the repeatability of the results, the sensitivity of the results to progressive increases in cognitive load imposed by attention-demanding tasks, and the extent to which the results can be generalized to the gait of older adults seems warranted. Copyright © 2018 Elsevier B.V. All rights reserved.

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

NASA Technical Reports Server (NTRS)

Rosenshein, E. B.

2003-01-01

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

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.

Flow field topology of submerged jets with fractal generated turbulence

NASA Astrophysics Data System (ADS)

Cafiero, Gioacchino; Discetti, Stefano; Astarita, Tommaso

2015-11-01

Fractal grids (FGs) have been recently an object of numerous investigations due to the interesting capability of generating turbulence at multiple scales, thus paving the way to tune mixing and scalar transport. The flow field topology of a turbulent air jet equipped with a square FG is investigated by means of planar and volumetric particle image velocimetry. The comparison with the well-known features of a round jet without turbulence generators is also presented. The Reynolds number based on the nozzle exit section diameter for all the experiments is set to about 15 000. It is demonstrated that the presence of the grid enhances the entrainment rate and, as a consequence, the scalar transfer of the jet. Moreover, due to the effect of the jet external shear layer on the wake shed by the grid bars, the turbulence production region past the grid is significantly shortened with respect to the documented behavior of fractal grids in free-shear conditions. The organization of the large coherent structures in the FG case is also analyzed and discussed. Differently from the well-known generation of toroidal vortices due to the growth of azimuthal disturbances within the jet shear layer, the fractal grid introduces cross-wise disturbs which produce streamwise vortices; these structures, although characterized by a lower energy content, have a deeper streamwise penetration than the ring vortices, thus enhancing the entrainment process.

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.

Discrete simulations of spatio-temporal dynamics of small water bodies under varied stream flow discharges

NASA Astrophysics Data System (ADS)

Daya Sagar, B. S.

2005-01-01

Spatio-temporal patterns of small water bodies (SWBs) under the influence of temporally varied stream flow discharge are simulated in discrete space by employing geomorphologically realistic expansion and contraction transformations. Cascades of expansion-contraction are systematically performed by synchronizing them with stream flow discharge simulated via the logistic map. Templates with definite characteristic information are defined from stream flow discharge pattern as the basis to model the spatio-temporal organization of randomly situated surface water bodies of various sizes and shapes. These spatio-temporal patterns under varied parameters (λs) controlling stream flow discharge patterns are characterized by estimating their fractal dimensions. At various λs, nonlinear control parameters, we show the union of boundaries of water bodies that traverse the water body and non-water body spaces as geomorphic attractors. The computed fractal dimensions of these attractors are 1.58, 1.53, 1.78, 1.76, 1.84, and 1.90, respectively, at λs of 1, 2, 3, 3.46, 3.57, and 3.99. These values are in line with general visual observations.

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

NASA Astrophysics Data System (ADS)

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

1992-10-01

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

On the formation and evolution of sinuous rilles: Morphologic and morphometric insights from the Marius Hills and Aristarchus Plateau regions

NASA Astrophysics Data System (ADS)

Roberts, Carolyn Eve

Lunar sinuous rilles are characteristically long (100-350 km), narrow (< 1 km wide) volcanic channels that shallow distally from their source. Despite the vast knowledge accumulated over decades of lunar exploration, sinuous rille formation remains poorly understood. To constrain formation processes, the morphology and morphometry of many rilles were examined using Lunar Orbiter IV/V and Lunar Reconnaissance Orbiter imagery. Morphologic observations suggest that sinuous rilles initially formed within expansive sheet flows as preferred pathways along the pre-eruptive surface that developed into lava tubes as the eruption continued. Geologic sketch maps reveal outcrop layering, exposed in rille walls, that is consistent with sheet flow emplacement and small, anastomosing "rillettes" around Rima Marius, suggesting that initial tubes intermingled and coalesced to form larger tubes. From terrestrial basalt flow emplacement observations, I infer that as the outer boundaries of the Rima Marius-forming sheet flow cooled, the remaining lava was forced toward the main tube and downcutting transpired at the flow base. Once the eruption concluded, lava drained out of the main tube; the dimensions of the hollow tube lead to roof collapse, resulting in the general rille structure observed today. Results from the morphometric analysis indicate that sinuous rille characteristics (length, width, sinuosity, radius of curvature, number of curves, and fractal dimension) are similar between the two highest lunar sinuous rille populations at Marius Hills and Aristarchus Plateau. Moreover, the number of curves increases linearly with rille length and a weak correlation exists between sinuosity and fractal dimension. Compared to terrestrial rivers, sinuous rilles have lower amplitudes, smaller sinuosity values and fractal dimension values. The preponderance of evidence indicates sinuous rilles formed through a combination of both constructional and erosional processes.

Jupiter Fractal Art

NASA Image and Video Library

2017-08-10

See Jupiter's Great Red Spot as you've never seen it before in this new Jovian work of art. Artist Mik Petter created this unique, digital artwork using data from the JunoCam imager on NASA's Juno spacecraft. The art form, known as fractals, uses mathematical formulas to create art with an infinite variety of form, detail, color and light. The tumultuous atmospheric zones in and around the Great Red Spot are highlighted by the author's use of colorful fractals. Vibrant colors of various tints and hues, combined with the almost organic-seeming shapes, make this image seem to be a colorized and crowded petri dish of microorganisms, or a close-up view of microscopic and wildly-painted seashells. The original JunoCam image was taken on July 10, 2017 at 7:10 p.m. PDT (10:10 p.m. EDT), as the Juno spacecraft performed its seventh close flyby of Jupiter. The spacecraft captured the image from about 8,648 miles (13,917 kilometers) above the tops of the clouds of the planet at a latitude of -32.6 degrees. https://photojournal.jpl.nasa.gov/catalog/PIA21777

Finite element based contact analysis of radio frequency MEMs switch membrane surfaces

NASA Astrophysics Data System (ADS)

Liu, Jin-Ya; Chalivendra, Vijaya; Huang, Wenzhen

2017-10-01

Finite element simulations were performed to determine the contact behavior of radio frequency (RF) micro-electro-mechanical (MEM) switch contact surfaces under monotonic and cyclic loading conditions. Atomic force microscopy (AFM) was used to capture the topography of RF-MEM switch membranes and later they were analyzed for multi-scale regular as well as fractal structures. Frictionless, non-adhesive contact 3D finite element analysis was carried out at different length scales to investigate the contact behavior of the regular-fractal surface using an elasto-plastic material model. Dominant micro-scale regular patterns were found to significantly change the contact behavior. Contact areas mainly cluster around the regular pattern. The contribution from the fractal structure is not significant. Under cyclic loading conditions, plastic deformation in the 1st loading/unloading cycle smooth the surface. The subsequent repetitive loading/unloading cycles undergo elastic contact without changing the morphology of the contacting surfaces. The work is expected to shed light on the quality of the switch surface contact as well as the optimum design of RF MEM switch surfaces.

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.

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.

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.

Flow interaction with a flexible viscoelastic sheet

NASA Astrophysics Data System (ADS)

Shoele, Kourosh

2017-11-01

Many new engineered materials and almost all soft biological tissues are made up of heterogeneous multi-scale components with complex viscoelastic behavior. This implies that their macro constitutive relations cannot be modeled sufficiently with a typical integer-order viscoelastic relation and a more general mode is required. Here, we study the flow-induced vibration of a viscoelastic sheet where a generalized fractional constitutive model is employed to represent the relation between the bending stress and the temporal response of the structure. A new method is proposed for the calculation of the convolution integral inside the fractal model and its computational benefits will be discussed. Using a coupled fluid-structure interaction (FSI) methodology based on the immersed boundary technique, dynamic fluttering modes of the structure as a result of the fluid force will be presented and the role of fractal viscoelasticity on the dynamic of the structure will be shown. Finally, it will be argued how the stress relaxation modifies the flow-induced oscillatory responses of this benchmark problem.

Two-Phase Flow Simulations through Experimentally Studied Porous Media Analogies

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

Crandall, D.M.; Ahmadi, G.; Smith, D.H.

2007-07-01

The amount of CO2 that can be sequestered in deep brine reservoirs is dependant on fluid-fluid-solid interactions within heterogeneous porous media. Displacement of an in-place fluid by a less viscous invading fluid does not displace 100% of the defending fluid, due to capillary and viscous fingering. This has been studied experimentally and numerically with the use of pore-throat flow cells and pore-level models, respectively, in the last two decades. This current work solves the full Navier-Stokes and continuity equations in a random pore-throat geometry using the Volume of Fluid (VOF) method. To verify that the VOF model can be accuratelymore » applied within narrow apertures, qualitative agreement with the well-documented phenomenon of viscous fingering in a Hele-Shaw cell is first presented. While this motion is similar to the fingering observed in geological media, the random structure of rock restricts flow patterns not captured by flow in Hele-Shaw cells. To mimic this heterogeneous natural geometry, a novel experimental flowcell was created. Experiments of constant-rate injection of air into the water saturated model are described. This situation, where a non-wetting, invading fluid displaces a surface-wetting, more-viscous fluid, is known as drainage. As the injection flow rate was increased, a change from stable displacement fronts to dendritic fingering structures was observed, with a corresponding decrease in the fractal dimension of the interface and a decrease in the final saturation of invading air. Predictions of the VOF computational modeling within the same flowcell geometry are then shown to be in good agreement with the experimental results. Percent saturation and the fractal dimension of the invading fluid were calculated from the numerical model and shown to be similar to the experimental findings for air invasion of a watersaturated domain. The fluid properties (viscosity and density) were than varied and the viscosity ratio and capillary number of the fluids were shown to affect the percent of displaced fluid, with lower capillary number and higher viscosity ratio displacing a greater amount of the wetting fluid. Displacement of a non-wetting, in-place fluid by a less viscous, wetting fluid (the case of imbibition; contact angle > 90°) is then studied with the numerical model. The invading fluid is shown to preferentially move into small throats and displace a larger percent of the in-place fluid than observed in the drainage case. The interface was also observed to have a higher fractal dimension, closer to 2. These results highlight the potential for greater fundamental understanding of liquid-gas-solid interactions in heterogeneous, porous media that can be obtained from computational fluid dynamics (CFD). Situations, which are difficult to experimentally study, can be examined with CFD in a manner that more accurately accounts for the geological conditions relevant to CO2 sequestration. This allows for greater accuracy in the prediction of storage capacity within known geological structures. This study shows that as the contact angle between the invading fluid and the defending fluid increase, a greater portion of the porous medium is invaded. Thus, a greater portion of CO2 can be sequestered in reservoirs that are not strongly water wet. Low flow rates are shown to increase the final percent saturation of the invading fluid as well, regardless of wetting conditions.« less

Texture segmentation of non-cooperative spacecrafts images based on wavelet and fractal dimension

NASA Astrophysics Data System (ADS)

Wu, Kanzhi; Yue, Xiaokui

2011-06-01

With the increase of on-orbit manipulations and space conflictions, missions such as tracking and capturing the target spacecrafts are aroused. Unlike cooperative spacecrafts, fixing beacons or any other marks on the targets is impossible. Due to the unknown shape and geometry features of non-cooperative spacecraft, in order to localize the target and obtain the latitude, we need to segment the target image and recognize the target from the background. The data and errors during the following procedures such as feature extraction and matching can also be reduced. Multi-resolution analysis of wavelet theory reflects human beings' recognition towards images from low resolution to high resolution. In addition, spacecraft is the only man-made object in the image compared to the natural background and the differences will be certainly observed between the fractal dimensions of target and background. Combined wavelet transform and fractal dimension, in this paper, we proposed a new segmentation algorithm for the images which contains complicated background such as the universe and planet surfaces. At first, Daubechies wavelet basis is applied to decompose the image in both x axis and y axis, thus obtain four sub-images. Then, calculate the fractal dimensions in four sub-images using different methods; after analyzed the results of fractal dimensions in sub-images, we choose Differential Box Counting in low resolution image as the principle to segment the texture which has the greatest divergences between different sub-images. This paper also presents the results of experiments by using the algorithm above. It is demonstrated that an accurate texture segmentation result can be obtained using the proposed technique.

Inverse Proportional Relationship Between Switching-Time Length and Fractal-Like Structure for Continuous Tracking Movement

NASA Astrophysics Data System (ADS)

Hirakawa, Takehito; Suzuki, Hiroo; Gohara, Kazutoshi; Yamamoto, Yuji

We investigate the relationship between the switching-time length T and the fractal-like feature that characterizes the behavior of dissipative dynamical systems excited by external temporal inputs for tracking movement. Seven healthy right-handed male participants were asked to continuously track light-emitting diodes that were located on the right and left sides in front of them. These movements were performed under two conditions: when the same input pattern was repeated (the periodic-input condition) and when two different input patterns were switched stochastically (the switching-input condition). The repeated time lengths of input patterns during these conditions were 2.00, 1.00, 0.75, 0.50, 0.35, and 0.25s. The movements of a lever held between a participant’s thumb and index finger were measured by a motion-capture system and were analyzed with respect to position and velocity. The condition in which the same input was repeated revealed that two different stable trajectories existed in a cylindrical state space, while the condition in which the inputs were switched induced transitions between these two trajectories. These two different trajectories were considered as excited attractors. The transitions between the two excited attractors produced eight trajectories; they were then characterized by a fractal-like feature as a third-order sequence effect. Moreover, correlation dimensions, which are typically used to evaluate fractal-like features, calculated from the set on the Poincaré section increased as the switching-time length T decreased. These results suggest that an inverse proportional relationship exists between the switching-time length T and the fractal-like feature of human movement.

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.

Fractal Dimension of EEG Activity Senses Neuronal Impairment in Acute Stroke

PubMed Central

Zappasodi, Filippo; Olejarczyk, Elzbieta; Marzetti, Laura; Assenza, Giovanni; Pizzella, Vittorio; Tecchio, Franca

2014-01-01

The brain is a self-organizing system which displays self-similarities at different spatial and temporal scales. Thus, the complexity of its dynamics, associated to efficient processing and functional advantages, is expected to be captured by a measure of its scale-free (fractal) properties. Under the hypothesis that the fractal dimension (FD) of the electroencephalographic signal (EEG) is optimally sensitive to the neuronal dysfunction secondary to a brain lesion, we tested the FD’s ability in assessing two key processes in acute stroke: the clinical impairment and the recovery prognosis. Resting EEG was collected in 36 patients 4–10 days after a unilateral ischemic stroke in the middle cerebral artery territory and 19 healthy controls. National Health Institute Stroke Scale (NIHss) was collected at T0 and 6 months later. Highuchi FD, its inter-hemispheric asymmetry (FDasy) and spectral band powers were calculated for EEG signals. FD was smaller in patients than in controls (1.447±0.092 vs 1.525±0.105) and its reduction was paired to a worse acute clinical status. FD decrease was associated to alpha increase and beta decrease of oscillatory activity power. Larger FDasy in acute phase was paired to a worse clinical recovery at six months. FD in our patients captured the loss of complexity reflecting the global system dysfunction resulting from the structural damage. This decrease seems to reveal the intimate nature of structure-function unity, where the regional neural multi-scale self-similar activity is impaired by the anatomical lesion. This picture is coherent with neuronal activity complexity decrease paired to a reduced repertoire of functional abilities. FDasy result highlights the functional relevance of the balance between homologous brain structures’ activities in stroke recovery. PMID:24967904

Fractal dimension of EEG activity senses neuronal impairment in acute stroke.

PubMed

Zappasodi, Filippo; Olejarczyk, Elzbieta; Marzetti, Laura; Assenza, Giovanni; Pizzella, Vittorio; Tecchio, Franca

2014-01-01

The brain is a self-organizing system which displays self-similarities at different spatial and temporal scales. Thus, the complexity of its dynamics, associated to efficient processing and functional advantages, is expected to be captured by a measure of its scale-free (fractal) properties. Under the hypothesis that the fractal dimension (FD) of the electroencephalographic signal (EEG) is optimally sensitive to the neuronal dysfunction secondary to a brain lesion, we tested the FD's ability in assessing two key processes in acute stroke: the clinical impairment and the recovery prognosis. Resting EEG was collected in 36 patients 4-10 days after a unilateral ischemic stroke in the middle cerebral artery territory and 19 healthy controls. National Health Institute Stroke Scale (NIHss) was collected at T0 and 6 months later. Highuchi FD, its inter-hemispheric asymmetry (FDasy) and spectral band powers were calculated for EEG signals. FD was smaller in patients than in controls (1.447±0.092 vs 1.525±0.105) and its reduction was paired to a worse acute clinical status. FD decrease was associated to alpha increase and beta decrease of oscillatory activity power. Larger FDasy in acute phase was paired to a worse clinical recovery at six months. FD in our patients captured the loss of complexity reflecting the global system dysfunction resulting from the structural damage. This decrease seems to reveal the intimate nature of structure-function unity, where the regional neural multi-scale self-similar activity is impaired by the anatomical lesion. This picture is coherent with neuronal activity complexity decrease paired to a reduced repertoire of functional abilities. FDasy result highlights the functional relevance of the balance between homologous brain structures' activities in stroke recovery.

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.

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.

Stochastic dislocation kinetics and fractal structures in deforming metals probed by acoustic emission and surface topography measurements

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

Vinogradov, A.; Laboratory of Hybrid Nanostructured Materials, NITU MISiS, Moscow 119490; Yasnikov, I. S.

2014-06-21

We demonstrate that the fractal dimension (FD) of the dislocation population in a deforming material is an important quantitative characteristic of the evolution of the dislocation structure. Thus, we show that peaking of FD signifies a nearing loss of uniformity of plastic flow and the onset of strain localization. Two techniques were employed to determine FD: (i) inspection of surface morphology of the deforming crystal by white light interferometry and (ii) monitoring of acoustic emission (AE) during uniaxial tensile deformation. A connection between the AE characteristics and the fractal dimension determined from surface topography measurements was established. As a commonmore » platform for the two methods, the dislocation density evolution in the bulk was used. The relations found made it possible to identify the occurrence of a peak in the median frequency of AE as a harbinger of plastic instability leading to necking. It is suggested that access to the fractal dimension provided by AE measurements and by surface topography analysis makes these techniques important tools for monitoring the evolution of the dislocation structure during plastic deformation—both as stand-alone methods and especially when used in tandem.« less

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

PubMed

Spicer; Keller; Pratsinis

1996-12-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

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.

Theoretical Study on Stress Sensitivity of Fractal Porous Media with Irreducible Water

NASA Astrophysics Data System (ADS)

Lei, Gang; Dong, Zhenzhen; Li, Weirong; Wen, Qingzhi; Wang, Cai

The couple flow deformation behavior in porous media has drawn tremendous attention in various scientific and engineering fields. However, though the coupled flow deformation mechanism has been intensively investigated in the last decades, the essential controls on stress sensitivity are not determined. It is of practical significance to use analytic methods to study stress sensitivity of porous media. Unfortunately, because of the disordered and extremely complicated microstructures of porous media, the theoretical model for stress sensitivity is scarce. The goal of this work is to establish a novel and reasonable quantitative model to determine the essential controls on stress sensitivity. The predictions of the theoretical model, derived from the Hertzian contact theory and fractal geometry, agree well with the available experimental data. Compared with the previous models, our model takes into account more factors, including the influence of the water saturation and the microstructural parameters of the pore space. The proposed models can reveal more mechanisms that affect the coupled flow deformation behavior in fractal porous media. The results show that the irreducible water saturation increases with the increase of effective stress, and decreases with the increased rock elastic modulus (or increased power law index) at a given effective stress. The effect of stress variation on porosity is smaller than that on permeability. Under a given effective stress, the normalized permeability (or the normalized porosity) becomes smaller with the decrease of rock elastic modulus (or the decrease of power law index). And a lower capillary pressure will correspond to an increased rock elastic modulus (or an increased power law index) under a given water saturation.

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

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.

“Feathered” fractal surfaces to minimize secondary electron emission for a wide range of incident angles

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

Swanson, Charles; Kaganovich, Igor D.

Complex structures on a material surface can significantly reduce the total secondary electron emission from that surface. The reduction occurs due to the capture of low-energy, true secondary electrons emitted at one point of the structure and intersecting another. We performed Monte Carlo calculations to demonstrate that fractal surfaces can reduce net secondary electron emission produced by the surface as compared to the flat surface. Specifically, we describe one surface, a “feathered” surface, which reduces the secondary electron emission yield more effectively than other previously considered configurations. Specifically, feathers grown onto a surface suppress secondary electron emission from shallow anglesmore » of incidence more effectively than velvet. Here, we find that, for the surface simulated, secondary electron emission yield remains below 20% of its un-suppressed value, even for shallow incident angles, where the velvet-only surface gives reduction factor of only 50%.« less

Modeling small cell lung cancer (SCLC) biology through deterministic and stochastic mathematical models.

PubMed

Salgia, Ravi; Mambetsariev, Isa; Hewelt, Blake; Achuthan, Srisairam; Li, Haiqing; Poroyko, Valeriy; Wang, Yingyu; Sattler, Martin

2018-05-25

Mathematical cancer models are immensely powerful tools that are based in part on the fractal nature of biological structures, such as the geometry of the lung. Cancers of the lung provide an opportune model to develop and apply algorithms that capture changes and disease phenotypes. We reviewed mathematical models that have been developed for biological sciences and applied them in the context of small cell lung cancer (SCLC) growth, mutational heterogeneity, and mechanisms of metastasis. The ultimate goal is to develop the stochastic and deterministic nature of this disease, to link this comprehensive set of tools back to its fractalness and to provide a platform for accurate biomarker development. These techniques may be particularly useful in the context of drug development research, such as combination with existing omics approaches. The integration of these tools will be important to further understand the biology of SCLC and ultimately develop novel therapeutics.

“Feathered” fractal surfaces to minimize secondary electron emission for a wide range of incident angles

DOE PAGES

Swanson, Charles; Kaganovich, Igor D.

2017-07-24

Complex structures on a material surface can significantly reduce the total secondary electron emission from that surface. The reduction occurs due to the capture of low-energy, true secondary electrons emitted at one point of the structure and intersecting another. We performed Monte Carlo calculations to demonstrate that fractal surfaces can reduce net secondary electron emission produced by the surface as compared to the flat surface. Specifically, we describe one surface, a “feathered” surface, which reduces the secondary electron emission yield more effectively than other previously considered configurations. Specifically, feathers grown onto a surface suppress secondary electron emission from shallow anglesmore » of incidence more effectively than velvet. Here, we find that, for the surface simulated, secondary electron emission yield remains below 20% of its un-suppressed value, even for shallow incident angles, where the velvet-only surface gives reduction factor of only 50%.« less

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.

"Feathered" fractal surfaces to minimize secondary electron emission for a wide range of incident angles

NASA Astrophysics Data System (ADS)

Swanson, Charles; Kaganovich, Igor D.

2017-07-01

Complex structures on a material surface can significantly reduce the total secondary electron emission from that surface. The reduction occurs due to the capture of low-energy, true secondary electrons emitted at one point of the structure and intersecting another. We performed Monte Carlo calculations to demonstrate that fractal surfaces can reduce net secondary electron emission produced by the surface as compared to the flat surface. Specifically, we describe one surface, a "feathered" surface, which reduces the secondary electron emission yield more effectively than other previously considered configurations. Specifically, feathers grown onto a surface suppress secondary electron emission from shallow angles of incidence more effectively than velvet. We find that, for the surface simulated, secondary electron emission yield remains below 20% of its un-suppressed value, even for shallow incident angles, where the velvet-only surface gives reduction factor of only 50%.

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

NASA Astrophysics Data System (ADS)

Wu, J. Z.; Fang, L.

2018-02-01

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

Mixing and diffusion in intermittent overturning turbulence

NASA Astrophysics Data System (ADS)

Redondo, Jose M.; Mahjoub, Otman B.; Gonzalez-Nieto, Pilar L.; Lawry, Andrew

2014-05-01

The improvements in experimental methods and high resolution image analysis are nowadays able to detect subtle changes in the structure of the turbulence over a wide range of temporal and spatial scales [1], we compare the scaling shown by different mixing fronts driven by buoyancy that form a Rayleigh-Taylor mixing front. We use PIV and density front tracking in several experimental configurations akin to geophysical overturning [2-7]. We parametrize the role of unstable stratification by means of the Atwood number and compare both the scaling and the multifractal and the maximum local fractal structure functions of the different markers used to visualize the front. Both reactive and passive scalar tracers are used to investigate the mixing structure and the intermittency of the flow. Different initial conditions are compared and the mixing efficiency of the overal turbulent process evaluated [6-7]. An interesting approach, relating the Multi-Fractal dimension spectra, the intermittency and the spectral exponent is to find relationships that may be used to parameterise the sub-grid turbulence in terms of generalized diffusivities [4 ] that take into account the topology and the self-similarity of the Mixing RT and RM flows. As an example, a relationship between the diffusivity, the exponent β, the intermittency μ, and D(i), may be found for the volume fraction or the concentration, at the same time other locally measured parameters such as the enstrophy or the gradient alignment as well as their multi-fractal structures may turn out to be physically relevant indicators of the local turbulence and the mixing. Several methods of deriving local eddy diffusivity and local entrainment should give more realistic estimates of the spatial/temporal non-homogeneities (and intermittencies in the Kolmogorov 62 sense obtained as spatial correlations of the turbulent dissipation, or from structure functions) and these values may be used to parameterise turbulence at a variety of scales. The method involving the multi-fractal dimension measurements is much more elaborated and seems to have a better theoretical justification in the sense that it is possible that different concentrations showing different fractal dimensions may be due to different levels of intermittency (and thus different spectra, which are not generally in equilibrium as dscribed by[9,10]. Using topological descriptors we can establish now a theoretical baseline pattern for the turbulence behaviour that is reflected in the different structures (volume fraction, velocity, vorticity, helicity) we can thus obtain a classification relating D3 and the integral of the different fractal dimensions D2 for different levels of scalar (volume fraction reaction intensity or temperature). [5,8,11] Vorticity evolution is more smooth and quite different than that of volume fraction or density and these seem also different for the RT and RM instability driven mixing showing a wider range of even higher mixing efficiencies 0- 0.66 Thanks to European Union project ERBIC15-CT96-0111 Multi-scale complex fluid flows and interfacial phenomena (PITN-GA-2008-214919). ERCOFTAC and GenCat. grant 2001SGR00221. [1] Mahjoub O.B., Redondo J.M. and Babiano A. (2000) Hyerarchy flux in nonhomogeneous flows in Turbulent diffusion in the environment Eds. Redondo J.M. and Babiano A. 249-260. . [2] Dalziel, S. B.,(1994) Perturbations and coherent flow in Rayleigh-Taylor instability: in 4th International Workshop on the Physics of Compressible Turbulent Mixing, ed. P. F. Linden, D. L. Youngs, & S. B. Dalziel; 32-41. [3] Linden, P. F., Redondo, J. M., and Youngs, D. (1994) Molecular mixing in Rayleigh-Taylor instability, J. Fluid Mech. 265, 97-124 [4] Vindel, J.M., Yague, C. and Redondo, J.M. Nuovo Cimento (2008) 31, [5]Redondo J.M. (1993) Fractal models of density interfaces. Wavelets, Fractals and Fourier transforms. (Eds.) M. Farge, J.C.R. Hunt and J.C. Vassilicos. 353-370. IMA number 43, Clarendon Press, Oxford 1993 [6] J.M Redondo, J.M. Grau, A. Platonov, G. Garzon, (2008) Rev. Int. Met. Num. Ing. 24, 23. [7] Fraunie P., Berreba S. Chashechkin Y., Velasco D. and Redondo J.M. (2008) LES and laboratory experiments on the decay of grid wakes in strongly stratified flows. Il Nuovo Cimento C 31, 909-930. [8] Redondo J.M. (2002) "Mixing efficiencies of different kinds of turbulent processes and instabilities, Applications to the environment in Turbulent mixing in geophysical flows". Eds. Linden P.F. and Redondo J.M. 131-157. [9] Redondo J.M. (1990). The structure of density interfaces, Ph. D. Thesis, DAMTP University of Cambridge. [10]Redondo J.M. (1987). Effects of ground proximity on dense gas entrainment, Journal of Hazardous Materials, 16, 381-393. [11] Lopez, P., Cano, J.L. and Redondo, J.M.(2008) An experimental model of mixing processes generated by an array of top-heavy turbulent plumes, Il Nuovo Cimento, 31C, 679-698.

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.

Pneumatic fractures in confined granular media.

PubMed

Eriksen, Fredrik K; Toussaint, Renaud; Turquet, Antoine L; Måløy, Knut J; Flekkøy, Eirik G

2017-06-01

We perform experiments where air is injected at a constant overpressure P_{in}, ranging from 5 to 250 kPa, into a dry granular medium confined within a horizontal linear Hele-Shaw cell. The setup allows us to explore compacted configurations by preventing decompaction at the outer boundary, i.e., the cell outlet has a semipermeable filter such that beads are stopped while air can pass. We study the emerging patterns and dynamic growth of channels in the granular media due to fluid flow, by analyzing images captured with a high speed camera (1000 images/s). We identify four qualitatively different flow regimes, depending on the imposed overpressure, ranging from no channel formation for P_{in} below 10 kPa, to large thick channels formed by erosion and fingers merging for high P_{in} around 200 kPa. The flow regimes where channels form are characterized by typical finger thickness, final depth into the medium, and growth dynamics. The shape of the finger tips during growth is studied by looking at the finger width w as function of distance d from the tip. The tip profile is found to follow w(d)∝d^{β}, where β=0.68 is a typical value for all experiments, also over time. This indicates a singularity in the curvature d^{2}d/dw^{2}∼κ∼d^{1-2β}, but not of the slope dw/dd∼d^{β-1}, i.e., more rounded tips rather than pointy cusps, as they would be for the case β>1. For increasing P_{in}, the channels generally grow faster and deeper into the medium. We show that the channel length along the flow direction has a linear growth with time initially, followed by a power-law decay of growth velocity with time as the channel approaches its final length. A closer look reveals that the initial growth velocity v_{0} is found to scale with injection pressure as v_{0}∝P_{in}^{3/2}, while at a critical time t_{c} there is a cross-over to the behavior v(t)∝t^{-α}, where α is close to 2.5 for all experiments. Finally, we explore the fractal dimension of the fully developed patterns. For example, for patterns resulting from intermediate P_{in} around 100-150 kPa, we find that the box-counting dimensions lie within the range D_{B}∈[1.53,1.62], similar to viscous fingering fractals in porous media.

Pneumatic fractures in confined granular media

NASA Astrophysics Data System (ADS)

Eriksen, Fredrik K.; Toussaint, Renaud; Turquet, Antoine L.; Mâløy, Knut J.; Flekkøy, Eirik G.

2017-06-01

We perform experiments where air is injected at a constant overpressure Pin, ranging from 5 to 250 kPa, into a dry granular medium confined within a horizontal linear Hele-Shaw cell. The setup allows us to explore compacted configurations by preventing decompaction at the outer boundary, i.e., the cell outlet has a semipermeable filter such that beads are stopped while air can pass. We study the emerging patterns and dynamic growth of channels in the granular media due to fluid flow, by analyzing images captured with a high speed camera (1000 images/s). We identify four qualitatively different flow regimes, depending on the imposed overpressure, ranging from no channel formation for Pin below 10 kPa, to large thick channels formed by erosion and fingers merging for high Pin around 200 kPa. The flow regimes where channels form are characterized by typical finger thickness, final depth into the medium, and growth dynamics. The shape of the finger tips during growth is studied by looking at the finger width w as function of distance d from the tip. The tip profile is found to follow w (d ) ∝dβ , where β =0.68 is a typical value for all experiments, also over time. This indicates a singularity in the curvature d2d /d w2˜κ ˜d1 -2 β , but not of the slope d w /d d ˜dβ -1 , i.e., more rounded tips rather than pointy cusps, as they would be for the case β >1 . For increasing Pin, the channels generally grow faster and deeper into the medium. We show that the channel length along the flow direction has a linear growth with time initially, followed by a power-law decay of growth velocity with time as the channel approaches its final length. A closer look reveals that the initial growth velocity v0 is found to scale with injection pressure as v0∝Pin3/2 , while at a critical time tc there is a cross-over to the behavior v (t ) ∝t-α , where α is close to 2.5 for all experiments. Finally, we explore the fractal dimension of the fully developed patterns. For example, for patterns resulting from intermediate Pin around 100-150 kPa, we find that the box-counting dimensions lie within the range DB∈[1.53 ,1.62 ] , similar to viscous fingering fractals in porous media.

Stiffness Indices and Fractal Dimension relationship in Arterial Pressure and Diameter Time Series in-Vitro

NASA Astrophysics Data System (ADS)

Cymberknop, L.; Legnani, W.; Pessana, F.; Bia, D.; Zócalo, Y.; Armentano, R. L.

2011-12-01

The advent of vascular diseases, such as hypertension and atherosclerosis, is associated to significant alterations in the physical properties of arterial vessels. Evaluation of arterial biomechanical behaviour is related to the assessment of three representative indices: arterial compliance, arterial distensibility and arterial stiffness index. Elasticity is the most important mechanical property of the arterial wall, whose natures is strictly non-linear. Intervention of elastin and collagen fibres, passive constituent elements of the arterial wall, is related to the applied wall stress level. Concerning this, appropriate tools are required to analyse the temporal dynamics of the signals involved, in order to characterize the whole phenomenon. Fractal geometry can be mentioned as one of those techniques. The aim of this study consisted on arterial pressure and diameter signals processing, by means of nonlinear techniques based on fractal geometry. Time series morphology was related to different arterial stiffness states, generated by means of blood flow variations, during experiences performed in vitro.

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.

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).

Percolation Laws of a Fractal Fracture-Pore Double Medium

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

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.

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…

Diffusion in fractal wakes and convective thermoelectric flows

NASA Astrophysics Data System (ADS)

Vila, Teresa; Tellez, Jackson; Sanchez, Jesus Maria; Sotillos, Laura; Diez, Margarita; Redondo, Jose Manuel

2014-05-01

We calculate diffusion and scaling of the velocity ald vorticity in a thermoelectric driven heating and cooling experimental device in order to map the different transitions between two and three dimensional convection in an enclosure and complex driven flows. The size of the water tank is of 0.2 x 0.2 x 0.1 m and the heat sources or sinks can be regulated both in power and sign [1-3]. The thermal convective driven flows are generated by Seebeck and Peltier effects in 4 wall extended positions of 0.05 x 0.05 cm each. The parameter range of convective cell array varies strongly with the Topology of the boundary conditions. At present side heat fluxes are considered and estimated as a function of Rayleigh, Peclet and Nusselt numbers,[4-6] Visualizations are performed by PIV, Particle tracking and shadowgraph. Diffusion is measured in the transition from a homogeneous linearly stratified fluid to a cellular or layered structure by means of stirring. Patterns arise by setting up a convective flow generated by a buoyant heat flux [5,6]. The experiments described here investigate high Prandtl number mixing using brine and fresh water in order to form a density interface and low Prandtl number mixing with temperature gradients. Using ESS and selfsimilarity structures in the velocity and vorticity fieds and intermittency [2] that forms in the flow is related to mixing and stiring. The evolution of the mixing fronts are compared and the topological characteristics of the merging of the plumes and jets are examined for different configurations. We also present a detailed comparison of the evolution of RM and RT, Jets and Plumes in overall mixing. The relation between fractal analysis and spectral analysis can be very useful to determine the evolution of scales. Experimental and numerical results on the advance of a mixing or nonmixing front occurring at a density interface due to gravitational acceleration are analyzed considering the fractal and spectral structure of the fronts like removable plate experiments [7] for Rayleigh-Taylor flows. The evolution of the turbulent mixing layer and its complex configuration is studied taking into account the dependence on the initial modes at the early stages and its spectral, self-similar information [8,9]. Spectral and Fractal analysis on the images has been used in order to estimate dominant mixing structures as well as the dispersion relations of basic instabilities [2,10]. [1] Redondo J.M. (1992) Termodinámica de los procesos irreversibles, efectos termoeléctricos Rev. Termoelectricidad 2, 16-29.AIT.Pamplona. [2] Mahjoub O.B., Redondo J.M. and Babiano A.(2000) "Hyerarchy flux in nonhomogeneous flows" in Turbulent diffusion in the environment Eds. Redondo J.M. and Babiano A. 249-260. [3] Redondo J.M., Sanchez J.M. Pascual I. Noriega, G.F.(1995)."Thermoelectric regulation for electric cabinets".XVI International Conference in Thermoelectrics, 02-G20. Ed. V. Vedernikov. 456-468. St. Petersburg, Russia. [4] Kuramitsu, M.; Redondo, J.M.; Noriega, G. (2003) Measurements of anisotropy, thermoelectric behaviour and multi-fractal aspects of FeSi and of complex custom made TE materials Twenty-Second International Conference on Thermoelectric- ICT,IEEE, DOI:10.1109/ICT.2003.1287570, 541-545. [5] López González-Nieto, P., Cano, J. L. and Redondo, J. M., "Buoyant mixing processes generated in turbulent pluma arrays" in Experimental and Modelling Micrometeorology, Física de la Tierra, vol. 19, pp. 205-219, 2007. [6] Kimura R. and Iga, I. (1995) Bubble Convection in Mixing in Geophysical Flows Eds. Redondo J.M: and Metais, 35-51. Ed CIMNE, Barcelona. [7] Linden, P. F., Redondo, J. M. and Caulfield, C. P.: (1992), Advances in Compressible Turbulent Mixing, edited by W.P. Dannevik, A.C. Buckingham and C.E. Leith, Princenton University. [8] Nicolleau, F.C.G.A.; Cambon, C.; Redondo, J.M.; Vassilicos, J.C.; Reeks, M.; Nowakowski, A.F. (Eds.) New Approaches in Modeling Multiphase Flows and Dispersion in Turbulence, Fractual Methods and Synthetic Turbulence. ERCOFTAC Series, Vol. 18 1st Edition., 2011, 250 p. ISBN 978-94-007-2505-8 [9] F Ciuchi; L Sorriso-Valvo; A Mazzulla and J. M. Redondo (2009).Fractal aggregates evolution of methyl red in liquid crystal. European physical journal E.29 - 2,pp. 139 - 147.06/2009 . [10]Platonov A. Carrillo A. Matulka A, Sekula E., Grau J. Redondo J.M. and Tarquis A. (2008)Multifractal observations of eddies, oil spills and natural slicks in the ocean surface. Il Nuovo Cimento C 31,5-6, 861-880.

Theoretical study of nanoparticle formation in thermal plasma processing: Nucleation, coagulation and aggregation

NASA Astrophysics Data System (ADS)

Mendoza Gonzalez, Norma Yadira

This work presents a mathematical modeling study of the synthesis of nanoparticles in radio frequency (RF) inductively coupled plasma (ICP) reactors. The purpose is to further investigate the influence of process parameters on the final size and morphology of produced particles. The proposed model involves the calculation of flow and temperature fields of the plasma gas. Evaporation of raw particles is also accounted with the particle trajectory and temperature history calculated with a Lagrangian approach. The nanoparticle formation is considered by homogeneous nucleation and the growth is caused by condensation and Brownian coagulation. The growth of fractal aggregates is considered by introducing a power law exponent Df. Transport of nanoparticles occurs by convection, thermophoresis and Brownian diffusion. The method of moments is used to solve the particle dynamics equation. The model is validated using experimental results from plasma reactors at laboratory scale. The results are presented in the following manner. First, use is made of the computational fluid dynamics software (CFD), Fluent 6.1 with a commercial companion package specifically developped for aerosols named: Fine Particle Model (FPM). This package is used to study the relationship between the operating parameters effect and the properties of the end products at the laboratory scale. Secondly, a coupled hybrid model for the synthesis of spherical particles and fractal aggregates is developped in place of the FPM package. Results obtained from this model will allow to identify the importance of each parameter in defining the morphology of spherical primary particles and fractal aggregates of nanoparticles. The solution of the model was made using the geometries and operating conditions of existing reactors at the Centre de Recherche en Energie, Plasma et Electrochimie (CREPE) of the Universite de Sherbrooke, for which experimental results were obtained experimentally. Additionally, this study demonstrates the importance of the flow and temperature fields on the growth of fractal particles; namely the aggregates.

Strongly Stratified Turbulence Wakes and Mixing Produced by Fractal Wakes

NASA Astrophysics Data System (ADS)

Dimitrieva, Natalia; Redondo, Jose Manuel; Chashechkin, Yuli; Fraunie, Philippe; Velascos, David

2017-04-01

This paper describes Shliering and Shadowgraph experiments of the wake induced mixing produced by tranversing a vertical or horizontal fractal grid through the interfase between two miscible fluids at low Atwood and Reynolds numbers. This is a configuration design to models the mixing across isopycnals in stably-stratified flows in many environmental relevant situations (either in the atmosphere or in the ocean. The initial unstable stratification is characterized by a reduced gravity: g' = gΔρ ρ where g is gravity, Δρ being the initial density step and ρ the reference density. Here the Atwood number is A = g' _ 2 g . The topology of the fractal wake within the strong stratification, and the internal wave field produces both a turbulent cascade and a wave cascade, with frecuen parametric resonances, the envelope of the mixing front is found to follow a complex non steady 3rd order polinomial function with a maximum at about 4-5 Brunt-Vaisalla non-dimensional time scales: t/N δ = c1(t/N) + c2g Δρ ρ (t/N)2 -c3(t/N)3. Conductivity probes and Shliering and Shadowgraph visual techniques, including CIV with (Laser induced fluorescence and digitization of the light attenuation across the tank) are used in order to investigate the density gradients and the three-dimensionality of the expanding and contracting wake. Fractal analysis is also used in order to estimate the fastest and slowest growing wavelengths. The large scale structures are observed to increase in wave-length as the mixing progresses, and the processes involved in this increase in scale are also examined.Measurements of the pointwise and horizontally averaged concentrations confirm the picture obtained from past flow visualization studies. They show that the fluid passes through the mixing region with relatively small amounts of molecular mixing,and the molecular effects only dominate on longer time scales when the small scales have penetrated through the large scale structures. The Non-stationary dynamicss and structure of stratified fluid flows around a wedge were also studied based of the fundamental equations set using numerical modeling. Due to breaking of naturally existing background diffusion flux of stratifying agent by an impermeable surface of the wedge a complex multi-level vortex system of compensatory fluid motions is formed around the obstacle. The flow is characterized by a wide range of values of internal scales that are absent in a homogeneous liquid. Numerical solution of the fundamental system with the boundary conditions is constructed using a solver such as stratifiedFoam developed within the frame of the open source computational package OpenFOAM using the finite volume method. The computations were performed in parallel using computing resources of the Scientific Research Supercomputer Complex of MSU (SRCC MSU) and the technological platform UniHUB. The evolution of the flow pattern of the wedge by stratified flow has been demonstrated. The complex structure of the fields of physical quantities and their gradients has been shown. Observed in experiment are multiple flow components, including upstream disturbances, internal waves and the downstream wake with submerged transient vortices well reproduced. Structural elements of flow differ in size and laws of variation in space and time. Rich fine flow structure visualized in vicinity and far from the obstacle. The global efficiency of the mixing process is measured and compared with previous estimates of mixing efficiency.

Scaling phenomena in the Internet: Critically examining criticality

PubMed Central

Willinger, Walter; Govindan, Ramesh; Jamin, Sugih; Paxson, Vern; Shenker, Scott

2002-01-01

Recent Internet measurements have found pervasive evidence of some surprising scaling properties. The two we focus on in this paper are self-similar scaling in the burst patterns of Internet traffic and, in some contexts, scale-free structure in the network's interconnection topology. These findings have led to a number of proposed models or “explanations” of such “emergent” phenomena. Many of these explanations invoke concepts such as fractals, chaos, or self-organized criticality, mainly because these concepts are closely associated with scale invariance and power laws. We examine these criticality-based explanations of self-similar scaling behavior—of both traffic flows through the Internet and the Internet's topology—to see whether they indeed explain the observed phenomena. To do so, we bring to bear a simple validation framework that aims at testing whether a proposed model is merely evocative, in that it can reproduce the phenomenon of interest but does not necessarily capture and incorporate the true underlying cause, or indeed explanatory, in that it also captures the causal mechanisms (why and how, in addition to what). We argue that the framework can provide a basis for developing a useful, consistent, and verifiable theory of large networks such as the Internet. Applying the framework, we find that, whereas the proposed criticality-based models are able to produce the observed “emergent” phenomena, they unfortunately fail as sound explanations of why such scaling behavior arises in the Internet. PMID:11875212

Investigation on flow and mixing characteristics of supersonic mixing layer induced by forced vibration of cantilever

NASA Astrophysics Data System (ADS)

Zhang, Dongdong; Tan, Jianguo; Lv, Liang

2015-12-01

The mixing process has been an important issue for the design of supersonic combustion ramjet engine, and the mixing efficiency plays a crucial role in the improvement of the combustion efficiency. In the present study, nanoparticle-based planar laser scattering (NPLS), particle image velocimetry (PIV) and large eddy simulation (LES) are employed to investigate the flow and mixing characteristics of supersonic mixing layer under different forced vibration conditions. The indexes of fractal dimension, mixing layer thickness, momentum thickness and scalar mixing level are applied to describe the mixing process. Results show that different from the development and evolution of supersonic mixing layer without vibration, the flow under forced vibration is more likely to present the characteristics of three-dimensionality. The laminar flow region of mixing layer under forced vibration is greatly shortened and the scales of rolled up Kelvin-Helmholtz vortices become larger, which promote the mixing process remarkably. The fractal dimension distribution reveals that comparing with the flow without vibration, the turbulent fluctuation of supersonic mixing layer under forced vibration is more intense. Besides, the distribution of mixing layer thickness, momentum thickness and scalar mixing level are strongly influenced by forced vibration. Especially, when the forcing frequency is 4000 Hz, the mixing layer thickness and momentum thickness are 0.0391 m and 0.0222 m at the far field of 0.16 m, 83% and 131% higher than that without vibration at the same position, respectively.

Quantification of ultrasonic texture intra-heterogeneity via volumetric stochastic modeling for tissue characterization.

PubMed

Al-Kadi, Omar S; Chung, Daniel Y F; Carlisle, Robert C; Coussios, Constantin C; Noble, J Alison

2015-04-01

Intensity variations in image texture can provide powerful quantitative information about physical properties of biological tissue. However, tissue patterns can vary according to the utilized imaging system and are intrinsically correlated to the scale of analysis. In the case of ultrasound, the Nakagami distribution is a general model of the ultrasonic backscattering envelope under various scattering conditions and densities where it can be employed for characterizing image texture, but the subtle intra-heterogeneities within a given mass are difficult to capture via this model as it works at a single spatial scale. This paper proposes a locally adaptive 3D multi-resolution Nakagami-based fractal feature descriptor that extends Nakagami-based texture analysis to accommodate subtle speckle spatial frequency tissue intensity variability in volumetric scans. Local textural fractal descriptors - which are invariant to affine intensity changes - are extracted from volumetric patches at different spatial resolutions from voxel lattice-based generated shape and scale Nakagami parameters. Using ultrasound radio-frequency datasets we found that after applying an adaptive fractal decomposition label transfer approach on top of the generated Nakagami voxels, tissue characterization results were superior to the state of art. Experimental results on real 3D ultrasonic pre-clinical and clinical datasets suggest that describing tumor intra-heterogeneity via this descriptor may facilitate improved prediction of therapy response and disease characterization. Copyright © 2014 The Authors. Published by Elsevier B.V. All rights reserved.

Heterogeneous recurrence monitoring and control of nonlinear stochastic processes

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

Yang, Hui, E-mail: huiyang@usf.edu; Chen, Yun

Recurrence is one of the most common phenomena in natural and engineering systems. Process monitoring of dynamic transitions in nonlinear and nonstationary systems is more concerned with aperiodic recurrences and recurrence variations. However, little has been done to investigate the heterogeneous recurrence variations and link with the objectives of process monitoring and anomaly detection. Notably, nonlinear recurrence methodologies are based on homogeneous recurrences, which treat all recurrence states in the same way as black dots, and non-recurrence is white in recurrence plots. Heterogeneous recurrences are more concerned about the variations of recurrence states in terms of state properties (e.g., valuesmore » and relative locations) and the evolving dynamics (e.g., sequential state transitions). This paper presents a novel approach of heterogeneous recurrence analysis that utilizes a new fractal representation to delineate heterogeneous recurrence states in multiple scales, including the recurrences of both single states and multi-state sequences. Further, we developed a new set of heterogeneous recurrence quantifiers that are extracted from fractal representation in the transformed space. To that end, we integrated multivariate statistical control charts with heterogeneous recurrence analysis to simultaneously monitor two or more related quantifiers. Experimental results on nonlinear stochastic processes show that the proposed approach not only captures heterogeneous recurrence patterns in the fractal representation but also effectively monitors the changes in the dynamics of a complex system.« less

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.

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.

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.

Complex Critical Exponents for Percolation Transitions in Josephson-Junction Arrays, Antiferromagnets, and Interacting Bosons

NASA Astrophysics Data System (ADS)

Fernandes, Rafael M.; Schmalian, Jörg

2011-02-01

We show that the critical behavior of the XY quantum-rotor model undergoing a percolation transition is dramatically affected by its topological Berry phase 2πρ. In particular, for irrational ρ, its low-energy excitations emerge as spinless fermions with fractal spectrum. As a result, critical properties not captured by the usual Ginzburg-Landau-Wilson description of phase transitions arise, such as complex critical exponents, log-periodic oscillations and dynamically broken scale invariance.

Time-resolved forward-light-scattering monitoring of protein–lysozyme aggregation in precrystalline solutions

NASA Astrophysics Data System (ADS)

Wakamatsu, Takashi; Onoda, Takashi; Ogata, Makoto

2018-05-01

An in situ measurement method of monitoring protein aggregation in precrystalline solutions is presented. The method is based on a small-angle forward static light scattering (F-SLS) technique. This technique uses an accurate optical arrangement of a combination of a collimating lens and a CCD to obtain an F-SLS pattern from an aggregate-containing protein solution in one shot. The real-time observation of a crystallizing lysozyme captured the formation of fractal aggregates in the initial formation stage.

Reaction patterns in a blinking vortex flow

NASA Astrophysics Data System (ADS)

Nugent, Carolyn

2005-11-01

We study the patterns formed by the excitable Belousov-Zhabotinsky reaction in a blinking vortex flow produced by magnetohydrodynamic forcing. Mixing in this flow is chaotic, as has been documented extensively in previous studies. The reaction is triggered by a silver wire, and the result is a pulse (``trigger wave'') that propagates through the system. We investigate the patterns formed by the propagating pulse and compare them with theoriesootnotetextT. Tel, A. de Moura, C. Grebogi and G. Karolyi, Phys. Rep. 413, 91 (2005). that predict fractal patterns determined by the unstable manifolds of the flow. We also consider ``burn-like'' reaction fronts, and compare the results with previous experiments for patterns of oscillatory reactions in this flow.

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.

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.

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)

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 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.

Linking deposit morphology and clogging in subsurface remediation: Final Technical Report

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

Mays, David C.

2013-12-11

Groundwater is a crucial resource for water supply, especially in arid and semiarid areas of the United States west of the 100th meridian. Accordingly, remediation of contaminated groundwater is an important application of science and technology, particularly for the U.S. Department of Energy (DOE), which oversees a number of groundwater remediation sites from Cold War era mining. Groundwater remediation is complex, because it depends on identifying, locating, and treating contaminants in the subsurface, where remediation reactions depend on interacting geological, hydrological, geochemical, and microbiological factors. Within this context, permeability is a fundamental concept, because it controls the rates and pathwaysmore » of groundwater flow. Colloid science is intimately related to permeability, because when colloids are present (particles with equivalent diameters between 1 nanometer and 10 micrometers), changes in hydrological or geochemical conditions can trigger a detrimental reduction in permeability called clogging. Accordingly, clogging is a major concern in groundwater remediation. Several lines of evidence suggest that clogging by colloids depends on (1) colloid deposition, and (2) deposit morphology, that is, the structure of colloid deposits, which can be quantified as a fractal dimension. This report describes research, performed under a 2-year, exploratory grant from the DOE’s Subsurface Biogeochemical Research (SBR) program. This research employed a novel laboratory technique to simultaneously measure flow, colloid deposition, deposit morphology, and permeability in a flow cell, and also collected field samples from wells at the DOE’s Old Rifle remediation site. Field results indicate that suspended solids at the Old Rifle site have fractal structures. Laboratory results indicate that clogging is associated with colloid deposits with smaller fractal dimensions, in accordance with previous studies on initially clean granular media. Preliminary modeling has identified the deposit radius of gyration as a candidate variable to account for clogging as a function of (1) colloid accumulation and (2) deposit morphology.« less

The Impact of The Fractal Paradigm on Geography

NASA Astrophysics Data System (ADS)

De Cola, L.

2001-12-01

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

Fractal 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.

Recurrence Quantification of Fractal Structures

PubMed Central

Webber, Charles L.

2012-01-01

By definition, fractal structures possess recurrent patterns. At different levels repeating patterns can be visualized at higher magnifications. The purpose of this chapter is threefold. First, general characteristics of dynamical systems are addressed from a theoretical mathematical perspective. Second, qualitative and quantitative recurrence analyses are reviewed in brief, but the reader is directed to other sources for explicit details. Third, example mathematical systems that generate strange attractors are explicitly defined, giving the reader the ability to reproduce the rich dynamics of continuous chaotic flows or discrete chaotic iterations. The challenge is then posited for the reader to study for themselves the recurrent structuring of these different dynamics. With a firm appreciation of the power of recurrence analysis, the reader will be prepared to turn their sights on real-world systems (physiological, psychological, mechanical, etc.). PMID:23060808

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...

Three-Dimensional Inverse Opal Photonic Crystal Substrates toward Efficient Capture of Circulating Tumor Cells.

PubMed

Xu, Hongwei; Dong, Biao; Xiao, Qiaoqin; Sun, Xueke; Zhang, Xinran; Lyu, Jiekai; Yang, Yudan; Xu, Lin; Bai, Xue; Zhang, Shuang; Song, Hongwei

2017-09-13

Artificial fractal structures have attracted considerable scientific interest in circulating tumor cells (CTCs) detection and capture, which plays a pivotal role in the diagnosis and prognosis of cancer. Herein, we designed a bionic TiO 2 inverse opal photonic crystal (IOPC) structure for highly efficient immunocapture of CTCs by combination of a magnetic Fe 3 O 4 @C6@silane nanoparticles with anti-EpCAM (antiepithelial cell adhesion molecule) and microchannel structure. Porous structure and dimension of IOPC TiO 2 can be precisely controlled for mimicking cellular components, and anti-EpCAM antibody was further modified on IOPC interface by conjugating with polydopamine (PDA). The improvement of CTCs capture efficiency reaches a surprising factor of 20 for the IOPC interface compared to that on flat glass, suggesting that the IOPCs are responsible for the dramatic enhancement of the capture efficiency of MCF-7 cells. IOPC substrate with pore size of 415 nm leads to the optimal CTCs capture efficiency of 92% with 1 mL/h. Besides the cell affinity, IOPCs also have the advantage of light scattering property which can enhance the excitation and emission light of fluorescence labels, facilitating the real-time monitoring of CTCs capture. The IOPC-based platform demonstrates excellent performance in CTCs capture, which will take an important step toward specific recognition of disease-related rare cells.

Multi-scale interactions affecting transport, storage, and processing of solutes and sediments in stream corridors (Invited)

NASA Astrophysics Data System (ADS)

Harvey, J. W.; Packman, A. I.

2010-12-01

Surface water and groundwater flow interact with the channel geomorphology and sediments in ways that determine how material is transported, stored, and transformed in stream corridors. Solute and sediment transport affect important ecological processes such as carbon and nutrient dynamics and stream metabolism, processes that are fundamental to stream health and function. Many individual mechanisms of transport and storage of solute and sediment have been studied, including surface water exchange between the main channel and side pools, hyporheic flow through shallow and deep subsurface flow paths, and sediment transport during both baseflow and floods. A significant challenge arises from non-linear and scale-dependent transport resulting from natural, fractal fluvial topography and associated broad, multi-scale hydrologic interactions. Connections between processes and linkages across scales are not well understood, imposing significant limitations on system predictability. The whole-stream tracer experimental approach is popular because of the spatial averaging of heterogeneous processes; however the tracer results, implemented alone and analyzed using typical models, cannot usually predict transport beyond the very specific conditions of the experiment. Furthermore, the results of whole stream tracer experiments tend to be biased due to unavoidable limitations associated with sampling frequency, measurement sensitivity, and experiment duration. We recommend that whole-stream tracer additions be augmented with hydraulic and topographic measurements and also with additional tracer measurements made directly in storage zones. We present examples of measurements that encompass interactions across spatial and temporal scales and models that are transferable to a wide range of flow and geomorphic conditions. These results show how the competitive effects between the different forces driving hyporheic flow, operating at different spatial scales, creates a situation where hyporheic fluxes cannot be accurately estimated without considering multi-scale effects. Our modeling captures the dominance of small-scale features such as bedforms that drive the majority of hyporheic flow, but it also captures how hyporheic flow is substantially modified by relatively small changes in streamflow or groundwater flow. The additional field measurements add sensitivity and power to whole stream tracer additions by improving resolution of the relative importance of storage at different scales (e.g. bar-scale versus bedform-scale). This information is critical in identifying hot spots where important biogeochemical reactions occur. In summary, interpreting multi-scale interactions in streams requires models that are physically based and that incorporate non-linear process dynamics. Such models can take advantage of increasingly comprehensive field data to integrate transport processes across spatially variable flow and geomorphic conditions. The most useful field and modeling approaches will be those that are simple enough to be easily implemented by users from various disciplines but comprehensive enough to produce meaningful predictions for a wide range of flow and geomorphic scenarios. This capability is needed to support improved strategies for protecting stream ecological health in the face of accelerating land use and climate change.

Turbulent Flow Structure Inside a Canopy with Complex Multi-Scale Elements

NASA Astrophysics Data System (ADS)

Bai, Kunlun; Katz, Joseph; Meneveau, Charles

2015-06-01

Particle image velocimetry laboratory measurements are carried out to study mean flow distributions and turbulent statistics inside a canopy with complex geometry and multiple scales consisting of fractal, tree-like objects. Matching the optical refractive indices of the tree elements with those of the working fluid provides unobstructed optical paths for both illuminations and image acquisition. As a result, the flow fields between tree branches can be resolved in great detail, without optical interference. Statistical distributions of mean velocity, turbulence stresses, and components of dispersive fluxes are documented and discussed. The results show that the trees leave their signatures in the flow by imprinting wake structures with shapes similar to the trees. The velocities in both wake and non-wake regions significantly deviate from the spatially-averaged values. These local deviations result in strong dispersive fluxes, which are important to account for in canopy-flow modelling. In fact, we find that the streamwise normal dispersive flux inside the canopy has a larger magnitude (by up to four times) than the corresponding Reynolds normal stress. Turbulent transport in horizontal planes is studied in the framework of the eddy viscosity model. Scatter plots comparing the Reynolds shear stress and mean velocity gradient are indicative of a linear trend, from which one can calculate the eddy viscosity and mixing length. Similar to earlier results from the wake of a single tree, here we find that inside the canopy the mean mixing length decreases with increasing elevation. This trend cannot be scaled based on a single length scale, but can be described well by a model, which considers the coexistence of multi-scale branches. This agreement indicates that the multi-scale information and the clustering properties of the fractal objects should be taken into consideration in flows inside multi-scale canopies.

Morphology and Three-Dimensional Inhalation Flow in Human Airways in Healthy and Diseased Subjects

NASA Astrophysics Data System (ADS)

Van de Moortele, Tristan

We investigate experimentally the relation between anatomical structure and respiratory function in healthy and diseased airways. Computed Tomography (CT) scans of human lungs are analyzed from the data base of a large multi-institution clinical study on Chronic Obstructive Pulmonary Disease (COPD). Through segmentation, the 3D volumes of the airways are determined at total lung capacity. A geometric analysis provides data on the morphometry of the airways, including the length and diameter of branches, the child-to-parent diameter ratio, and branching angles. While several geometric parameters are confirmed to match past studies for healthy subjects, previously unreported trends are reported on the length of branches. Specifically, in most dichotomous airway bifurcation, the branch of smaller diameter tends to be significantly longer than the one of larger diameter. Additionally, the branch diameter tends to be smaller in diseased airways than in healthy airways up to the 7th generation of bronchial branching. 3D fractal analysis is also performed on the airway volume. Fractal dimensions of 1.89 and 1.83 are found for healthy non-smokers and declining COPD subjects, respectively, furthering the belief that COPD (and lung disease in general) significantly affects the morphometry of the airways already in early stages of the disease. To investigate the inspiratory flow, 3D flow models of the airways are generated using Computer Aided Design (CAD) software and 3D printed. Using Magnetic Resonance Velocimetry (MRV), 3-component 3D flow fields are acquired for steady inhalation at Reynolds number Re 2000 defined at the trachea. Analysis of the flow data reveals that diseased subjects may experience greater secondary flow strength in their conducting airways, especially in deeper generations.

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.

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.

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.

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.

Fractal analyses reveal independent complexity and predictability of gait

PubMed Central

Dierick, Frédéric; Nivard, Anne-Laure

2017-01-01

Locomotion is a natural task that has been assessed for decades and used as a proxy to highlight impairments of various origins. So far, most studies adopted classical linear analyses of spatio-temporal gait parameters. Here, we use more advanced, yet not less practical, non-linear techniques to analyse gait time series of healthy subjects. We aimed at finding more sensitive indexes related to spatio-temporal gait parameters than those previously used, with the hope to better identify abnormal locomotion. We analysed large-scale stride interval time series and mean step width in 34 participants while altering walking direction (forward vs. backward walking) and with or without galvanic vestibular stimulation. The Hurst exponent α and the Minkowski fractal dimension D were computed and interpreted as indexes expressing predictability and complexity of stride interval time series, respectively. These holistic indexes can easily be interpreted in the framework of optimal movement complexity. We show that α and D accurately capture stride interval changes in function of the experimental condition. Walking forward exhibited maximal complexity (D) and hence, adaptability. In contrast, walking backward and/or stimulation of the vestibular system decreased D. Furthermore, walking backward increased predictability (α) through a more stereotyped pattern of the stride interval and galvanic vestibular stimulation reduced predictability. The present study demonstrates the complementary power of the Hurst exponent and the fractal dimension to improve walking classification. Our developments may have immediate applications in rehabilitation, diagnosis, and classification procedures. PMID:29182659

Analysis and classification of commercial ham slice images using directional fractal dimension features.

PubMed

Mendoza, Fernando; Valous, Nektarios A; Allen, Paul; Kenny, Tony A; Ward, Paddy; Sun, Da-Wen

2009-02-01

This paper presents a novel and non-destructive approach to the appearance characterization and classification of commercial pork, turkey and chicken ham slices. Ham slice images were modelled using directional fractal (DF(0°;45°;90°;135°)) dimensions and a minimum distance classifier was adopted to perform the classification task. Also, the role of different colour spaces and the resolution level of the images on DF analysis were investigated. This approach was applied to 480 wafer thin ham slices from four types of hams (120 slices per type): i.e., pork (cooked and smoked), turkey (smoked) and chicken (roasted). DF features were extracted from digitalized intensity images in greyscale, and R, G, B, L(∗), a(∗), b(∗), H, S, and V colour components for three image resolution levels (100%, 50%, and 25%). Simulation results show that in spite of the complexity and high variability in colour and texture appearance, the modelling of ham slice images with DF dimensions allows the capture of differentiating textural features between the four commercial ham types. Independent DF features entail better discrimination than that using the average of four directions. However, DF dimensions reveal a high sensitivity to colour channel, orientation and image resolution for the fractal analysis. The classification accuracy using six DF dimension features (a(90°)(∗),a(135°)(∗),H(0°),H(45°),S(0°),H(90°)) was 93.9% for training data and 82.2% for testing data.

Mass-Mobility Characterization of Flame-made ZrO2 Aerosols: Primary Particle Diameter & Extent of Aggregation

PubMed Central

Eggersdorfer, M.L.; Gröhn, A.J.; Sorensen, C.M.; McMurry, P.H.; Pratsinis, S.E.

2013-01-01

Gas-borne nanoparticles undergoing coagulation and sintering form irregular or fractal-like structures affecting their transport, light scattering, effective surface area and density. Here, zirconia (ZrO2) nanoparticles are generated by scalable spray combustion, and their mobility diameter and mass are obtained nearly in-situ by differential mobility analyzer (DMA) and aerosol particle mass (APM) measurements. Using these data, the density of ZrO2 and a power law between mobility and primary particle diameters, the structure of fractal-like particles is determined (mass-mobility exponent, prefactor and average number and surface area mean diameter of primary particles, dva). The dva determined by DMA-APM measurements and this power law is in good agreement with the dva obtained by ex-situ nitrogen adsorption and microscopic analysis. Using this combination of measurements and above power law, the effect of flame spray process parameters (e.g. precursor solution and oxygen flow rate as well as zirconium concentration) on fractal-like particle structure characteristics is investigated in detail. This reveals that predominantly agglomerates (physically-bonded particles) and aggregates (chemically- or sinter-bonded particles) of nanoparticles are formed at low and high particle concentrations, respectively. PMID:22959835

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.

Application to recognition of ferrography image with fractal neural network

NASA Astrophysics Data System (ADS)

Tian, Xianzhong; Hu, Tongsen; Zhang, Jian

2005-10-01

Because wear particles have fractal characteristics, it is necessary that adding fractal parameters to studying wear particles and diagnosing machine troubles. This paper discusses fractal parameters of wear particles, presents arithmetic calculating fractal dimension, and constructs a fractal neural network which can recognize wear particles image. It is proved by experiments that this fractal neural network can recognize some characteristics of wear particles image, and can also classify wear types.

Instability mechanisms in microfluidics and nanomaterials

NASA Astrophysics Data System (ADS)

Thamida, Sunil Kumar

Recent scientific advances in chemical engineering are leading to synthesis of micro-scale and nano-scale functional devices and materials. However, optimal design and performance of these devices and materials requires a fundamental under standing of the interfacial phenomena at micro-scale and nano-scale. Due to new physical forces unique to small scales, new phenomena appear that are unexpected at large scales. A study of new interfacial patterns that arise from various interfacial instabilities at these scales is carried out in this dissertation. Nevertheless, interfacial patterns ranging from micro to macro scale are ubiquitous in multiphase systems and material synthesis involving a surface reaction. Fractal break up of a thin viscous oil film dewetting between two separating plates is studied experimentally. Unlike the classical patterns of pores and dendrites, it forms a fractal pattern like a branching tree with its origin at the center of the circular film. Lubrication theory is extended to such a fractal geometry, which is unlike the circular geometry of a classical dewetting problem. A power law scaling is obtained for the radial air finger length distribution to construct an idealized Cayley fractal structure. Our theory yields a result that the plate detach time decreases by half in the limit of a fully fractal pattern that is confirmed experimentally. Nanopore formation in anodized alumina is also found to bear similarities to the interfacial pattern formation of the dewetting film between two separating plates. The oxide layer formed on the aluminum during the initial stages of anodizing is found to be unstable to perturbations on the scale of a few nanometers and hence it leads to the nanopore formation. A linear stability analysis of the dual interfacial dynamics followed by a leading mode projection produces a single evolution equation for the pores. Numerical simulations of the nonlinear model reveals the hexagonal packing and self-organization dynamics of the pores. In microfluidic devices, electrokinetic flow produces spiral vortices and corner aggregation of particles and proteins at an inner corner of a channel turn that is unexplained by the short ranged DLVO forces. Field leakage effect due to the non perfectly insulating wall reveals a nonlinear singular and ejecting slip velocity condition at an acute angled sharp corner. The complete flow streamlines, vortices and the corner entrainment are revealed by conformal mapping, harmonic analysis and numerical simulation using Lattice-Boltzmann-Method (LBM). The method of hodograph transform developed for the earlier projects to solve the Laplace equation is also applied to find optimum shapes of dispersion free turns for electro-osmotic microfluidic channels.

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

Multifractal Modeling of Turbulent Mixing

NASA Astrophysics Data System (ADS)

Samiee, Mehdi; Zayernouri, Mohsen; Meerschaert, Mark M.

2017-11-01

Stochastic processes in random media are emerging as interesting tools for modeling anomalous transport phenomena. Applications include intermittent passive scalar transport with background noise in turbulent flows, which are observed in atmospheric boundary layers, turbulent mixing in reactive flows, and long-range dependent flow fields in disordered/fractal environments. In this work, we propose a nonlocal scalar transport equation involving the fractional Laplacian, where the corresponding fractional index is linked to the multifractal structure of the nonlinear passive scalar power spectrum. This work was supported by the AFOSR Young Investigator Program (YIP) award (FA9550-17-1-0150) and partially by MURI/ARO (W911NF-15-1-0562).

Screening effects in flow through rough channels.

PubMed

Andrade, J S; Araújo, A D; Filoche, M; Sapoval, B

2007-05-11

A surprising similarity is found between the distribution of hydrodynamic stress on the wall of an irregular channel and the distribution of flux from a purely Laplacian field on the same geometry. This finding is a direct outcome of numerical simulations of the Navier-Stokes equations for flow at low Reynolds numbers in two-dimensional channels with rough walls presenting either deterministic or random self-similar geometries. For high Reynolds numbers, the distribution of wall stresses on deterministic and random fractal rough channels becomes substantially dependent on the microscopic details of the walls geometry. Finally, the effects on the flow behavior of the channel symmetry and aspect ratio are also investigated.

Karst-on-a-chip: microfluidic studies of dissolution of a gypsum fracture

NASA Astrophysics Data System (ADS)

Szymczak, Piotr; Dutka, Filip; Osselin, Florian

2017-04-01

Dissolution of fractured and porous media introduces a positive feedback between fluid transport and chemical reactions at mineral surfaces leading to self-focusing of the flow in pronounced wormhole-like channels [1,2]. We study the flow-induced dissolution in a simple microfluidic setup, with a gypsum block inserted in between two polycarbonate plates, which is the simplest model of a fracture [3]. This gives us a unique opportunity to observe the evolution of the dissolution patterns in-situ and in real-time. By changing the flow rate and the aperture of the fracture we can scan a relatively wide range of Peclet and Damkohler numbers, characterizing the relative magnitude of advection, diffusion and reaction in the system. Additionally, as the aperture is increased, a transition is observed between the fractal and regular dissolution patterns. For small gaps, the patterns are ramified fractals. For larger gaps, the dissolution fingers are found to have regular forms of two different kinds: either linear (for high flow rates) or parabolic (for lower flow rates). The experiments are supplemented with numerical simulations and analytical modeling which allow for a better understanding of evolving flow patterns. In particular, we find the shapes and propagation velocities of dominant fingers for different widths of the system, flow rates and reaction rates. Finally, we comment on the link between the experimentally observed patterns and the natural karst systems - both cave conduits and epikarst solution pipes. [1] Hoefner, M. L. and Fogler, H. S. Pore evolution and channel formation during flow and reaction in porous media. AIChE J. 34, 45-54, 1988 [2] P. Szymczak, A. J. C. Ladd, Wormhole formation in dissolving fractures, J. Geophys. Res., 114, B06203, 2009 [3] F. Osselin, P. Kondratiuk, A Budek, O. Cybulski, P. Garstecki, P. Szymczak Microfluidic observation of the onset of reactive infiltration instability in an analog fracture, Geophys. Res. Lett., 43, 6907-6915, 2016

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.

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.

Anomalous behaviors during infiltration into heterogeneous porous media

NASA Astrophysics Data System (ADS)

Aarão Reis, F. D. A.; Bolster, D.; Voller, V. R.

2018-03-01

Flow and transport in heterogeneous porous media often exhibit anomalous behavior. A physical analog example is the uni-directional infiltration of a viscous liquid into a horizontal oriented Hele-Shaw cell containing through thickness flow obstacles; a system designed to mimic a gravel/sand medium with impervious inclusions. When there are no obstacles present or the obstacles form a multi-repeating pattern, the change of the length of infiltration F with time t tends to follow a Fickian like scaling, F ∼t1/2 . In the presence of obstacle fields laid out as Sierpinski carpet fractals, infiltration is anomalous, i.e., F ∼ tn, n ≠ 1/2. Here, we study infiltration into such Hele-Shaw cells. First we investigate infiltration into a square cell containing one fractal carpet and make the observation that it is possible to generate both sub (n < 1/2) and super (n > 1/2) diffusive behaviors within identical heterogeneity configurations. We show that this can be explained in terms of a scaling analysis developed from results of random-walk simulations in fractal obstacles; a result indicating that the nature of the domain boundary controls the exponent n of the resulting anomalous transport. Further, we investigate infiltration into a rectangular cell containing several repeats of a given Sierpinski carpet. At very early times, before the liquid encounters any obstacles, the infiltration is Fickian. When the liquid encounters the first (smallest scale) obstacle the infiltration sharply transitions to sub-diffusive. Subsequently, around the time where the liquid has sampled all of the heterogeneity length scales in the system, there is a rapid transition back to Fickian behavior. An explanation for this second transition is obtained by developing a simplified infiltration model based on the definition of a representative averaged hydraulic conductivity.

A dynamic subgrid-scale parameterization of the effective wall stress in atmospheric boundary layer flows over multiscale, fractal-like surfaces

NASA Astrophysics Data System (ADS)

Anderson, William; Meneveau, Charles

2010-05-01

A dynamic subgrid-scale (SGS) parameterization for hydrodynamic surface roughness is developed for large-eddy simulation (LES) of atmospheric boundary layer (ABL) flow over multiscale, fractal-like surfaces. The model consists of two parts. First, a baseline model represents surface roughness at horizontal length-scales that can be resolved in the LES. This model takes the form of a force using a prescribed drag coefficient. This approach is tested in LES of flow over cubes, wavy surfaces, and ellipsoidal roughness elements for which there are detailed experimental data available. Secondly, a dynamic roughness model is built, accounting for SGS surface details of finer resolution than the LES grid width. The SGS boundary condition is based on the logarithmic law of the wall, where the unresolved roughness of the surface is modeled as the product of local root-mean-square (RMS) of the unresolved surface height and an unknown dimensionless model coefficient. This coefficient is evaluated dynamically by comparing the plane-average hydrodynamic drag at two resolutions (grid- and test-filter scale, Germano et al., 1991). The new model is tested on surfaces generated through superposition of random-phase Fourier modes with prescribed, power-law surface-height spectra. The results show that the method yields convergent results and correct trends. Limitations and further challenges are highlighted. Supported by the US National Science Foundation (EAR-0609690).

A quasi-molecular dynamics simulation study on the effect of particles collisions in pulsed-laser desorption

NASA Astrophysics Data System (ADS)

Xinyu-Tan; Duanming-Zhang; Shengqin-Feng; Li, Zhi-hua; Li, Guan; Li, Li; Dan, Liu

2006-05-01

The dynamics characteristic and effect of atoms and particulates ejected from the surface generated by nanosecond pulsed-laser ablation are very important. In this work, based on the consideration of the inelasticity and non-uniformity of the plasma particles thermally desorbed from a plane surface into vacuum induced by nanosecond laser ablation, the one-dimensional particles flow is studied on the basis of a quasi-molecular dynamics (QMD) simulation. It is assumed that atoms and particulates ejected from the surface of a target have a Maxwell velocity distribution corresponding to the surface temperature. Particles collisions in the ablation plume. The particles mass is continuous and satisfies fractal theory distribution. Meanwhile, the particles are inelastic. Our results show that inelasticity and non-uniformity strongly affect the dynamics behavior of the particles flow. Along with the decrease of restitution coefficient e and increase of fractional dimension D, velocity distributions of plasma particles system all deviate from the initial Gaussian distribution. The increasing of dissipation energy ΔE leads to density distribution clusterized and closed up to the center mass. Predictions of the particles action based on the proposed fractal and inelasticity model are found to be in agreement with the experimental observation. This verifies the validity of the present model for the dynamics behavior of pulsed-laser-induced particles flow.

Freeze the Moment: High Speed Capturing of Weakly Bonded Dynamic Nanoparticle Assemblies in Solution by Ag Ion Soldering.

PubMed

Wang, Yueliang; Fang, Lingling; Chen, Gaoli; Song, Lei; Deng, Zhaoxiang

2018-02-01

Despite the versatile forms of colloidal aggregates, these spontaneously formed structures are often hard to find a suitable application in nanotechnology and materials science. A determinate reason is the lack of a suitable method to capture the transiently formed and quickly evolving colloidal structures in solution. To address this challenge, a simple but highly efficient strategy is herein reported to capture the dynamic and metastable colloidal assemblies formed in an aqueous or nonaqueous solution. This process takes advantage of a recently developed Ag ion soldering reaction to realize a rapid fixation of as-formed metastable assemblies. This method works efficiently for both solid (3D) nanoparticle aggregates and weakly bonded fractal nanoparticle chains (1D). In both cases, very high capturing speed and close to 100% efficiency are achieved to fully retain a quickly growing structure. The soldered nanochains further enable a fabrication of discrete, uniform, and functionalizable nanoparticle clusters with enriched linear conformation by mechanical shearing, which would otherwise be difficult to make. The captured products are water dispersible and mechanically robust, favoring an exploration of their properties toward possible applications. The work paves a way to previously untouched aspects of colloidal science and thus would create new chances in nanotechnology. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Landsat 7 Reveals Large-scale Fractal Motion of Clouds

NASA Technical Reports Server (NTRS)

2002-01-01

This Landsat 7 image of clouds off the Chilean coast near the Juan Fernandez Islands (also known as the Robinson Crusoe Islands) on September 15, 1999, shows a unique pattern called a 'von Karman vortex street.' This pattern has long been studied in the laboratory, where the vortices are created by oil flowing past a cylindrical obstacle, making a string of vortices only several tens of centimeters long. Study of this classic 'flow past a circular cylinder' has been very important in the understanding of laminar and turbulent fluid flow that controls a wide variety of phenomena, from the lift under an aircraft wing to Earth's weather. Here, the cylinder is replaced by Alejandro Selkirk Island (named after the true 'Robinson Crusoe,' who was stranded here for many months in the early 1700s). The island is about 1.5 km in diameter, and rises 1.6 km into a layer of marine stratocumulus clouds. This type of cloud is important for its strong cooling of the Earth's surface, partially counteracting the Greenhouse warming. An extended, steady equatorward wind creates vortices with clockwise flow off the eastern edge and counterclockwise flow off the western edge of the island. The vortices grow as they advect hundreds of kilometers downwind, making a street 10,000 times longer than those made in the laboratory. Observing the same phenomenon extended over such a wide range of sizes dramatizes the 'fractal' nature of atmospheric convection and clouds. Fractals are characteristic of fluid flow and other dynamic systems that exhibit 'chaotic' motions. Both clockwise and counter-clockwise vortices are generated by flow around the island. As the flow separates from the island's leeward (away from the source of the wind) side, the vortices 'swallow' some of the clear air over the island. (Much of the island air is cloudless due to a local 'land breeze' circulation set up by the larger heat capacity of the waters surrounding the island.) The 'swallowed' gulps of clear island air get carried along within the vortices, but these are soon mixed into the surrounding clouds. Landsat is unique in its ability to image both the small-scale eddies that mix clear and cloudy air, down to the 30 meter pixel size of Landsat, but also having a wide enough field-of-view, 180 km, to reveal the connection of the turbulence to large-scale flows such as the subtropical oceanic gyres. Landsat 7, with its new onboard digital recorder, has extended this capability away from the few Landsat ground stations to remote areas such as Alejandro Island, and thus is gradually providing a global dynamic picture of evolving human-scale phenomena. (For more details on von Karman vortices, refer to http://climate.gsfc.nasa.gov/cahalan) Image and caption courtesy Bob Cahalan, NASA GSFC

Fractal scaling analysis of groundwater dynamics in confined aquifers

NASA Astrophysics Data System (ADS)

Tu, Tongbi; Ercan, Ali; Kavvas, M. Levent

2017-10-01

Groundwater closely interacts with surface water and even climate systems in most hydroclimatic settings. Fractal scaling analysis of groundwater dynamics is of significance in modeling hydrological processes by considering potential temporal long-range dependence and scaling crossovers in the groundwater level fluctuations. In this study, it is demonstrated that the groundwater level fluctuations in confined aquifer wells with long observations exhibit site-specific fractal scaling behavior. Detrended fluctuation analysis (DFA) was utilized to quantify the monofractality, and multifractal detrended fluctuation analysis (MF-DFA) and multiscale multifractal analysis (MMA) were employed to examine the multifractal behavior. The DFA results indicated that fractals exist in groundwater level time series, and it was shown that the estimated Hurst exponent is closely dependent on the length and specific time interval of the time series. The MF-DFA and MMA analyses showed that different levels of multifractality exist, which may be partially due to a broad probability density distribution with infinite moments. Furthermore, it is demonstrated that the underlying distribution of groundwater level fluctuations exhibits either non-Gaussian characteristics, which may be fitted by the Lévy stable distribution, or Gaussian characteristics depending on the site characteristics. However, fractional Brownian motion (fBm), which has been identified as an appropriate model to characterize groundwater level fluctuation, is Gaussian with finite moments. Therefore, fBm may be inadequate for the description of physical processes with infinite moments, such as the groundwater level fluctuations in this study. It is concluded that there is a need for generalized governing equations of groundwater flow processes that can model both the long-memory behavior and the Brownian finite-memory behavior.

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.

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.

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.

Chaotic flows and fast magnetic dynamos

NASA Technical Reports Server (NTRS)

Finn, John M.; Ott, Edward

1988-01-01

The kinematic dynamo problem is considered in the R(m) approaching infinity limit. It is shown that the magnetic field tends to concentrate on a zero volume fractal set; moreover, it displays arbitrarily fine-scaled oscillations between parallel and antiparallel directions. Consideration is given to the relationship between the dynamo growth rate and quantitative measures of chaos, such as the Liapunov element and topological entropy.

Transition to chaos in an open unforced 2D flow

NASA Technical Reports Server (NTRS)

Pulliam, Thomas H.; Vastano, John A.

1993-01-01

The present numerical study of unsteady, low Reynolds number flow past a 2D airfoil attempts to ascertain the bifurcation sequence leading from simple periodic to complex aperiodic flow with rising Reynolds number, as well as to characterize the degree of chaos present in the aperiodic flow and assess the role of numerics in the modification and control of the observed bifurcation scenario. The ARC2D Navier-Stokes code is used in an unsteady time-accurate mode for most of these computations. The system undergoes a period-doubling bifurcation to chaos as the Reynolds number is increased from 800 to 1600; its chaotic attractors are characterized by estimates of the fractal dimension and partial Liapunov exponent spectra.

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…

Fractal nematic colloids

PubMed Central

Hashemi, S. M.; Jagodič, U.; Mozaffari, M. R.; Ejtehadi, M. R.; Muševič, I.; Ravnik, M.

2017-01-01

Fractals are remarkable examples of self-similarity where a structure or dynamic pattern is repeated over multiple spatial or time scales. However, little is known about how fractal stimuli such as fractal surfaces interact with their local environment if it exhibits order. Here we show geometry-induced formation of fractal defect states in Koch nematic colloids, exhibiting fractal self-similarity better than 90% over three orders of magnitude in the length scales, from micrometers to nanometres. We produce polymer Koch-shaped hollow colloidal prisms of three successive fractal iterations by direct laser writing, and characterize their coupling with the nematic by polarization microscopy and numerical modelling. Explicit generation of topological defect pairs is found, with the number of defects following exponential-law dependence and reaching few 100 already at fractal iteration four. This work demonstrates a route for generation of fractal topological defect states in responsive soft matter. PMID:28117325

Hierarchical socioeconomic fractality: The rich, the poor, and the middle-class

NASA Astrophysics Data System (ADS)

Eliazar, Iddo; Cohen, Morrel H.

2014-05-01

Since the seminal work of the Italian economist Vilfredo Pareto, the study of wealth and income has been a topic of active scientific exploration engaging researches ranging from economics and political science to econophysics and complex systems. This paper investigates the intrinsic fractality of wealth and income. To that end we introduce and characterize three forms of socioeconomic scale-invariance-poor fractality, rich fractality, and middle-class fractality-and construct hierarchical fractal approximations of general wealth and income distributions, based on the stitching of these three forms of fractality. Intertwining the theoretical results with real-world empirical data we then establish that the three forms of socioeconomic fractality-amalgamated into a composite hierarchical structure-underlie the distributions of wealth and income in human societies. We further establish that the hierarchical socioeconomic fractality of wealth and income is also displayed by empirical rank distributions observed across the sciences.

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.

Hydrodynamic Capture and Release of Passively Driven Particles by Active Particles Under Hele-Shaw Flows

NASA Astrophysics Data System (ADS)

Mishler, Grant; Tsang, Alan Cheng Hou; Pak, On Shun

2018-03-01

The transport of active and passive particles plays central roles in diverse biological phenomena and engineering applications. In this paper, we present a theoretical investigation of a system consisting of an active particle and a passive particle in a confined micro-fluidic flow. The introduction of an external flow is found to induce the capture of the passive particle by the active particle via long-range hydrodynamic interactions among the particles. This hydrodynamic capture mechanism relies on an attracting stable equilibrium configuration formed by the particles, which occurs when the external flow intensity exceeds a certain threshold. We evaluate this threshold by studying the stability of the equilibrium configurations analytically and numerically. Furthermore, we study the dynamics of typical capture and non-capture events and characterize the basins of attraction of the equilibrium configurations. Our findings reveal a critical dependence of the hydrodynamic capture mechanism on the external flow intensity. Through adjusting the external flow intensity across the stability threshold, we demonstrate that the active particle can capture and release the passive particle in a controllable manner. Such a capture-and-release mechanism is desirable for biomedical applications such as the capture and release of therapeutic payloads by synthetic micro-swimmers in targeted drug delivery.

Fractally Fourier decimated homogeneous turbulent shear flow in noninteger dimensions.

PubMed

Fathali, Mani; Khoei, Saber

2017-02-01

Time evolution of the fully resolved incompressible homogeneous turbulent shear flow in noninteger Fourier dimensions is numerically investigated. The Fourier dimension of the flow field is extended from the integer value 3 to the noninteger values by projecting the Navier-Stokes equation on the fractal set of the active Fourier modes with dimensions 2.7≤d≤3.0. The results of this study revealed that the dynamics of both large and small scale structures are nontrivially influenced by changing the Fourier dimension d. While both turbulent production and dissipation are significantly hampered as d decreases, the evolution of their ratio is almost independent of the Fourier dimension. The mechanism of the energy distribution among different spatial directions is also impeded by decreasing d. Due to this deficient energy distribution, turbulent field shows a higher level of the large-scale anisotropy in lower Fourier dimensions. In addition, the persistence of the vortex stretching mechanism and the forward spectral energy transfer, which are three-dimensional turbulence characteristics, are examined at changing d, from the standard case d=3.0 to the strongly decimated flow field for d=2.7. As the Fourier dimension decreases, these forward energy transfer mechanisms are strongly suppressed, which in turn reduces both the small-scale intermittency and the deviation from Gaussianity. Besides the energy exchange intensity, the variations of d considerably modify the relative weights of local to nonlocal triadic interactions. It is found that the contribution of the nonlocal triads to the total turbulent kinetic energy exchange increases as the Fourier dimension increases.

Identification of varying time scales in sediment transport using the Hilbert-Huang Transform method

NASA Astrophysics Data System (ADS)

Kuai, Ken Z.; Tsai, Christina W.

2012-02-01

SummarySediment transport processes vary at a variety of time scales - from seconds, hours, days to months and years. Multiple time scales exist in the system of flow, sediment transport and bed elevation change processes. As such, identification and selection of appropriate time scales for flow and sediment processes can assist in formulating a system of flow and sediment governing equations representative of the dynamic interaction of flow and particles at the desired details. Recognizing the importance of different varying time scales in the fluvial processes of sediment transport, we introduce the Hilbert-Huang Transform method (HHT) to the field of sediment transport for the time scale analysis. The HHT uses the Empirical Mode Decomposition (EMD) method to decompose a time series into a collection of the Intrinsic Mode Functions (IMFs), and uses the Hilbert Spectral Analysis (HSA) to obtain instantaneous frequency data. The EMD extracts the variability of data with different time scales, and improves the analysis of data series. The HSA can display the succession of time varying time scales, which cannot be captured by the often-used Fast Fourier Transform (FFT) method. This study is one of the earlier attempts to introduce the state-of-the-art technique for the multiple time sales analysis of sediment transport processes. Three practical applications of the HHT method for data analysis of both suspended sediment and bedload transport time series are presented. The analysis results show the strong impact of flood waves on the variations of flow and sediment time scales at a large sampling time scale, as well as the impact of flow turbulence on those time scales at a smaller sampling time scale. Our analysis reveals that the existence of multiple time scales in sediment transport processes may be attributed to the fractal nature in sediment transport. It can be demonstrated by the HHT analysis that the bedload motion time scale is better represented by the ratio of the water depth to the settling velocity, h/ w. In the final part, HHT results are compared with an available time scale formula in literature.

Modeling and Measurements of Multiphase Flow and Bubble Entrapment in Steel Continuous Casting

NASA Astrophysics Data System (ADS)

Jin, Kai; Thomas, Brian G.; Ruan, Xiaoming

2016-02-01

In steel continuous casting, argon gas is usually injected to prevent clogging, but the bubbles also affect the flow pattern, and may become entrapped to form defects in the final product. To investigate this behavior, plant measurements were conducted, and a computational model was applied to simulate turbulent flow of the molten steel and the transport and capture of argon gas bubbles into the solidifying shell in a continuous slab caster. First, the flow field was solved with an Eulerian k- ɛ model of the steel, which was two-way coupled with a Lagrangian model of the large bubbles using a discrete random walk method to simulate their turbulent dispersion. The flow predicted on the top surface agreed well with nailboard measurements and indicated strong cross flow caused by biased flow of Ar gas due to the slide-gate orientation. Then, the trajectories and capture of over two million bubbles (25 μm to 5 mm diameter range) were simulated using two different capture criteria (simple and advanced). Results with the advanced capture criterion agreed well with measurements of the number, locations, and sizes of captured bubbles, especially for larger bubbles. The relative capture fraction of 0.3 pct was close to the measured 0.4 pct for 1 mm bubbles and occurred mainly near the top surface. About 85 pct of smaller bubbles were captured, mostly deeper down in the caster. Due to the biased flow, more bubbles were captured on the inner radius, especially near the nozzle. On the outer radius, more bubbles were captured near to narrow face. The model presented here is an efficient tool to study the capture of bubbles and inclusion particles in solidification processes.

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.

Fractal-Based Image Analysis In Radiological Applications

NASA Astrophysics Data System (ADS)

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

1987-10-01

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

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

Fractal Bread.

ERIC Educational Resources Information Center

Esbenshade, Donald H., Jr.

1991-01-01

Develops the idea of fractals through a laboratory activity that calculates the fractal dimension of ordinary white bread. Extends use of the fractal dimension to compare other complex structures as other breads and sponges. (MDH)

Fractal free energy landscapes in structural glasses.

PubMed

Charbonneau, Patrick; Kurchan, Jorge; Parisi, Giorgio; Urbani, Pierfrancesco; Zamponi, Francesco

2014-04-24

Glasses are amorphous solids whose constituent particles are caged by their neighbours and thus cannot flow. This sluggishness is often ascribed to the free energy landscape containing multiple minima (basins) separated by high barriers. Here we show, using theory and numerical simulation, that the landscape is much rougher than is classically assumed. Deep in the glass, it undergoes a 'roughness transition' to fractal basins, which brings about isostaticity and marginal stability on approaching jamming. Critical exponents for the basin width, the weak force distribution and the spatial spread of quasi-contacts near jamming can be analytically determined. Their value is found to be compatible with numerical observations. This advance incorporates the jamming transition of granular materials into the framework of glass theory. Because temperature and pressure control what features of the landscape are experienced, glass mechanics and transport are expected to reflect the features of the topology we discuss here.

Time scale defined by the fractal structure of the price fluctuations in foreign exchange markets

NASA Astrophysics Data System (ADS)

Kumagai, Yoshiaki

2010-04-01

In this contribution, a new time scale named C-fluctuation time is defined by price fluctuations observed at a given resolution. The intraday fractal structures and the relations of the three time scales: real time (physical time), tick time and C-fluctuation time, in foreign exchange markets are analyzed. The data set used is trading prices of foreign exchange rates; US dollar (USD)/Japanese yen (JPY), USD/Euro (EUR), and EUR/JPY. The accuracy of the data is one minute and data within a minute are recorded in order of transaction. The series of instantaneous velocity of C-fluctuation time flowing are exponentially distributed for small C when they are measured by real time and for tiny C when they are measured by tick time. When the market is volatile, for larger C, the series of instantaneous velocity are exponentially distributed.

Band structures in fractal grading porous phononic crystals

NASA Astrophysics Data System (ADS)

Wang, Kai; Liu, Ying; Liang, Tianshu; Wang, Bin

2018-05-01

In this paper, a new grading porous structure is introduced based on a Sierpinski triangle routine, and wave propagation in this fractal grading porous phononic crystal is investigated. The influences of fractal hierarchy and porosity on the band structures in fractal graidng porous phononic crystals are clarified. Vibration modes of unit cell at absolute band gap edges are given to manifest formation mechanism of absolute band gaps. The results show that absolute band gaps are easy to form in fractal structures comparatively to the normal ones with the same porosity. Structures with higher fractal hierarchies benefit multiple wider absolute band gaps. This work provides useful guidance in design of fractal porous phononic crystals.

Fractals in geology and geophysics

NASA Technical Reports Server (NTRS)

Turcotte, Donald L.

1989-01-01

The definition of a fractal distribution is that the number of objects N with a characteristic size greater than r scales with the relation N of about r exp -D. The frequency-size distributions for islands, earthquakes, fragments, ore deposits, and oil fields often satisfy this relation. This application illustrates a fundamental aspect of fractal distributions, scale invariance. The requirement of an object to define a scale in photograhs of many geological features is one indication of the wide applicability of scale invariance to geological problems; scale invariance can lead to fractal clustering. Geophysical spectra can also be related to fractals; these are self-affine fractals rather than self-similar fractals. Examples include the earth's topography and geoid.

Comparison of two fractal interpolation methods

NASA Astrophysics Data System (ADS)

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

2017-03-01

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

Applications and Implications of Fractional Dynamics for Dielectric Relaxation

NASA Astrophysics Data System (ADS)

Hilfer, R.

This article summarizes briefly the presentation given by the author at the NATO Advanced Research Workshop on "Broadband Dielectric Spectroscopy and its Advanced Technological Applications", held in Perpignan, France, in September 2011. The purpose of the invited presentation at the workshop was to review and summarize the basic theory of fractional dynamics (Hilfer, Phys Rev E 48:2466, 1993; Hilfer and Anton, Phys Rev E Rapid Commun 51:R848, 1995; Hilfer, Fractals 3(1):211, 1995; Hilfer, Chaos Solitons Fractals 5:1475, 1995; Hilfer, Fractals 3:549, 1995; Hilfer, Physica A 221:89, 1995; Hilfer, On fractional diffusion and its relation with continuous time random walks. In: Pekalski et al. (eds) Anomalous diffusion: from basis to applications. Springer, Berlin, p 77, 1999; Hilfer, Fractional evolution equations and irreversibility. In: Helbing et al. (eds) Traffic and granular flow'99. Springer, Berlin, p 215, 2000; Hilfer, Fractional time evolution. In: Hilfer (ed) Applications of fractional calculus in physics. World Scientific, Singapore, p 87, 2000; Hilfer, Remarks on fractional time. In: Castell and Ischebeck (eds) Time, quantum and information. Springer, Berlin, p 235, 2003; Hilfer, Physica A 329:35, 2003; Hilfer, Threefold introduction to fractional derivatives. In: Klages et al. (eds) Anomalous transport: foundations and applications. Wiley-VCH, Weinheim, pp 17-74, 2008; Hilfer, Foundations of fractional dynamics: a short account. In: Klafter et al. (eds) Fractional dynamics: recent advances. World Scientific, Singapore, p 207, 2011) and demonstrate its relevance and application to broadband dielectric spectroscopy (Hilfer, J Phys Condens Matter 14:2297, 2002; Hilfer, Chem Phys 284:399, 2002; Hilfer, Fractals 11:251, 2003; Hilfer et al., Fractional Calc Appl Anal 12:299, 2009). It was argued, that broadband dielectric spectroscopy might be useful to test effective field theories based on fractional dynamics.

Hydrodynamic Capture of Particles by Micro-swimmers under Hele-Shaw Flows

NASA Astrophysics Data System (ADS)

Mishler, Grant; Tsang, Alan Cheng Hou; Pak, On Shun

2017-11-01

We explore a hydrodynamic capture mechanism of a driven particle by a micro-swimmer in confined microfluidic environments with an idealized model. The capture is mediated by the hydrodynamic interactions between the micro-swimmer, the driven particle, and the background flow. This capture mechanism relies on the existence of attractive stable equilibrium configurations between the driven particle and the micro-swimmer, which occurs when the background flow is larger than a certain critical threshold. Dynamics and stability of capture and non-capture events will be discussed. This study may have potential applications in the study of capture and delivery of therapeutic payloads by micro-swimmers as well as particle self-assembly under confinements.

Order-fractal transitions in abstract paintings

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

Calleja, E.M. de la, E-mail: elsama79@gmail.com; Cervantes, F.; Calleja, J. de la

2016-08-15

In this study, we determined the degree of order for 22 Jackson Pollock paintings using the Hausdorff–Besicovitch fractal dimension. Based on the maximum value of each multi-fractal spectrum, the artworks were classified according to the year in which they were painted. It has been reported that Pollock’s paintings are fractal and that this feature was more evident in his later works. However, our results show that the fractal dimension of these paintings ranges among values close to two. We characterize this behavior as a fractal-order transition. Based on the study of disorder-order transition in physical systems, we interpreted the fractal-ordermore » transition via the dark paint strokes in Pollock’s paintings as structured lines that follow a power law measured by the fractal dimension. We determined self-similarity in specific paintings, thereby demonstrating an important dependence on the scale of observations. We also characterized the fractal spectrum for the painting entitled Teri’s Find. We obtained similar spectra for Teri’s Find and Number 5, thereby suggesting that the fractal dimension cannot be rejected completely as a quantitative parameter for authenticating these artworks. -- Highlights: •We determined the degree of order in Jackson Pollock paintings using the Hausdorff–Besicovitch dimension. •We detected a fractal-order transition from Pollock’s paintings between 1947 and 1951. •We suggest that Jackson Pollock could have painted Teri’s Find.« less

[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.

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.

Exploring fractal behaviour of blood oxygen saturation in preterm babies

NASA Astrophysics Data System (ADS)

Zahari, Marina; Hui, Tan Xin; Zainuri, Nuryazmin Ahmat; Darlow, Brian A.

2017-04-01

Recent evidence has been emerging that oxygenation instability in preterm babies could lead to an increased risk of retinal injury such as retinopathy of prematurity. There is a potential that disease severity could be better understood using nonlinear methods for time series data such as fractal theories [1]. Theories on fractal behaviours have been employed by researchers in various disciplines who were motivated to look into the behaviour or structure of irregular fluctuations in temporal data. In this study, an investigation was carried out to examine whether fractal behaviour could be detected in blood oxygen time series. Detection for the presence of fractals in oxygen data of preterm infants was performed using the methods of power spectrum, empirical probability distribution function and autocorrelation function. The results from these fractal identification methods indicate the possibility that these data exhibit fractal nature. Subsequently, a fractal framework for future research was suggested for oxygen time series.

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Roughness Perception of Haptically Displayed Fractal Surfaces

NASA Technical Reports Server (NTRS)

Costa, Michael A.; Cutkosky, Mark R.; Lau, Sonie (Technical Monitor)

2000-01-01

Surface profiles were generated by a fractal algorithm and haptically rendered on a force feedback joystick, Subjects were asked to use the joystick to explore pairs of surfaces and report to the experimenter which of the surfaces they felt was rougher. Surfaces were characterized by their root mean square (RMS) amplitude and their fractal dimension. The most important factor affecting the perceived roughness of the fractal surfaces was the RMS amplitude of the surface. When comparing surfaces of fractal dimension 1.2-1.35 it was found that the fractal dimension was negatively correlated with perceived roughness.

A fractal growth model: Exploring the connection pattern of hubs in complex networks

NASA Astrophysics Data System (ADS)

Li, Dongyan; Wang, Xingyuan; Huang, Penghe

2017-04-01

Fractal is ubiquitous in many real-world networks. Previous researches showed that the strong disassortativity between the hub-nodes on all length scales was the key principle that gave rise to the fractal architecture of networks. Although fractal property emerged in some models, there were few researches about the fractal growth model and quantitative analyses about the strength of the disassortativity for fractal model. In this paper, we proposed a novel inverse renormalization method, named Box-based Preferential Attachment (BPA), to build the fractal growth models in which the Preferential Attachment was performed at box level. The proposed models provided a new framework that demonstrated small-world-fractal transition. Also, we firstly demonstrated the statistical characteristic of connection patterns of the hubs in fractal networks. The experimental results showed that, given proper growing scale and added edges, the proposed models could clearly show pure small-world or pure fractal or both of them. It also showed that the hub connection ratio showed normal distribution in many real-world networks. At last, the comparisons of connection pattern between the proposed models and the biological and technical networks were performed. The results gave useful reference for exploring the growth principle and for modeling the connection patterns for real-world networks.

Assessment of the spatial pattern of colorectal tumour perfusion estimated at perfusion CT using two-dimensional fractal analysis.

PubMed

Goh, Vicky; Sanghera, Bal; Wellsted, David M; Sundin, Josefin; Halligan, Steve

2009-06-01

The aim was to evaluate the feasibility of fractal analysis for assessing the spatial pattern of colorectal tumour perfusion at dynamic contrast-enhanced CT (perfusion CT). Twenty patients with colorectal adenocarcinoma underwent a 65-s perfusion CT study from which a perfusion parametric map was generated using validated commercial software. The tumour was identified by an experienced radiologist, segmented via thresholding and fractal analysis applied using in-house software: fractal dimension, abundance and lacunarity were assessed for the entire outlined tumour and for selected representative areas within the tumour of low and high perfusion. Comparison was made with ten patients with normal colons, processed in a similar manner, using two-way mixed analysis of variance with statistical significance at the 5% level. Fractal values were higher in cancer than normal colon (p < or = 0.001): mean (SD) 1.71 (0.07) versus 1.61 (0.07) for fractal dimension and 7.82 (0.62) and 6.89 (0.47) for fractal abundance. Fractal values were lower in 'high' than 'low' perfusion areas. Lacunarity curves were shifted to the right for cancer compared with normal colon. In conclusion, colorectal cancer mapped by perfusion CT demonstrates fractal properties. Fractal analysis is feasible, potentially providing a quantitative measure of the spatial pattern of tumour perfusion.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

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

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

NASA Technical Reports Server (NTRS)

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

1993-01-01

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

Iris Recognition Using Feature Extraction of Box Counting Fractal Dimension

NASA Astrophysics Data System (ADS)

Khotimah, C.; Juniati, D.

2018-01-01

Biometrics is a science that is now growing rapidly. Iris recognition is a biometric modality which captures a photo of the eye pattern. The markings of the iris are distinctive that it has been proposed to use as a means of identification, instead of fingerprints. Iris recognition was chosen for identification in this research because every human has a special feature that each individual is different and the iris is protected by the cornea so that it will have a fixed shape. This iris recognition consists of three step: pre-processing of data, feature extraction, and feature matching. Hough transformation is used in the process of pre-processing to locate the iris area and Daugman’s rubber sheet model to normalize the iris data set into rectangular blocks. To find the characteristics of the iris, it was used box counting method to get the fractal dimension value of the iris. Tests carried out by used k-fold cross method with k = 5. In each test used 10 different grade K of K-Nearest Neighbor (KNN). The result of iris recognition was obtained with the best accuracy was 92,63 % for K = 3 value on K-Nearest Neighbor (KNN) method.

Computerized morphometry as an aid in distinguishing recurrent versus nonrecurrent meningiomas.

PubMed

Noy, Shawna; Vlodavsky, Euvgeni; Klorin, Geula; Drumea, Karen; Ben Izhak, Ofer; Shor, Eli; Sabo, Edmond

2011-06-01

To use novel digital and morphometric methods to identify variables able to better predict the recurrence of intracranial meningiomas. Histologic images from 30 previously diagnosed meningioma tumors that recurred over 10 years of follow-up were consecutively selected from the Rambam Pathology Archives. Images were captured and morphometrically analyzed. Novel algorithms of digital pattern recognition using Fourier transformation and fractal and nuclear texture analyses were applied to evaluate the overall growth pattern complexity of the tumors, as well as the chromatin texture of individual tumor nuclei. The extracted parameters were then correlated with patient prognosis. Kaplan-Meier analyses revealed statistically significant associations between tumor morphometric parameters and recurrence times. Tumors with less nuclear orientation, more nuclear density, higher fractal dimension, and less regular chromatin textures tended to recur faster than those with a higher degree of nuclear order, less pattern complexity, lower density, and more homogeneous chromatin nuclear textures (p < 0.01). To our knowledge, these digital morphometric methods were used for the first time to accurately predict tumor recurrence in patients with intracranial meningiomas. The use of these methods may bring additional valuable information to the clinician regarding the optimal management of these patients.

Extremes and bursts in complex multi-scale plasmas

NASA Astrophysics Data System (ADS)

Watkins, N. W.; Chapman, S. C.; Hnat, B.

2012-04-01

Quantifying the spectrum of sizes and durations of large and/or long-lived fluctuations in complex, multi-scale, space plasmas is a topic of both theoretical and practical importance. The predictions of inherently multi-scale physical theories such as MHD turbulence have given one direct stimulus for its investigation. There are also space weather implications to an improved ability to assess the likelihood of an extreme fluctuation of a given size. Our intuition as scientists tends to be formed on the familiar Gaussian "normal" distribution, which has a very low likelihood of extreme fluctuations. Perhaps surprisingly, there is both theoretical and observational evidence that favours non-Gaussian, heavier-tailed, probability distributions for some space physics datasets. Additionally there is evidence for the existence of long-ranged memory between the values of fluctuations. In this talk I will show how such properties can be captured in a preliminary way by a self-similar, fractal model. I will show how such a fractal model can be used to make predictions for experimental accessible quantities like the size and duration of a buurst (a sequence of values that exceed a given threshold), or the survival probability of a burst [c.f. preliminary results in Watkins et al, PRE, 2009]. In real-world time series scaling behaviour need not be "mild" enough to be captured by a single self-similarity exponent H, but might instead require a "wild" multifractal spectrum of scaling exponents [e.g. Rypdal and Rypdal, JGR, 2011; Moloney and Davidsen, JGR, 2011] to give a complete description. I will discuss preliminary work on extending the burst approach into the multifractal domain [see also Watkins et al, chapter in press for AGU Chapman Conference on Complexity and Extreme Events in the Geosciences, Hyderabad].

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 process of hydrogen diffusion in a-Si:H with exponential energy distribution

NASA Astrophysics Data System (ADS)

Hikita, Harumi; Ishikawa, Hirohisa; Morigaki, Kazuo

2017-04-01

Hydrogen diffusion in a-Si:H with exponential distribution of the states in energy exhibits the fractal structure. It is shown that a probability P(t) of the pausing time t has a form of tα (α: fractal dimension). It is shown that the fractal dimension α = Tr/T0 (Tr: hydrogen temperature, T0: a temperature corresponding to the width of exponential distribution of the states in energy) is in agreement with the Hausdorff dimension. A fractal graph for the case of α ≤ 1 is like the Cantor set. A fractal graph for the case of α > 1 is like the Koch curves. At α = ∞, hydrogen migration exhibits Brownian motion. Hydrogen diffusion in a-Si:H should be the fractal process.

[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.

Description and application of capture zone delineation for a wellfield at Hilton Head Island, South Carolina

USGS Publications Warehouse

Landmeyer, J.E.

1994-01-01

Ground-water capture zone boundaries for individual pumped wells in a confined aquffer were delineated by using groundwater models. Both analytical and numerical (semi-analytical) models that more accurately represent the $round-water-flow system were used. All models delineated 2-dimensional boundaries (capture zones) that represent the areal extent of groundwater contribution to a pumped well. The resultant capture zones were evaluated on the basis of the ability of each model to realistically rapresent the part of the ground-water-flow system that contributed water to the pumped wells. Analytical models used were based on a fixed radius approach, and induded; an arbitrary radius model, a calculated fixed radius model based on the volumetric-flow equation with a time-of-travel criterion, and a calculated fixed radius model derived from modification of the Theis model with a drawdown criterion. Numerical models used induded the 2-dimensional, finite-difference models RESSQC and MWCAP. The arbitrary radius and Theis analytical models delineated capture zone boundaries that compared least favorably with capture zones delineated using the volumetric-flow analytical model and both numerical models. The numerical models produced more hydrologically reasonable capture zones (that were oriented parallel to the regional flow direction) than the volumetric-flow equation. The RESSQC numerical model computed more hydrologically realistic capture zones than the MWCAP numerical model by accounting for changes in the shape of capture zones caused by multiple-well interference. The capture zone boundaries generated by using both analytical and numerical models indicated that the curnmtly used 100-foot radius of protection around a wellhead in South Carolina is an underestimate of the extent of ground-water capture for pumped wetis in this particular wellfield in the Upper Floridan aquifer. The arbitrary fixed radius of 100 feet was shown to underestimate the upgradient contribution of ground-water flow to a pumped well.

Scaling of Ln(Permeability) in Sediments and Velocity Distributions in Turbulence: The Possibility of an Analogy.

NASA Astrophysics Data System (ADS)

Molz, F. J.; Kozubowski, T. J.; Miller, R. S.; Podgorski, K.

2005-12-01

The theory of non-stationary stochastic processes with stationary increments gives rise to stochastic fractals. When such fractals are used to represent measurements of (assumed stationary) physical properties, such as ln(k) increments in sediments or velocity increments "delta(v)" in turbulent flows, the resulting measurements exhibit scaling, either spatial, temporal or both. (In the present context, such scaling refers to systematic changes in the statistical properties of the increment distributions, such as variance, with the lag size over which the increments are determined.) Depending on the class of probability density functions (PDFs) that describe the increment distributions, the resulting stochastic fractals will display different properties. Until recently, the stationary increment process was represented using mainly Gaussian, Gamma or Levy PDFs. However, measurements in both sediments and fluid turbulence indicate that these PDFs are not commonly observed. Based on recent data and previous studies referenced and discussed in Meerschaert et al. (2004) and Molz et al. (2005), the measured increment PDFs display an approximate double exponential (Laplace) shape at smaller lags, and this shape evolves towards Gaussian at larger lags. A model for this behavior based on the Generalized Laplace PDF family called fractional Laplace motion, in analogy with its Gaussian counterpart - fractional Brownian motion, has been suggested (Meerschaert et al., 2004) and the necessary mathematics elaborated (Kozubowski et al., 2005). The resulting stochastic fractal is not a typical self-affine monofractal, but it does exhibit monofractal-like scaling in certain lag size ranges. To date, it has been shown that the Generalized Laplace family fits ln(k) increment distributions and reproduces the original 1941 theory of Kolmogorov when applied to Eulerian turbulent velocity increments. However, to make a physically self-consistent application to turbulence, one must adopt a Lagrangian viewpoint, and the details of this approach are still being developed. The potential analogy between turbulent delta(v) and sediment delta[ln(k)] is intriguing, and perhaps offers insight into the underlying chaotic processes that constitute turbulence and may result also in the pervasive heterogeneity observed in most natural sediments. Properties of the new Laplace fractal are presented, and potential applications to both sediments and fluid turbulence are discussed.

Exposure of chick embryos to cadmium changes the extra-embryonic vascular branching pattern and alters expression of VEGF-A and VEGF-R2

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

Gheorghescu, Anna Kaskova; Tywoniuk, Bartlomiej; Complex and Adaptive Systems Laboratory, University College Dublin, Belfield, Dublin 4

Cadmium (Cd) has several industrial applications, and is found in tobacco products, a notable source of human exposure. Vascular endothelial cells are key targets of Cd toxicity. Here, we aim to quantify the alteration to vascular branching pattern following Cd exposure in the chick extra-embryonic membrane (EEM) using fractal analysis, and explore molecular cues to angiogenesis such as VEGF-A and VEGF-R2 expression following Cd treatment. Chicken embryos were incubated for 60 h to Hamburger–Hamilton developmental stage 16–17, then explanted and treated with 50 μL of 50 μmol cadmium acetate (CdAc) or an equivalent volume of equimolar sodium acetate (NaAc). Imagesmore » of embryos and their area vasculosa (AV) were captured and analyzed at 4 different time points (4, 8, 24 and 48 h) following treatment. Vascular branching in the AV was quantified using its fractal dimension (D{sub f}), estimated using a box counting method. Gallinaceous VEGF ELISA was used to measure the VEGF-A concentration in the EEM following treatment, with determination of the relative expression of VEGF-A and VEGF-R2 using quantitative real-time RT-PCR. Vascular branching increased monotonically in the control group at all time points. The anti-angiogenic effect of Cd exposure on the AV was reflected by a significant reduction in D{sub f} when compared with controls. D{sub f} was more markedly reduced in cultures with abnormal embryos. The expression of VEGF-A protein, and VEGF-A and VEGF-R2 mRNA were reduced in Cd-exposed EEMs. Both molecules contribute to growth, vessel sprouting and branching processes, which supports our findings using fractal analysis. - Highlights: • The chick area vasculosa was undersized in embryos exposed to 50 μM cadmium acetate. • Fractal dimension was reduced in the AV after Cd exposure, indicating decreased branching. • VEGF-A protein was decreased in Cd-treated extraembryonic membranes. • VEGF-A and VEGF-R2 mRNA was decreased in Cd-treated extraembryonic membranes. • Vascular effects were more notable in malformed embryo's AVs after Cd exposure.« less

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.

Towards a physics on fractals: Differential vector calculus in three-dimensional continuum with fractal metric

NASA Astrophysics Data System (ADS)

Balankin, Alexander S.; Bory-Reyes, Juan; Shapiro, Michael

2016-02-01

One way to deal with physical problems on nowhere differentiable fractals is the mapping of these problems into the corresponding problems for continuum with a proper fractal metric. On this way different definitions of the fractal metric were suggested to account for the essential fractal features. In this work we develop the metric differential vector calculus in a three-dimensional continuum with a non-Euclidean metric. The metric differential forms and Laplacian are introduced, fundamental identities for metric differential operators are established and integral theorems are proved by employing the metric version of the quaternionic analysis for the Moisil-Teodoresco operator, which has been introduced and partially developed in this paper. The relations between the metric and conventional operators are revealed. It should be emphasized that the metric vector calculus developed in this work provides a comprehensive mathematical formalism for the continuum with any suitable definition of fractal metric. This offers a novel tool to study physics on fractals.

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

NASA Astrophysics Data System (ADS)

Satija, Indubala I.

2016-11-01

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

Design and optimization of non-clogging counter-flow microconcentrator for enriching epidermoid cervical carcinoma cells.

PubMed

Tran-Minh, Nhut; Dong, Tao; Su, Qianhua; Yang, Zhaochu; Jakobsen, Henrik; Karlsen, Frank

2011-02-01

Clogging failure is common for microfilters in living cells concentration; for instance, the CaSki Cell-lines (Epidermoid cervical carcinoma cells) utilizing the flat membrane structure. In order to avoid the clogging, counter-flow concentration units with turbine blade-like micropillar are proposed in microconcentrator design. Due to the unusual geometrical-profiles and extraordinary microfluidic performance, the cells blocking does not occur even at permeate entrances. A counter-flow microconcentrator was designed, with both processing layer and collecting layer arranged in terms of the fractal based honeycomb structure. The device was optimized by coupling Artificial Neuron Network (ANN) and Computational Fluid Dynamics (CFD). The excellent concentration ratio of a final microconcentrator was presented in numerical results.

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.

Methods of nanoassembly of a fractal polymer and materials formed thereby

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

Newkome, George R; Moorefield, Charles N

2012-07-24

The invention relates to the formation of synthesized fractal constructs and the methods of chemical self-assembly for the preparation of a non-dendritic, nano-scale, fractal constructs or molecules. More particularly, the invention relates to fractal constructs formed by molecular self-assembly, to create synthetic, nanometer-scale fractal shapes. In an embodiment, a nanoscale Sierpinski hexagonal gasket is formed. This non-dendritic, perfectly self-similar fractal macromolecule is comprised of bisterpyridine building blocks that are bound together by coordination to 36 Ru and 6 Fe ions to form a nearly planar array of increasingly larger hexagons around a hollow center.

Methods of nanoassembly of a fractal polymer and materials formed thereby

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

Newkome, George R; Moorefield, Charles N

2014-09-23

The invention relates to the formation of synthesized fractal constructs and the methods of chemical self-assembly for the preparation of a non-dendritic, nano-scale, fractal constructs or molecules. More particularly, the invention relates to fractal constructs formed by molecular self-assembly, to create synthetic, nanometer-scale fractal shapes. In an embodiment, a nanoscale Sierpinski hexagonal gasket is formed. This non-dendritic, perfectly self-similar fractal macromolecule is comprised of bisterpyridine building blocks that are bound together by coordination to (36) Ru and (6) Fe ions to form a nearly planar array of increasingly larger hexagons around a hollow center.

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.

Variability of fractal dimension of solar radio flux

NASA Astrophysics Data System (ADS)

Bhatt, Hitaishi; Sharma, Som Kumar; Trivedi, Rupal; Vats, Hari Om

2018-04-01

In the present communication, the variation of the fractal dimension of solar radio flux is reported. Solar radio flux observations on a day to day basis at 410, 1415, 2695, 4995, and 8800 MHz are used in this study. The data were recorded at Learmonth Solar Observatory, Australia from 1988 to 2009 covering an epoch of two solar activity cycles (22 yr). The fractal dimension is calculated for the listed frequencies for this period. The fractal dimension, being a measure of randomness, represents variability of solar radio flux at shorter time-scales. The contour plot of fractal dimension on a grid of years versus radio frequency suggests high correlation with solar activity. Fractal dimension increases with increasing frequency suggests randomness increases towards the inner corona. This study also shows that the low frequency is more affected by solar activity (at low frequency fractal dimension difference between solar maximum and solar minimum is 0.42) whereas, the higher frequency is less affected by solar activity (here fractal dimension difference between solar maximum and solar minimum is 0.07). A good positive correlation is found between fractal dimension averaged over all frequencies and yearly averaged sunspot number (Pearson's coefficient is 0.87).

Electromagnetism on anisotropic fractal media

NASA Astrophysics Data System (ADS)

Ostoja-Starzewski, Martin

2013-04-01

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

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

PubMed

Najafi, Elham; Darooneh, Amir H

2015-01-01

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

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

PubMed Central

Najafi, Elham; Darooneh, Amir H.

2015-01-01

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

Fractals in the Classroom

ERIC Educational Resources Information Center

Fraboni, Michael; Moller, Trisha

2008-01-01

Fractal geometry offers teachers great flexibility: It can be adapted to the level of the audience or to time constraints. Although easily explained, fractal geometry leads to rich and interesting mathematical complexities. In this article, the authors describe fractal geometry, explain the process of iteration, and provide a sample exercise.…

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.

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

Multifractal spectrum and lacunarity as measures of complexity of osseointegration.

PubMed

de Souza Santos, Daniel; Dos Santos, Leonardo Cavalcanti Bezerra; de Albuquerque Tavares Carvalho, Alessandra; Leão, Jair Carneiro; Delrieux, Claudio; Stosic, Tatijana; Stosic, Borko

2016-07-01

The goal of this study is to contribute to a better quantitative description of the early stages of osseointegration, by application of fractal, multifractal, and lacunarity analysis. Fractal, multifractal, and lacunarity analysis are performed on scanning electron microscopy (SEM) images of titanium implants that were first subjected to different treatment combinations of i) sand blasting, ii) acid etching, and iii) exposition to calcium phosphate, and were then submersed in a simulated body fluid (SBF) for 30 days. All the three numerical techniques are applied to the implant SEM images before and after SBF immersion, in order to provide a comprehensive set of common quantitative descriptors. It is found that implants subjected to different physicochemical treatments before submersion in SBF exhibit a rather similar level of complexity, while the great variety of crystal forms after SBF submersion reveals rather different quantitative measures (reflecting complexity), for different treatments. In particular, it is found that acid treatment, in most combinations with the other considered treatments, leads to a higher fractal dimension (more uniform distribution of crystals), lower lacunarity (lesser variation in gap sizes), and narrowing of the multifractal spectrum (smaller fluctuations on different scales). The current quantitative description has shown the capacity to capture the main features of complex images of implant surfaces, for several different treatments. Such quantitative description should provide a fundamental tool for future large scale systematic studies, considering the large variety of possible implant treatments and their combinations. Quantitative description of early stages of osseointegration on titanium implants with different treatments should help develop a better understanding of this phenomenon, in general, and provide basis for further systematic experimental studies. Clinical practice should benefit from such studies in the long term, by more ready access to implants of higher quality.

Some problems in fractal differential equations

NASA Astrophysics Data System (ADS)

Su, Weiyi

2016-06-01

Based upon the fractal calculus on local fields, or p-type calculus, or Gibbs-Butzer calculus ([1],[2]), we suggest a constructive idea for "fractal differential equations", beginning from some special examples to a general theory. However, this is just an original idea, it needs lots of later work to support. In [3], we show example "two dimension wave equations with fractal boundaries", and in this note, other examples, as well as an idea to construct fractal differential equations are shown.

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.

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.

Investigation into How 8th Grade Students Define Fractals

ERIC Educational Resources Information Center

Karakus, Fatih

2015-01-01

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

Fractal 1/f Dynamics Suggest Entanglement of Measurement and Human Performance

ERIC Educational Resources Information Center

Holden, John G.; Choi, Inhyun; Amazeen, Polemnia G.; Van Orden, Guy

2011-01-01

Variability of repeated measurements in human performances exhibits fractal 1/f noise. Yet the relative strength of this fractal pattern varies widely across conditions, tasks, and individuals. Four experiments illustrate how subtle details of the conditions of measurement change the fractal patterns observed across task conditions. The results…

Stories about Benoit

NASA Astrophysics Data System (ADS)

Frame, Michael; Cohen, Nathan

2015-03-01

The Yale University mathematics department hosted a memorial for Benoit on April 29 and 30, 2011. The first day of the meeting consisted of three technical talks on some aspects of fractals, Benoit's principal intellectual legacy. Bernard Sapoval spoke on fractals in physics, Peter Jones on fractals in mathematics, and Nassim Taleb on fractals in finance...

Fractals and the irreducibility of consciousness in plants and animals

PubMed Central

Gardiner, John

2013-01-01

In both plants and animals consciousness is fractal. Since fractals can only pass information in one direction it is impossible to extrapolate backward to find the rule that governs the fractal. Thus, similarly, it will be impossible to completely determine the rule or rules that govern consciousness. PMID:23759545

Fractals and the irreducibility of consciousness in plants and animals.

PubMed

Gardiner, John

2013-08-01

In both plants and animals consciousness is fractal. Since fractals can only pass information in one direction it is impossible to extrapolate backward to find the rule that governs the fractal. Thus, similarly, it will be impossible to completely determine the rule or rules that govern consciousness.

Fractal analysis of time varying data

DOEpatents

Vo-Dinh, Tuan; Sadana, Ajit

2002-01-01

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

Do terrestrial hermit crabs sniff? Air flow and odorant capture by flicking antennules

PubMed Central

Koehl, M. A. R.

2016-01-01

Capture of odorant molecules by olfactory organs from the surrounding fluid is the first step of smelling. Sniffing intermittently moves fluid across sensory surfaces, increasing delivery rates of molecules to chemosensory receptors and providing discrete odour samples. Aquatic malacostracan crustaceans sniff by flicking olfactory antennules bearing arrays of chemosensory hairs (aesthetascs), capturing water in the arrays during downstroke and holding the sample during return stroke. Terrestrial malacostracans also flick antennules, but how their flicking affects odour capture from air is not understood. The terrestrial hermit crab, Coenobita rugosus, uses antennules bearing shingle-shaped aesthetascs to capture odours. We used particle image velocimetry to measure fine-scale fluid flow relative to a dynamically scaled physical model of a flicking antennule, and computational simulations to calculate diffusion to aesthetascs by odorant molecules carried in that flow. Air does not flow into the aesthetasc array during flick downstrokes or recovery strokes. Odorants are captured from air flowing around the outside of the array during flick downstrokes, when aesthetascs face upstream and molecule capture rates are 21% higher than for stationary antennules. Bursts of flicking followed by pauses deliver discrete odour samples to olfactory sensors, causing intermittency in odour capture by a different mechanism than aquatic crustaceans use. PMID:26763332

Do terrestrial hermit crabs sniff? Air flow and odorant capture by flicking antennules.

PubMed

Waldrop, Lindsay D; Koehl, M A R

2016-01-01

Capture of odorant molecules by olfactory organs from the surrounding fluid is the first step of smelling. Sniffing intermittently moves fluid across sensory surfaces, increasing delivery rates of molecules to chemosensory receptors and providing discrete odour samples. Aquatic malacostracan crustaceans sniff by flicking olfactory antennules bearing arrays of chemosensory hairs (aesthetascs), capturing water in the arrays during downstroke and holding the sample during return stroke. Terrestrial malacostracans also flick antennules, but how their flicking affects odour capture from air is not understood. The terrestrial hermit crab, Coenobita rugosus, uses antennules bearing shingle-shaped aesthetascs to capture odours. We used particle image velocimetry to measure fine-scale fluid flow relative to a dynamically scaled physical model of a flicking antennule, and computational simulations to calculate diffusion to aesthetascs by odorant molecules carried in that flow. Air does not flow into the aesthetasc array during flick downstrokes or recovery strokes. Odorants are captured from air flowing around the outside of the array during flick downstrokes, when aesthetascs face upstream and molecule capture rates are 21% higher than for stationary antennules. Bursts of flicking followed by pauses deliver discrete odour samples to olfactory sensors, causing intermittency in odour capture by a different mechanism than aquatic crustaceans use. © 2016 The Author(s).

Spatial and velocity statistics of inertial particles in turbulent flows

NASA Astrophysics Data System (ADS)

Bec, J.; Biferale, L.; Cencini, M.; Lanotte, A. S.; Toschi, F.

2011-12-01

Spatial and velocity statistics of heavy point-like particles in incompressible, homogeneous, and isotropic three-dimensional turbulence is studied by means of direct numerical simulations at two values of the Taylor-scale Reynolds number Reλ ~ 200 and Reλ ~ 400, corresponding to resolutions of 5123 and 20483 grid points, respectively. Particles Stokes number values range from St ≈ 0.2 to 70. Stationary small-scale particle distribution is shown to display a singular -multifractal- measure, characterized by a set of generalized fractal dimensions with a strong sensitivity on the Stokes number and a possible, small Reynolds number dependency. Velocity increments between two inertial particles depend on the relative weight between smooth events - where particle velocity is approximately the same of the fluid velocity-, and caustic contributions - when two close particles have very different velocities. The latter events lead to a non-differentiable small-scale behaviour for the relative velocity. The relative weight of these two contributions changes at varying the importance of inertia. We show that moments of the velocity difference display a quasi bi-fractal-behavior and that the scaling properties of velocity increments for not too small Stokes number are in good agreement with a recent theoretical prediction made by K. Gustavsson and B. Mehlig arXiv: 1012.1789v1 [physics.flu-dyn], connecting the saturation of velocity scaling exponents with the fractal dimension of particle clustering.

On the Plasticity of Amorphous Solids

NASA Astrophysics Data System (ADS)

Lin, Jie

Mechanical behaviors of amorphous materials under external stress are central to various phenomena including earthquakes and landslides. Most amorphous materials possess a well defined yield stress when thermal fluctuations are negligible. Only when the shear stress is above the yield stress, the material can flow as a fluid, otherwise it deforms as a solid. There are accumulating evidences that the yielding transition between the flowing and solid phase is a critical phenomenon, and one evidence is the long ranged correlations of plastic strain during adiabatic shear. In spite of this, we still have not fully understood the associated critical exponents and their scaling relations. In the last decade, it has been widely accepted that the elementary rearrangements in amorphous solids are not well-defined topological defects as crystals, instead they are local irreversible rearrangements of a few particles, denoted as shear transformations. Because a single shear transformation changes the local arrangement of particles, it therefore generates an elastic stress field propagating over the whole system. The resulting changes in the local stresses in other regions of the system may in turn trigger more shear transformations. A central feature that complicates the yielding transition is the long range and anisotropic stress field generated by shear transformations. This peculiar interaction between shear transformations leads to two important characteristics: 1.the mechanical noises generated by plastic deformation are broadly distributed 2.those regions that are undergoing plastic deformation has equal probability to make other parts of the material to be more stable or more unstable, depending on the direction between them. In this thesis, we show that these two important factors leads to a singular density of shear transformations, P( x) xtheta at small x, where x is a local measure of stability, namely, the extra stress one needs to add locally to reach the elastic instabilities. We denote such a singular distribution as a pseudo gap, and the theta exponent as the pseudo gap exponent. The fact that the plastic avalanche rates, i.e., number of avalanches per unit strain, during quasi-static shear is not proportional to system size implies the existence of a finite pseudo gap exponent. Arguments based on stability against local perturbations lead to a lower bound of the pseudo gap exponents. In the flowing phase, we construct the scaling description of the yielding transition of soft amorphous solids at zero temperature. The yielding transition shares similarities with another well studied dynamic phase transition, the depinning transition where an elastic interface is driven in a disordered medium, however, there are also striking differences between them. Avalanches are fractal in the yielding transition, characterized by a fractal dimension smaller than the spatial dimension, while avalanches are compact with a fractal dimension, not smaller than the spatial dimension in the depinning transition. We make connections between the Herschel-Bulkley exponent characterizing the singularity of the flow curve near the yield stress, the extension and duration of the avalanches of plasticity, and the pseudo gap exponent. On the other hand, in the solid phase, the pseudo gap also plays a significant role as one increases the shear stress adiabatically. We point out the connection between the local slope of stress-strain curve in the transient state and mean avalanche sizes as the system approaches failure. We argue that the entire solid phase below the yield stress is critical as long as there is finite amount of plastic strain, and plasticity always involves system-spanning events because of the finite pseudo gap exponent. We use the elasto-plastic model, a mesoscopic approach, to verify our theoretical predictions and obtain satisfying results. Finally, a mean field description of plastic flow in amorphous solids are proposed and solved analytically. The mean field models captures the broad distribution of mechanical noise generated by plasticity, leading to a biased Levy flight behavior of local stresses, with the elastic instabilities as the absorbing boundary. The mean field model implies an upper critical dimension as dc = 4.

GENERATING FRACTAL PATTERNS BY USING p-CIRCLE INVERSION

NASA Astrophysics Data System (ADS)

Ramírez, José L.; Rubiano, Gustavo N.; Zlobec, Borut Jurčič

2015-10-01

In this paper, we introduce the p-circle inversion which generalizes the classical inversion with respect to a circle (p = 2) and the taxicab inversion (p = 1). We study some basic properties and we also show the inversive images of some basic curves. We apply this new transformation to well-known fractals such as Sierpinski triangle, Koch curve, dragon curve, Fibonacci fractal, among others. Then we obtain new fractal patterns. Moreover, we generalize the method called circle inversion fractal be means of the p-circle inversion.

Fractals in physiology and medicine

NASA Technical Reports Server (NTRS)

Goldberger, Ary L.; West, Bruce J.

1987-01-01

The paper demonstrates how the nonlinear concepts of fractals, as applied in physiology and medicine, can provide an insight into the organization of such complex structures as the tracheobronchial tree and heart, as well as into the dynamics of healthy physiological variability. Particular attention is given to the characteristics of computer-generated fractal lungs and heart and to fractal pathologies in these organs. It is shown that alterations in fractal scaling may underlie a number of pathophysiological disturbances, including sudden cardiac death syndromes.

Intermittency and Topology of Shock Induced Mixing

NASA Astrophysics Data System (ADS)

Tellez, Jackson; Redondo, Jose M.; Ben Mahjoub, Otman; Malik, Nadeem; Vila, Teresa

2016-04-01

The advance of a Rayleigh-Taylor front is described in Linden & Redondo (1991),[1-3] and may be shown to follow a quadratic law in time where the width of the growing region of instability depends on the local mixing efficiency of the different density fluids that accelerate against each other g is the acceleration and A is the Atwood number defined as the diference of densities divided by their sum. This results show the independence of the large amplitude structures on the initial conditions the width of the mixing region depends also on the intermittency of the turbulence. Then dimensional analysis may also depend on the relevant reduced acceleration driven time and the molecular reactive time akin to Damkholer number and the fractal structure of the contact zone [2,4]. Detailed experiments and simulations on RT and RM shock induced fronts analized with respect to structure functions are able to determine which mechanisms are most effective in local mixing which increase the effective fractal dimension, as well as the effect of higher order geometrical parameters, such as the structure functions, in non-homogeneous fluids (Mahjoub et al 1998)[5]. The structure of a Mixing blob shows a relatively sharp head with most of the mixing taking place at the sides due to what seems to be shear instability very similar to the Kelvin-Helmholtz instabilities, but with sideways accelerations. The formation of the blobs and spikes with their secondary instabilities produces a turbulent cascade, evident just after about 1 non-dimensional time unit, from a virtual time origin that takes into account the linear growth phase, as can be seen by the growth of the fractal dimension for different volume fractions. Two-dimensional cuts of the 3D flow also show that vortex flows have closed or spiral streamlines around their core. Examples of such flows can be also seen in the laboratory, for example at the interface of atwo-layer stratified fluid in a tank in which case streamlines are more regular. Mixing in turbulent flows remains less well understood, and in spite research some basic problems are still virtually unexplored. Th e indications suggest that mixing in non-decaying and accelerating turbulent flows are different from those in vortical and steady flows. Fluid element pairs separate, neither linearly nor exponentially but according to a generalized intermittent Richardson's law. Fractal analysis in the laboratory shows that fluid element pairs travel close to each other for a long time until they separate quite suddenly suggest that straining regions around hyperbolic points play an important role in the violent turbulent stirring and in the mechanisms by which turbulence causes fluid element pairs to move apart [6,7]. So the eddies that are most effective in separating fluid elements are those that have a size comparable to the instantaneous separation between the two fluid elements. This is seen in both RT and RM instabilities. For a constant acceleration, the RT instability is found to grow self -similarly according to mixing coefficients which when measured over a comprehensive range of density ratio (Atwood nubers)show that the results are found applicable to supernova exlposions.For an impulsive acceleration (RM), there are two components. The RM impulse from a shock is greatly reduced at high Mach number due to compressive effects in reasonable agreement with linear theory. The ensuing motion is essentially incompressible and described by a power law However, the exponents obtained from the compressible RM experiments are larger than those obtained from incompressible RT experiments. The discrepancy is not well understood but intermittency differences could explain the role of compressibility in fractal media. [1] Linden P.F., Redondo J.M. and Youngs D. (1994) Molecular mixing in Rayleigh-Taylor Instability. Jour. Fluid Mech. 265, 97-124. [2] Redondo, J.M., 1990. The structure of density interfaces. Ph.D. Thesis. DAMTP, University of Cambridge. Cambridge [3] Redondo J.M. (1996) Vertical microstructure and mixing in stratified flows. Advances in Turbulence VI. Eds. S. Gavrilakis et al. 605-608. [4] Redondo J.M.,M.A. Sanchez y R. Castilla (2000) Vortical structures in stratified turbulent flows, Turbulent diffusion in the environment. Eds. Redondo J.M. and Babiano A. 113-120. [5] Mahjoub, O. B., Babiano A. and Redondo, J. M.: Structure functions in complex flows, Flow, Turbulence and Combustion, 59,299-313, 1998. [6] Malik, N.A. Vassilicos, J.C. 1999 A Lagrangian model of turbulent dispersion with turbulent-like flow structure: comparison with direct numerical simulation for two-particle statistics. Phys. Fluids, 11, 1572-1580. [7] Fung, J.C.H., Hunt, J.C.R., Malik, N.A. and Perkins, R.J.(1992. Kinematic simulation of homogeneous turbulence by unsteady random Fourier modes. J. Fluid Mech.236-281. [8] Tarquis, A. M., Platonov, A., Matulka, A., Grau, J., Sekula, E., Diez, M., & Redondo, J. M. (2014). Application of multifractal analysis to the study of SAR features and oil spills on the ocean surface. Nonlinear Processes in Geophysics, 21(2), 439-450. [9] Fraunie, P., Berreba, S., Chashechkin, Y. D., Velasco, D., & Redondo, J. M. (2008). Large eddy simulation and laboratory experiments on the decay of grid wakes in strongly stratified flows. Nuovo Cimento C, 31, 909-930.

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

PubMed

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

2011-01-01

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

Transport properties of electrons in fractal magnetic-barrier structures

NASA Astrophysics Data System (ADS)

Sun, Lifeng; Fang, Chao; Guo, Yong

2010-09-01

Quantum transport properties in fractal magnetically modulated structures are studied by the transfer-matrix method. It is found that the transmission spectra depend sensitively not only on the incident energy and the direction of the wave vector but also on the stage of the fractal structures. Resonance splitting, enhancement, and position shift of the resonance peaks under different magnetic modulation are observed at four different fractal stages, and the relationship between the conductance in the fractal structure and magnetic modulation is also revealed. The results indicate the spectra of the transmission can be considered as fingerprints for the fractal structures, which show the subtle correspondence between magnetic structures and transport behaviors.

Multifractal characteristics of optical turbulence measured through a single beam holographic process.

PubMed

Pérez, Darío G; Barillé, Regis; Morille, Yohann; Zielińska, Sonia; Ortyl, Ewelina

2014-08-11

We have previously shown that azopolymer thin films exposed to coherent light that has travelled through a turbulent medium produces a surface relief grating containing information about the intensity of the turbulence; for instance, a relation between the refractive index structure constant C(n)2 as a function of the surface parameters was obtained. In this work, we show that these films capture much more information about the turbulence dynamics. Multifractal detrended fluctuation and fractal dimension analysis from images of the surface roughness produced by the light on the azopolymer reveals scaling properties related to those of the optical turbulence.

Application of Refined Kolmogorov's Hypothesis For Numerical Modelling of Filtration In Porous Media

NASA Astrophysics Data System (ADS)

Kuz'min, G.; Soboleva, O.

We consider a flow of incompressible fluid through the fractal porous media. The scaling theory that uses the ideas of the Kolmogorovs (1962) paper is presented for the permeability field (x). The velocity is given by the Darcy's law v = (x) p, where p is the pressure. The incompressibility condition div v = 0 results in the equation for p (x) p(x) = 0. (1) xj xj In order to compute the steady realizations for the velocity, we use (256)3 grid, the iter- ation algorithm in combination with the fast Fourier transform and the sweep method. In order to replace the original problem by a simpler one, we seek for a subgrid model. The large scales l > l0 are retained in the equation. The scales l < l0 are simu- lated along the lines of the renormalization group theory. Using the scaling hypoth- esis for the latter, we derive the following expression for the effective permeability l -D 0 0l = 0 (), where 0 is a constant which is chosen according to the L experimental data for a natural sedimentary rock, D (which is equal to 3) is the spa- tial dimension. Thus, if one wishes to use a coarser grid, when computing the flow through a fractal matter, he should multiply the effective permeability by a constant factor according to() . For such a model we made some computational experiments. The reasonable agreement with numerical simulations has been obtained. For the nu- merically obtained realizations of velocity field, we calculate the trajectories of the labeled particles from the equations: dx m(x, l) = v(x), x = x0 , i = 1, ..., N, i (2) dt where i stands for the number of a particle, m(x, l) is the porosity. The correlated fractal fields of permeability and porosity are numerically generated using the scaling theory. For a cloud of the labeled particles, we study the dispersion within the exact and the subgrid models.

Fractal dimension analysis of complexity in Ligeti piano pieces

NASA Astrophysics Data System (ADS)

Bader, Rolf

2005-04-01

Fractal correlation dimensional analysis has been performed with whole solo piano pieces by Gyrgy Ligeti at every 50ms interval of the pieces. The resulting curves of development of complexity represented by the fractal dimension showed up a very reasonable correlation with the perceptional density of events during these pieces. The seventh piece of Ligeti's ``Musica ricercata'' was used as a test case. Here, each new part of the piece was followed by an increase of the fractal dimension because of the increase of information at the part changes. The second piece ``Galamb borong,'' number seven of the piano Etudes was used, because Ligeti wrote these Etudes after studying fractal geometry. Although the piece is not fractal in the strict mathematical sense, the overall structure of the psychoacoustic event-density as well as the detailed event development is represented by the fractal dimension plot.

Human somatic cells acquire the plasticity to generate embryoid-like metamorphosis via the actin cytoskeleton in injured tissues.

PubMed

Diaz, Jairo A; Murillo, Mauricio F; Mendoza, Jhonan A; Barreto, Ana M; Poveda, Lina S; Sanchez, Lina K; Poveda, Laura C; Mora, Katherine T

2016-01-01

Emergent biological responses develop via unknown processes dependent on physical collision. In hypoxia, when the tissue architecture collapses but the geometric core is stable, actin cytoskeleton filament components emerge, revealing a hidden internal order that identifies how each molecule is reassembled into the original mold, using one common connection, i.e., a fractal self-similarity that guides the system from the beginning in reverse metamorphosis, with spontaneous self-assembly of past forms that mimics an embryoid phenotype. We captured this hidden collective filamentous assemblage in progress: Hypoxic deformed cells enter into intercellular collisions, generate migratory ejected filaments, and produce self-assembly of triangular chiral hexagon complexes; this dynamic geometry guides the microenvironment scaffold in which this biological process is incubated, recapitulating embryonic morphogenesis. In all injured tissues, especially in damaged skeletal (striated) muscle cells, visibly hypertrophic intercalated actin-myosin filaments are organized in zebra stripe pattern along the anterior-posterior axis in the interior of the cell, generating cephalic-caudal polarity segmentation, with a high selective level of immunopositivity for Actin, Alpha Skeletal Muscle antibody and for Neuron-Specific Enolase expression of ectodermal differentiation. The function of actin filaments in emergent responses to tissue injury is to reconstitute, reactivate and orchestrate cellular metamorphosis, involving the re-expression of fetal genes, providing evidence of the reverse flow of genetic information within a biological system. The resultant embryoid phenotype emerges as a microscopic fractal template copy of the organization of the whole body, likely allowing the modification and reprogramming of the phenotype of the tumor in which these structures develop, as well as establishing a reverse primordial microscopic mold to collectively re-form cellular building blocks to regenerate injured tissues. Tumorigenesis mimics a self-organizing process of early embryo development. All malignant tumors produce fetal proteins, we now know from which these proteins proceed. Embryoid-like metamorphosis phenomena would represent the anatomical and functional entity of the injury stem cell niche. The sufficiently fast identification, isolation, culture, and expansion of these self-organized structures or genetically derived products could, in our opinion, be used to develop new therapeutic strategies against cancer and in regenerative medicine.

Human somatic cells acquire the plasticity to generate embryoid-like metamorphosis via the actin cytoskeleton in injured tissues

PubMed Central

Diaz, Jairo A; Murillo, Mauricio F; Mendoza, Jhonan A; Barreto, Ana M; Poveda, Lina S; Sanchez, Lina K; Poveda, Laura C; Mora, Katherine T

2016-01-01

Emergent biological responses develop via unknown processes dependent on physical collision. In hypoxia, when the tissue architecture collapses but the geometric core is stable, actin cytoskeleton filament components emerge, revealing a hidden internal order that identifies how each molecule is reassembled into the original mold, using one common connection, i.e., a fractal self-similarity that guides the system from the beginning in reverse metamorphosis, with spontaneous self-assembly of past forms that mimics an embryoid phenotype. We captured this hidden collective filamentous assemblage in progress: Hypoxic deformed cells enter into intercellular collisions, generate migratory ejected filaments, and produce self-assembly of triangular chiral hexagon complexes; this dynamic geometry guides the microenvironment scaffold in which this biological process is incubated, recapitulating embryonic morphogenesis. In all injured tissues, especially in damaged skeletal (striated) muscle cells, visibly hypertrophic intercalated actin-myosin filaments are organized in zebra stripe pattern along the anterior-posterior axis in the interior of the cell, generating cephalic-caudal polarity segmentation, with a high selective level of immunopositivity for Actin, Alpha Skeletal Muscle antibody and for Neuron-Specific Enolase expression of ectodermal differentiation. The function of actin filaments in emergent responses to tissue injury is to reconstitute, reactivate and orchestrate cellular metamorphosis, involving the re-expression of fetal genes, providing evidence of the reverse flow of genetic information within a biological system. The resultant embryoid phenotype emerges as a microscopic fractal template copy of the organization of the whole body, likely allowing the modification and reprogramming of the phenotype of the tumor in which these structures develop, as well as establishing a reverse primordial microscopic mold to collectively re-form cellular building blocks to regenerate injured tissues. Tumorigenesis mimics a self-organizing process of early embryo development. All malignant tumors produce fetal proteins, we now know from which these proteins proceed. Embryoid-like metamorphosis phenomena would represent the anatomical and functional entity of the injury stem cell niche. The sufficiently fast identification, isolation, culture, and expansion of these self-organized structures or genetically derived products could, in our opinion, be used to develop new therapeutic strategies against cancer and in regenerative medicine. PMID:27725917

Fractal characterization of fracture surfaces in concrete

USGS Publications Warehouse

Saouma, V.E.; Barton, C.C.; Gamaleldin, N.A.

1990-01-01

Fractal geometry is used to characterize the roughness of cracked concrete surfaces through a specially built profilometer, and the fractal dimension is subsequently correlated to the fracture toughness and direction of crack propagation. Preliminary results indicate that the fracture surface is indeed fractal over two orders of magnitudes with a dimension of approximately 1.20. ?? 1990.

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

NASA Astrophysics Data System (ADS)

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

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

Fractal Theory and Field Cover Experiments: Implications for the Fractal Characteristics and Radon Diffusion Behavior of Soils and Rocks.

PubMed

Tan, Wanyu; Li, Yongmei; Tan, Kaixuan; Duan, Xianzhe; Liu, Dong; Liu, Zehua

2016-12-01

Radon diffusion and transport through different media is a complex process affected by many factors. In this study, the fractal theories and field covering experiments were used to study the fractal characteristics of particle size distribution (PSD) of six kinds of geotechnical materials (e.g., waste rock, sand, laterite, kaolin, mixture of sand and laterite, and mixture of waste rock and laterite) and their effects on radon diffusion. In addition, the radon diffusion coefficient and diffusion length were calculated. Moreover, new formulas for estimating diffusion coefficient and diffusion length functional of fractal dimension d of PSD were proposed. These results demonstrate the following points: (1) the fractal dimension d of the PSD can be used to characterize the property of soils and rocks in the studies of radon diffusion behavior; (2) the diffusion coefficient and diffusion length decrease with increasing fractal dimension of PSD; and (3) the effectiveness of final covers in reducing radon exhalation of uranium tailings impoundments can be evaluated on the basis of the fractal dimension of PSD of materials.

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.

Prediction of pork quality parameters by applying fractals and data mining on MRI.

PubMed

Caballero, Daniel; Pérez-Palacios, Trinidad; Caro, Andrés; Amigo, José Manuel; Dahl, Anders B; ErsbØll, Bjarne K; Antequera, Teresa

2017-09-01

This work firstly investigates the use of MRI, fractal algorithms and data mining techniques to determine pork quality parameters non-destructively. The main objective was to evaluate the capability of fractal algorithms (Classical Fractal algorithm, CFA; Fractal Texture Algorithm, FTA and One Point Fractal Texture Algorithm, OPFTA) to analyse MRI in order to predict quality parameters of loin. In addition, the effect of the sequence acquisition of MRI (Gradient echo, GE; Spin echo, SE and Turbo 3D, T3D) and the predictive technique of data mining (Isotonic regression, IR and Multiple linear regression, MLR) were analysed. Both fractal algorithm, FTA and OPFTA are appropriate to analyse MRI of loins. The sequence acquisition, the fractal algorithm and the data mining technique seems to influence on the prediction results. For most physico-chemical parameters, prediction equations with moderate to excellent correlation coefficients were achieved by using the following combinations of acquisition sequences of MRI, fractal algorithms and data mining techniques: SE-FTA-MLR, SE-OPFTA-IR, GE-OPFTA-MLR, SE-OPFTA-MLR, with the last one offering the best prediction results. Thus, SE-OPFTA-MLR could be proposed as an alternative technique to determine physico-chemical traits of fresh and dry-cured loins in a non-destructive way with high accuracy. Copyright © 2017. Published by Elsevier Ltd.

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

Quantitative assessment of early diabetic retinopathy using fractal analysis.

PubMed

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

2009-01-01

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

The fractal geometry of life.

PubMed

Losa, Gabriele A

2009-01-01

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

Investigation of changes in fractal dimension from layered retinal structures of healthy and diabetic eyes with optical coherence tomography

NASA Astrophysics Data System (ADS)

Gao, Wei; Zakharov, Valery P.; Myakinin, Oleg O.; Bratchenko, Ivan A.; Artemyev, Dmitry N.; Kornilin, Dmitry V.

2015-07-01

Optical coherence tomography (OCT) is usually employed for the measurement of retinal thickness characterizing the structural changes of tissue. However, fractal dimension (FD) could also character the structural changes of tissue. Therefore, fractal dimension changes may provide further information regarding cellular layers and early damage in ocular diseases. We investigated the possibility of OCT in detecting changes in fractal dimension from layered retinal structures. OCT images were obtained from diabetic patients without retinopathy (DM, n = 38 eyes) or mild diabetic retinopathy (MDR, n = 43 eyes) and normal healthy subjects (Controls, n = 74 eyes). Fractal dimension was calculated using the differentiate box counting methodology. We evaluated the usefulness of quantifying fractal dimension of layered structures in the detection of retinal damage. Generalized estimating equations considering within-subject intereye relations were used to test for differences between the groups. A modified p value of <0.001 was considered statistically significant. Receiver operating characteristic (ROC) curves were constructed to describe the ability of fractal dimension to discriminate between the eyes of DM, MDR and healthy eyes. Significant decreases of fractal dimension were observed in all layers in the MDR eyes compared with controls except in the inner nuclear layer (INL). Significant decreases of fractal dimension were also observed in all layers in the MDR eyes compared with DM eyes. The highest area under receiver operating characteristic curve (AUROC) values estimated for fractal dimension were observed for the outer plexiform layer (OPL) and outer segment photoreceptors (OS) when comparing MDR eyes with controls. The highest AUROC value estimated for fractal dimension were also observed for the retinal nerve fiber layer (RNFL) and OS when comparing MDR eyes with DM eyes. Our results suggest that fractal dimension of the intraretinal layers may provide useful information to differentiate pathological from healthy eyes. Further research is warranted to determine how this approach may be used to improve diagnosis of early retinal neurodegeneration.

Twenty-Third Lunar and Planetary Science Conference

NASA Technical Reports Server (NTRS)

1992-01-01

Presented here is a collection of papers from the Twenty-Third Lunar and Planetary Science Conference that were chosen for having the greatest potential interest for the general reading public. The presentations avoid jargon and unnecessarily complex terms. Topics covered include electron microscopy studies of a circumstellar rock, the fractal analysis of lava flows, volcanic activity on Venus, the isotopic signature of recent solar wind nitrogen, and the implications of impact crater distribution on Venus.

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).

Fractal tomography and its application in 3D vision

NASA Astrophysics Data System (ADS)

Trubochkina, N.

2018-01-01

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

FAST TRACK COMMUNICATION: Weyl law for fat fractals

NASA Astrophysics Data System (ADS)

Spina, María E.; García-Mata, Ignacio; Saraceno, Marcos

2010-10-01

It has been conjectured that for a class of piecewise linear maps the closure of the set of images of the discontinuity has the structure of a fat fractal, that is, a fractal with positive measure. An example of such maps is the sawtooth map in the elliptic regime. In this work we analyze this problem quantum mechanically in the semiclassical regime. We find that the fraction of states localized on the unstable set satisfies a modified fractal Weyl law, where the exponent is given by the exterior dimension of the fat fractal.

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.

Electro-chemical manifestation of nanoplasmonics in fractal media

NASA Astrophysics Data System (ADS)

Baskin, Emmanuel; Iomin, Alexander

2013-06-01

Electrodynamics of composite materials with fractal geometry is studied in the framework of fractional calculus. This consideration establishes a link between fractal geometry of the media and fractional integrodifferentiation. The photoconductivity in the vicinity of the electrode-electrolyte fractal interface is studied. The methods of fractional calculus are employed to obtain an analytical expression for the giant local enhancement of the optical electric field inside the fractal composite structure at the condition of the surface plasmon excitation. This approach makes it possible to explain experimental data on photoconductivity in the nano-electrochemistry.

Study on Conversion Between Momentum and Contrarian Based on Fractal Game

NASA Astrophysics Data System (ADS)

Wu, Xu; Song, Guanghui; Deng, Yan; Xu, Lin

2015-06-01

Based on the fractal game which is performed by the majority and the minority, the fractal market theory (FMT) is employed to describe the features of investors' decision-making. Accordingly, the process of fractal games is formed in order to analyze the statistical features of conversion between momentum and contrarian. The result shows that among three fractal game mechanisms, the statistical feature of simulated return rate series is much more similar to log returns on actual series. In addition, the conversion between momentum and contrarian is also extremely similar to real situation, which can reflect the effectiveness of using fractal game in analyzing the conversion between momentum and contrarian. Moreover, it also provides decision-making reference which helps investors develop effective investment strategy.

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.

The fractal-multifractal method and temporal resolution: Application to precipitation and streamflow

NASA Astrophysics Data System (ADS)

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

2017-12-01

In the past, we have established that the deterministic fractal-multifractal (FM) method is a promising geometric tool to analyze hydro-climatic variables, such as precipitation, river flow, and temperature. In this study, we address the issue of temporal resolution to advance the suitability and usefulness of the FM approach in hydro-climate. Specifically, we elucidate the evolution of FM geometric parameters as computed at different time scales ranging from a day to a month (30-day) in increments of a day. For this purpose, both rainfall and river discharge records at Sacramento, California gathered over a year are encoded at different time scales. The analysis reveals that: (a) the FM approach yields faithful encodings of both kinds of data sets at the resolutions considered with reasonably small errors; and (b) the "best" FM parameters ultimately converge when the resolution is increased, thus allowing visualizing both hydrologic attributes. By addressing the scalability of the geometric patterns, these results further advance the suitability of the FM approach.

Fractal Approach to Erosion Threshold of Bentonites

NASA Astrophysics Data System (ADS)

Xu, Y. F.; Li, X. Y.

Bentonite has been considered as a candidate buffer material for the disposal of high-level radioactive waste (HLW) because of its low permeability, high sorption capacity, self-sealing characteristics and durability in a natural environment. Bentonite erosion caused by groundwater flow may take place at the interface of the compacted bentonite and fractured granite. Surface erosion of bentonite flocs is represented typically as an erosion threshold. Predicting the erosion threshold of bentonite flocs requires taking into account cohesion, which results from interactions between clay particles. Beyond the usual dependence on grain size, a significant correlation between erosion threshold and porosity measurements is confirmed for bentonite flocs. A fractal model for erosion threshold of bentonite flocs is proposed. Cohesion forces, the long-range van der Waals interaction between two clay particles are taken as the resource of the erosion threshold. The model verification is conducted by the comparison with experiments published in the literature. The results show that the proposed model for erosion threshold is in good agreement with the experimental data.

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.

...And Kronos Ate His Sons

NASA Astrophysics Data System (ADS)

Vitiello, Giuseppe

In closed systems, energy is conserved. The origin of the time axis is completely arbitrary due to the invariance under continuous time-translations. The flowing of time swallows those fictitious origins one might assign on its axis, as Kronos ate his sons. Dissipation breaks such a scenario. It implies a non-forgettable origin of time. Open systems need their complement (their "double") in order to become, together, a closed system. Time emerges as an observable measured by the evolution of the open system complement, which acts as a clock. The conservation of the energy-momentum tensor in electrodynamics is considered and its relation with dissipative systems and self-similar fractal structures is discussed. The isomorphism with coherent states in quantum field theory (QFT) is established and the generator of transitions among unitarily inequivalent representations of the canonical commutation relations (CCR) is shown to provide sequences in time of phases, which defines the arrow of time. Merging properties of electrodynamics, fractal self-similarity, dissipation and coherent states point to an integrated vision of Nature.

Current quantization and fractal hierarchy in a driven repulsive lattice gas.

PubMed

Rotondo, Pietro; Sellerio, Alessandro Luigi; Glorioso, Pietro; Caracciolo, Sergio; Cosentino Lagomarsino, Marco; Gherardi, Marco

2017-11-01

Driven lattice gases are widely regarded as the paradigm of collective phenomena out of equilibrium. While such models are usually studied with nearest-neighbor interactions, many empirical driven systems are dominated by slowly decaying interactions such as dipole-dipole and Van der Waals forces. Motivated by this gap, we study the nonequilibrium stationary state of a driven lattice gas with slow-decayed repulsive interactions at zero temperature. By numerical and analytical calculations of the particle current as a function of the density and of the driving field, we identify (i) an abrupt breakdown transition between insulating and conducting states, (ii) current quantization into discrete phases where a finite current flows with infinite differential resistivity, and (iii) a fractal hierarchy of excitations, related to the Farey sequences of number theory. We argue that the origin of these effects is the competition between scales, which also causes the counterintuitive phenomenon that crystalline states can melt by increasing the density.

Analysis of the interplay among charge, hydration and shape of proteins through the modeling of their CZE mobility data.

PubMed

Piaggio, Maria V; Peirotti, Marta B; Deiber, Julio A

2009-07-01

Electrophoretic mobility data of four proteins are analyzed and interpreted through a physicochemical CZE model, which provides estimates of quantities like equivalent hydrodynamic radius (size), effective charge number, shape orientation factor, hydration, actual pK values of ionizing groups, and pH near molecule, among others. Protein friction coefficients are simulated through the creeping flow theory of prolate spheroidal particles. The modeling of the effective electrophoretic mobility of proteins requires consideration of hydrodynamic size and shape coupled to hydration and effective charge. The model proposed predicts native protein hydration within the range of values obtained experimentally from other techniques. Therefore, this model provides consistently other physicochemical properties such as average friction and diffusion coefficients and packing fractal dimension. As the pH varies from native conditions to those that are denaturing the protein, hydration and packing fractal dimension change substantially. Needs for further research are also discussed and proposed.

Current quantization and fractal hierarchy in a driven repulsive lattice gas

NASA Astrophysics Data System (ADS)

Rotondo, Pietro; Sellerio, Alessandro Luigi; Glorioso, Pietro; Caracciolo, Sergio; Cosentino Lagomarsino, Marco; Gherardi, Marco

2017-11-01

Driven lattice gases are widely regarded as the paradigm of collective phenomena out of equilibrium. While such models are usually studied with nearest-neighbor interactions, many empirical driven systems are dominated by slowly decaying interactions such as dipole-dipole and Van der Waals forces. Motivated by this gap, we study the nonequilibrium stationary state of a driven lattice gas with slow-decayed repulsive interactions at zero temperature. By numerical and analytical calculations of the particle current as a function of the density and of the driving field, we identify (i) an abrupt breakdown transition between insulating and conducting states, (ii) current quantization into discrete phases where a finite current flows with infinite differential resistivity, and (iii) a fractal hierarchy of excitations, related to the Farey sequences of number theory. We argue that the origin of these effects is the competition between scales, which also causes the counterintuitive phenomenon that crystalline states can melt by increasing the density.

Physics in space-time with scale-dependent metrics

NASA Astrophysics Data System (ADS)

Balankin, Alexander S.

2013-10-01

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

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.

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.

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 .

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

PubMed

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

2018-03-01

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

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.

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

NASA Technical Reports Server (NTRS)

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

2001-01-01

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

a Fractal Network Model for Fractured Porous Media

NASA Astrophysics Data System (ADS)

Xu, Peng; Li, Cuihong; Qiu, Shuxia; Sasmito, Agus Pulung

2016-04-01

The transport properties and mechanisms of fractured porous media are very important for oil and gas reservoir engineering, hydraulics, environmental science, chemical engineering, etc. In this paper, a fractal dual-porosity model is developed to estimate the equivalent hydraulic properties of fractured porous media, where a fractal tree-like network model is used to characterize the fracture system according to its fractal scaling laws and topological structures. The analytical expressions for the effective permeability of fracture system and fractured porous media, tortuosity, fracture density and fraction are derived. The proposed fractal model has been validated by comparisons with available experimental data and numerical simulation. It has been shown that fractal dimensions for fracture length and aperture have significant effect on the equivalent hydraulic properties of fractured porous media. The effective permeability of fracture system can be increased with the increase of fractal dimensions for fracture length and aperture, while it can be remarkably lowered by introducing tortuosity at large branching angle. Also, a scaling law between the fracture density and fractal dimension for fracture length has been found, where the scaling exponent depends on the fracture number. The present fractal dual-porosity model may shed light on the transport physics of fractured porous media and provide theoretical basis for oil and gas exploitation, underground water, nuclear waste disposal and geothermal energy extraction as well as chemical engineering, etc.

Observations, theoretical ideas and modeling of turbulent flows: Past, present and future

NASA Technical Reports Server (NTRS)

Chapman, G. T.; Tobak, M.

1985-01-01

Turbulence was analyzed in a historical context featuring the interactions between observations, theoretical ideas, and modeling within three successive movements. These are identified as predominantly statistical, structural and deterministic. The statistical movement is criticized for its failure to deal with the structural elements observed in turbulent flows. The structural movement is criticized for its failure to embody observed structural elements within a formal theory. The deterministic movement is described as having the potential of overcoming these deficiencies by allowing structural elements to exhibit chaotic behavior that is nevertheless embodied within a theory. Four major ideas of this movement are described: bifurcation theory, strange attractors, fractals, and the renormalization group. A framework for the future study of turbulent flows is proposed, based on the premises of the deterministic movement.

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.

ABC of multi-fractal spacetimes and fractional sea turtles

NASA Astrophysics Data System (ADS)

Calcagni, Gianluca

2016-04-01

We clarify what it means to have a spacetime fractal geometry in quantum gravity and show that its properties differ from those of usual fractals. A weak and a strong definition of multi-scale and multi-fractal spacetimes are given together with a sketch of the landscape of multi-scale theories of gravitation. Then, in the context of the fractional theory with q-derivatives, we explore the consequences of living in a multi-fractal spacetime. To illustrate the behavior of a non-relativistic body, we take the entertaining example of a sea turtle. We show that, when only the time direction is fractal, sea turtles swim at a faster speed than in an ordinary world, while they swim at a slower speed if only the spatial directions are fractal. The latter type of geometry is the one most commonly found in quantum gravity. For time-like fractals, relativistic objects can exceed the speed of light, but strongly so only if their size is smaller than the range of particle-physics interactions. We also find new results about log-oscillating measures, the measure presentation and their role in physical observations and in future extensions to nowhere-differentiable stochastic spacetimes.

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

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.

Fractal Geometry in the Arts: AN Overview across the Different Cultures

NASA Astrophysics Data System (ADS)

Sala, Nicoletta

Fractal, in mathematics, is a geometric shape that is complex and detailed in structure at any level of magnification. The word "fractal" was coined less than thirty years ago by one of history's most creative and mathematicians, Benoit Mandelbrot, whose work, The Fractal Geometry of Nature, first introduced and explained concepts underlying this new vision of the geometry. Although other mathematical thinkers like Georg Cantor (1845-1918), Felix Hausdorff (1868-1942), Gaston Julia (1893-1978), Helge von Koch (1870-1924), Giuseppe Peano (1858-1932), Lewis Richardson (1891-1953), Waclaw Sierpinski (1882-1969) and others had attained isolated insights of fractal understanding, such ideas were largely ignored until Mandelbrot's genius forged them at a single blow into a gorgeously coherent and fascinating discipline. Fractal geometry is applied in different field now: engineering, physics, chemistry, biology, and architecture. The aim of this paper is to introduce an approach where the arts are analysed using a fractal point of view.

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

NASA Astrophysics Data System (ADS)

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

2016-05-01

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

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

PubMed Central

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

2013-01-01

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

Super liquid-repellent gas membranes for carbon dioxide capture and heart-lung machines.

PubMed

Paven, Maxime; Papadopoulos, Periklis; Schöttler, Susanne; Deng, Xu; Mailänder, Volker; Vollmer, Doris; Butt, Hans-Jürgen

2013-01-01

In a gas membrane, gas is transferred between a liquid and a gas through a microporous membrane. The main challenge is to achieve a high gas transfer while preventing wetting and clogging. With respect to the oxygenation of blood, haemocompatibility is also required. Here we coat macroporous meshes with a superamphiphobic-or liquid repellent-layer to meet this challenge. The superamphiphobic layer consists of a fractal-like network of fluorinated silicon oxide nanospheres; gas trapped between the nanospheres keeps the liquid from contacting the wall of the membrane. We demonstrate the capabilities of the membrane by capturing carbon dioxide gas into a basic aqueous solution and in addition use it to oxygenate blood. Usually, blood tends to clog membranes because of the abundance of blood cells, platelets, proteins and lipids. We show that human blood stored in a superamphiphobic well for 24 h can be poured off without leaving cells or adsorbed protein behind.

Fractal fluctuations in gaze speed visual search.

PubMed

Stephen, Damian G; Anastas, Jason

2011-04-01

Visual search involves a subtle coordination of visual memory and lower-order perceptual mechanisms. Specifically, the fluctuations in gaze may provide support for visual search above and beyond what may be attributed to memory. Prior research indicates that gaze during search exhibits fractal fluctuations, which allow for a wide sampling of the field of view. Fractal fluctuations constitute a case of fast diffusion that may provide an advantage in exploration. We present reanalyses of eye-tracking data collected by Stephen and Mirman (Cognition, 115, 154-165, 2010) for single-feature and conjunction search tasks. Fluctuations in gaze during these search tasks were indeed fractal. Furthermore, the degree of fractality predicted decreases in reaction time on a trial-by-trial basis. We propose that fractality may play a key role in explaining the efficacy of perceptual exploration.

A conservation law, entropy principle and quantization of fractal dimensions in hadron interactions

NASA Astrophysics Data System (ADS)

Zborovský, I.

2018-04-01

Fractal self-similarity of hadron interactions demonstrated by the z-scaling of inclusive spectra is studied. The scaling regularity reflects fractal structure of the colliding hadrons (or nuclei) and takes into account general features of fragmentation processes expressed by fractal dimensions. The self-similarity variable z is a function of the momentum fractions x1 and x2 of the colliding objects carried by the interacting hadron constituents and depends on the momentum fractions ya and yb of the scattered and recoil constituents carried by the inclusive particle and its recoil counterpart, respectively. Based on entropy principle, new properties of the z-scaling concept are found. They are conservation of fractal cumulativity in hadron interactions and quantization of fractal dimensions characterizing hadron structure and fragmentation processes at a constituent level.

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 Fractal Dimension Survey of Active Region Complexity

NASA Technical Reports Server (NTRS)

McAteer, R. T. James; Gallagher, Peter; Ireland, Jack

2005-01-01

A new approach to quantifying the magnetic complexity of active regions using a fractal dimension measure is presented. This fully-automated approach uses full disc MDI magnetograms of active regions from a large data set (2742 days of the SoHO mission; 9342 active regions) to compare the calculated fractal dimension to both Mount Wilson classification and flare rate. The main Mount Wilson classes exhibit no distinct fractal dimension distribution, suggesting a self-similar nature of all active regions. Solar flare productivity exhibits an increase in both the frequency and GOES X-ray magnitude of flares from regions with higher fractal dimensions. Specifically a lower threshold fractal dimension of 1.2 and 1.25 exists as a necessary, but not sufficient, requirement for an active region to produce M- and X-class flares respectively .

A Tutorial Review on Fractal Spacetime and Fractional Calculus

NASA Astrophysics Data System (ADS)

He, Ji-Huan

2014-11-01

This tutorial review of fractal-Cantorian spacetime and fractional calculus begins with Leibniz's notation for derivative without limits which can be generalized to discontinuous media like fractal derivative and q-derivative of quantum calculus. Fractal spacetime is used to elucidate some basic properties of fractal which is the foundation of fractional calculus, and El Naschie's mass-energy equation for the dark energy. The variational iteration method is used to introduce the definition of fractional derivatives. Fractal derivative is explained geometrically and q-derivative is motivated by quantum mechanics. Some effective analytical approaches to fractional differential equations, e.g., the variational iteration method, the homotopy perturbation method, the exp-function method, the fractional complex transform, and Yang-Laplace transform, are outlined and the main solution processes are given.

Contour fractal analysis of grains

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

An analytical study on groundwater flow in drainage basins with horizontal wells

NASA Astrophysics Data System (ADS)

Wang, Jun-Zhi; Jiang, Xiao-Wei; Wan, Li; Wang, Xu-Sheng; Li, Hailong

2014-06-01

Analytical studies on release/capture zones are often limited to a uniform background groundwater flow. In fact, for basin-scale problems, the undulating water table would lead to the development of hierarchically nested flow systems, which are more complex than a uniform flow. Under the premise that the water table is a replica of undulating topography and hardly influenced by wells, an analytical solution of hydraulic head is derived for a two-dimensional cross section of a drainage basin with horizontal injection/pumping wells. Based on the analytical solution, distributions of hydraulic head, stagnation points and flow systems (including release/capture zones) are explored. The superposition of injection/pumping wells onto the background flow field leads to the development of new internal stagnation points and new flow systems (including release/capture zones). Generally speaking, the existence of n injection/pumping wells would result in up to n new internal stagnation points and up to 2n new flow systems (including release/capture zones). The analytical study presented, which integrates traditional well hydraulics with the theory of regional groundwater flow, is useful in understanding basin-scale groundwater flow influenced by human activities.

Variable High Order Multiblock Overlapping Grid Methods for Mixed Steady and Unsteady Multiscale Viscous Flows

NASA Technical Reports Server (NTRS)

Sjogreen, Bjoern; Yee, H. C.

2007-01-01

Flows containing steady or nearly steady strong shocks in parts of the flow field, and unsteady turbulence with shocklets on other parts of the flow field are difficult to capture accurately and efficiently employing the same numerical scheme even under the multiblock grid or adaptive grid refinement framework. On one hand, sixth-order or higher shock-capturing methods are appropriate for unsteady turbulence with shocklets. On the other hand, lower order shock-capturing methods are more effective for strong steady shocks in terms of convergence. In order to minimize the shortcomings of low order and high order shock-capturing schemes for the subject flows,a multi- block overlapping grid with different orders of accuracy on different blocks is proposed. Test cases to illustrate the performance of the new solver are included.

Editorial

NASA Astrophysics Data System (ADS)

Liu, Shuai

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

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.

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.

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

NASA Astrophysics Data System (ADS)

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

2016-04-01

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

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

PubMed

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

2014-01-01

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

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

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).

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

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.

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

Ulam method and fractal Weyl law for Perron-Frobenius operators

NASA Astrophysics Data System (ADS)

Ermann, L.; Shepelyansky, D. L.

2010-06-01

We use the Ulam method to study spectral properties of the Perron-Frobenius operators of dynamical maps in a chaotic regime. For maps with absorption we show numerically that the spectrum is characterized by the fractal Weyl law recently established for nonunitary operators describing poles of quantum chaotic scattering with the Weyl exponent ν = d-1, where d is the fractal dimension of corresponding strange set of trajectories nonescaping in future times. In contrast, for dissipative maps we numerically find the Weyl exponent ν = d/2 where d is the fractal dimension of strange attractor. The Weyl exponent can be also expressed via the relation ν = d0/2 where d0 is the fractal dimension of the invariant sets. We also discuss the properties of eigenvalues and eigenvectors of such operators characterized by the fractal Weyl law.

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

PubMed

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

2016-01-01

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

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

A lateral electrophoretic flow diagnostic assay

PubMed Central

Lin, Robert; Skandarajah, Arunan; Gerver, Rachel E.; Neira, Hector D.; Fletcher, Daniel A.

2015-01-01

Immunochromatographic assays are a cornerstone tool in disease screening. To complement existing lateral flow assays (based on wicking flow) we introduce a lateral flow format that employs directed electrophoretic transport. The format is termed a “lateral e-flow assay” and is designed to support multiplexed detection using immobilized reaction volumes of capture antigen. To fabricate the lateral e-flow device, we employ mask-based UV photopatterning to selectively immobilize unmodified capture antigen along the microchannel in a barcode-like pattern. The channel-filling polyacrylamide hydrogel incorporates a photoactive moiety (benzophenone) to immobilize capture antigen to the hydrogel without a priori antigen modification. We report a heterogeneous sandwich assay using low-power electrophoresis to drive biospecimen through the capture antigen barcode. Fluorescence barcode readout is collected via a low-resource appropriate imaging system (CellScope). We characterize lateral e-flow assay performance and demonstrate a serum assay for antibodies to the hepatitis C virus (HCV). In a pilot study, the lateral e-flow assay positively identifies HCV+ human sera in 60 min. The lateral e-flow assay provides a flexible format for conducting multiplexed immunoassays relevant to confirmatory diagnosis in near-patient settings. PMID:25608872

Comprehensive Fractal Description of Porosity of Coal of Different Ranks

PubMed Central

Ren, Jiangang; Zhang, Guocheng; Song, Zhimin; Liu, Gaofeng; Li, Bing

2014-01-01

We selected, as the objects of our research, lignite from the Beizao Mine, gas coal from the Caiyuan Mine, coking coal from the Xiqu Mine, and anthracite from the Guhanshan Mine. We used the mercury intrusion method and the low-temperature liquid nitrogen adsorption method to analyze the structure and shape of the coal pores and calculated the fractal dimensions of different aperture segments in the coal. The experimental results show that the fractal dimension of the aperture segment of lignite, gas coal, and coking coal with an aperture of greater than or equal to 10 nm, as well as the fractal dimension of the aperture segment of anthracite with an aperture of greater than or equal to 100 nm, can be calculated using the mercury intrusion method; the fractal dimension of the coal pore, with an aperture range between 2.03 nm and 361.14 nm, can be calculated using the liquid nitrogen adsorption method, of which the fractal dimensions bounded by apertures of 10 nm and 100 nm are different. Based on these findings, we defined and calculated the comprehensive fractal dimensions of the coal pores and achieved the unity of fractal dimensions for full apertures of coal pores, thereby facilitating, overall characterization for the heterogeneity of the coal pore structure. PMID:24955407

Fractal Characteristics of Soil Retention Curve and Particle Size Distribution with Different Vegetation Types in Mountain Areas of Northern China.

PubMed

Niu, Xiang; Gao, Peng; Wang, Bing; Liu, Yu

2015-12-03

Based on fractal theory, the fractal characteristics of soil particle size distribution (PSD) and soil water retention curve (WRC) under the five vegetation types were studied in the mountainous land of Northern China. Results showed that: (1) the fractal parameters of soil PSD and soil WRC varied greatly under each different vegetation type, with Quercus acutissima Carr. and Robina pseudoacacia Linn. mixed plantation (QRM) > Pinus thunbergii Parl. and Pistacia chinensis Bunge mixed plantation (PPM) > Pinus thunbergii Parl. (PTP) > Juglans rigia Linn. (JRL) > abandoned grassland (ABG); (2) the soil fractal dimensions of woodlands (QRM, PPM, PTP and JRL) were significantly higher than that in ABG, and mixed forests (QRM and PPM) were higher than that in pure forests (PTP and JRL); (3) the fractal dimension of soil was positively correlated with the silt and clay content but negatively correlated with the sand content; and (4) the fractal dimension of soil PSD was positively correlated with the soil WRC. These indicated that the fractal parameters of soil PSD and soil WRC could act as quantitative indices to reflect the physical properties of the soil, and could be used to describe the influences of the Return Farmland to Forests Projects on soil structure.

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.

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

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 Characteristics of Soil Retention Curve and Particle Size Distribution with Different Vegetation Types in Mountain Areas of Northern China

PubMed Central

Niu, Xiang; Gao, Peng; Wang, Bing; Liu, Yu

2015-01-01

Based on fractal theory, the fractal characteristics of soil particle size distribution (PSD) and soil water retention curve (WRC) under the five vegetation types were studied in the mountainous land of Northern China. Results showed that: (1) the fractal parameters of soil PSD and soil WRC varied greatly under each different vegetation type, with Quercus acutissima Carr. and Robina pseudoacacia Linn. mixed plantation (QRM) > Pinus thunbergii Parl. and Pistacia chinensis Bunge mixed plantation (PPM) > Pinus thunbergii Parl. (PTP) > Juglans rigia Linn. (JRL) > abandoned grassland (ABG); (2) the soil fractal dimensions of woodlands (QRM, PPM, PTP and JRL) were significantly higher than that in ABG, and mixed forests (QRM and PPM) were higher than that in pure forests (PTP and JRL); (3) the fractal dimension of soil was positively correlated with the silt and clay content but negatively correlated with the sand content; and (4) the fractal dimension of soil PSD was positively correlated with the soil WRC. These indicated that the fractal parameters of soil PSD and soil WRC could act as quantitative indices to reflect the physical properties of the soil, and could be used to describe the influences of the Return Farmland to Forests Projects on soil structure. PMID:26633458

Effect of fractal silver electrodes on charge collection and light distribution in semiconducting organic polymer films

DOE PAGES

Chamousis, Rachel L.; Chang, Lilian; Watterson, William J.; ...

2014-08-21

Living organisms use fractal structures to optimize material and energy transport across regions of differing size scales. Here we test the effect of fractal silver electrodes on light distribution and charge collection in organic semiconducting polymer films made of P3HT and PCBM. The semiconducting polymers were deposited onto electrochemically grown fractal silver structures (5000 nm × 500 nm; fractal dimension of 1.71) with PEDOT:PSS as hole-selective interlayer. The fractal silver electrodes appear black due to increased horizontal light scattering, which is shown to improve light absorption in the polymer. According to surface photovoltage spectroscopy, fractal silver electrodes outperform the flatmore » electrodes when the BHJ film thickness is large (>400 nm, 0.4 V photovoltage). Photocurrents of up to 200 microamperes cm -2 are generated from the bulk heterojunction (BHJ) photoelectrodes under 435 nm LED (10–20 mW cm -2) illumination in acetonitrile solution containing 0.005 M ferrocenium hexafluorophosphate as the electron acceptor. In conclusion, the low IPCE values (0.3–0.7%) are due to slow electron transfer to ferrocenium ion and due to shunting along the large metal–polymer interface. Overall, this work provides an initial assessment of the potential of fractal electrodes for organic photovoltaic cells.« less

Power Scaling of the Mainland Shoreline of the Atlantic Coast of the United States

NASA Astrophysics Data System (ADS)

Vasko, E.; Barton, C. C.; Geise, G. R.; Rizki, M. M.

2017-12-01

The fractal dimension of the mainland shoreline of the Atlantic coast of the United Stated from Maine to Homestead, FL has been measured in 1000 km increments using the box-counting method. The shoreline analyzed is the NOAA Medium Resolution Shoreline (https://shoreline.noaa.gov/data/datasheets/medres.html). The shoreline was reconstituted into sequentially numbered X-Y coordinate points in UTM Zone 18N which are spaced 50 meters apart, as measured continuously along the shoreline. We created a MATLAB computer code to measure the fractal dimension by box counting while "walking" along the shoreline. The range of box sizes is 0.7 to 450 km. The fractal dimension ranges from 1.0 to1.5 along the mainland shoreline of the Atlantic coast. The fractal dimension is compared with beach particle sizes (bedrock outcrop, cobbles, pebbles, sand, clay), tidal range, rate of sea level rise, rate and direction of vertical crustal movement, and wave energy, looking for correlation with the measured fractal dimensions. The results show a correlation between high fractal dimensions (1.3 - 1.4) and tectonically emergent coasts, and low fractal dimensions (1.0 - 1.2) along submergent and stable coastal regions. Fractal dimension averages 1.3 along shorelines with shoreline protection structures such as seawalls, jetties, and groins.

Effect of deformation on the thermal conductivity of granular porous media with rough grain surface

NASA Astrophysics Data System (ADS)

Askari, Roohollah; Hejazi, S. Hossein; Sahimi, Muhammad

2017-08-01

Heat transfer in granular porous media is an important phenomenon that is relevant to a wide variety of problems, including geothermal reservoirs and enhanced oil recovery by thermal methods. Resistance to flow of heat in the contact area between the grains strongly influences the effective thermal conductivity of such porous media. Extensive experiments have indicated that the roughness of the grains' surface follows self-affine fractal stochastic functions, and thus, the contact resistance cannot be accounted for by models based on smooth surfaces. Despite the significance of rough contact area, the resistance has been accounted for by a fitting parameter in the models of heat transfer. In this Letter we report on a study of conduction in a packing of particles that contains a fluid of a given conductivity, with each grain having a rough self-affine surface, and is under an external compressive pressure. The deformation of the contact area depends on the fractal dimension that characterizes the grains' rough surface, as well as their Young's modulus. Excellent qualitative agreement is obtained with experimental data. Deformation of granular porous media with grains that have rough self-affine fractal surface is simulated. Thermal contact resistance between grains with rough surfaces is incorporated into the numerical simulation of heat conduction under compressive pressure. By increasing compressive pressure, thermal conductivity is enhanced more in the grains with smoother surfaces and lower Young's modulus. Excellent qualitative agreement is obtained with the experimental data.

Investigation of non-premixed flame combustion characters in GO2/GH2 shear coaxial injectors using non-intrusive optical diagnostics

NASA Astrophysics Data System (ADS)

Dai, Jian; Yu, NanJia; Cai, GuoBiao

2015-12-01

Single-element combustor experiments are conducted for three shear coaxial geometry configuration injectors by using gaseous oxygen and gaseous hydrogen (GO2/GH2) as propellants. During the combustion process, several spatially and timeresolved non-intrusive optical techniques, such as OH planar laser induced fluorescence (PLIF), high speed imaging, and infrared imaging, are simultaneously employed to observe the OH radical concentration distribution, flame fluctuations, and temperature fields. The results demonstrate that the turbulent flow phenomenon of non-premixed flame exhibits a remarkable periodicity, and the mixing ratio becomes a crucial factor to influence the combustion flame length. The high speed and infrared images have a consistent temperature field trend. As for the OH-PLIF images, an intuitionistic local flame structure is revealed by single-shot instantaneous images. Furthermore, the means and standard deviations of OH radical intensity are acquired to provide statistical information regarding the flame, which may be helpful for validation of numerical simulations in future. Parameters of structure configurations, such as impinging angle and oxygen post thickness, play an important role in the reaction zone distribution. Based on a successful flame contour extraction method assembled with non-linear anisotropic diffusive filtering and variational level-set, it is possible to implement a fractal analysis to describe the fractal characteristics of the non-premixed flame contour. As a result, the flame front cannot be regarded as a fractal object. However, this turbulent process presents a self-similarity characteristic.

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.

Scattering from fractals

NASA Astrophysics Data System (ADS)

Hurd, Alan J.

The realization that structures in Nature often can be described by Mandelbrot's fractals has led to a revolution in many areas of physics. The interaction of waves with fractal systems has, understandably, become intensely studied since scattering is the method of choice to probe delicate fractal structures such as chainlike particle aggregates. Not all of these waves are electromagnetic. Neutron scattering, for example, is an important complementary tool to structural studies by X-ray and light scattering. Since the phenomenology of small-angle neutron scattering (SANS), as it is applied to fractal systems, is identical to that of small-angle X-ray scattering (SAXS), it falls within the scope of this paper.

Thermodynamics of photons on fractals.

PubMed

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

2010-12-03

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

Fractals in biology and medicine

NASA Technical Reports Server (NTRS)

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

1995-01-01

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

Numerical Investigation of Vertical Plunging Jet Using a Hybrid Multifluid–VOF Multiphase CFD Solver

DOE PAGES

Shonibare, Olabanji Y.; Wardle, Kent E.

2015-06-28

A novel hybrid multiphase flow solver has been used to conduct simulations of a vertical plunging liquid jet. This solver combines a multifluid methodology with selective interface sharpening to enable simulation of both the initial jet impingement and the long-time entrained bubble plume phenomena. Models are implemented for variable bubble size capturing and dynamic switching of interface sharpened regions to capture transitions between the initially fully segregated flow types into the dispersed bubbly flow regime. It was found that the solver was able to capture the salient features of the flow phenomena under study and areas for quantitative improvement havemore » been explored and identified. In particular, a population balance approach is employed and detailed calibration of the underlying models with experimental data is required to enable quantitative prediction of bubble size and distribution to capture the transition between segregated and dispersed flow types with greater fidelity.« less

Chaos, Fractals, and Polynomials.

ERIC Educational Resources Information Center

Tylee, J. Louis; Tylee, Thomas B.

1996-01-01

Discusses chaos theory; linear algebraic equations and the numerical solution of polynomials, including the use of the Newton-Raphson technique to find polynomial roots; fractals; search region and coordinate systems; convergence; and generating color fractals on a computer. (LRW)

Is Fractal 1/f Scaling in Stream Chemistry Universal?

NASA Astrophysics Data System (ADS)

Hrachowitz, M.

2016-12-01

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/fαnoise 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, i.e. a slope of α=-1 may be a universal and intrinsic property of catchments. That would have considerable implications on the predictability of stream water chemistry, as both, temporal short- and long-range interdependence 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 (α <<-1) indicate the opposite. In fractal systems, i.e. α=-1, this therefore leads to inherent problems of predicting both, short and long-term response patterns. The hypothesis of catchments acting as fractal filters remains to be tested more profoundly. It is not yet clear, if observed inter-catchment variations in α need to be interpreted as noise in the signal or if the variations underlie a systematic pattern and can be explained by some characteristic of catchment function. Here we will 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-) from a wide range of catchments worldwide. The study catchments are physically contrasting, from distinct climate zones, and with distinct landscapes and vegetation. To identify patterns in the variations of α, firstly the power spectra of observed stream chemistry are compared with physical catchment characteristics using methods such as cluster analysis. In a subsequent step, the stream water dynamics of the study catchments are modelled using integrated catchment-scale models. Catchments for which the observed spectral signature can be meaningfully reproduced by the model, are used for further analysis, relating the modelled flux and state dynamics to variations in α, to explore links between flow processes α.

A simple method for estimating the size of nuclei on fractal surfaces

NASA Astrophysics Data System (ADS)

Zeng, Qiang

2017-10-01

Determining the size of nuclei on complex surfaces remains a big challenge in aspects of biological, material and chemical engineering. Here the author reported a simple method to estimate the size of the nuclei in contact with complex (fractal) surfaces. The established approach was based on the assumptions of contact area proportionality for determining nucleation density and the scaling congruence between nuclei and surfaces for identifying contact regimes. It showed three different regimes governing the equations for estimating the nucleation site density. Nuclei in the size large enough could eliminate the effect of fractal structure. Nuclei in the size small enough could lead to the independence of nucleation site density on fractal parameters. Only when nuclei match the fractal scales, the nucleation site density is associated with the fractal parameters and the size of the nuclei in a coupling pattern. The method was validated by the experimental data reported in the literature. The method may provide an effective way to estimate the size of nuclei on fractal surfaces, through which a number of promising applications in relative fields can be envisioned.

Diagnostics of multi-fractality of magnetized plasma inside coronal holes and quiet sun areas

NASA Astrophysics Data System (ADS)

Abramenko, Valentyna

Turbulent and multi-fractal properties of magnetized plasma in solar Coronal Holes (CHs) and Quiet Sun (QS) photosphere were explored using high-resolution magnetograms measured with the New Solar Telescope (NST) at the Big Bear Solar Observatory (BBSO, USA), Hinode/SOT and SDO/HMI instruments. Distribution functions of size and magnetic flux measured for small-scale magnetic elements follow the log-normal law, which implies multi-fractal organization of the magnetic field and the absence of a unique power law for all scales. The magnetograms show multi-fractality in CHs on scales 400 - 10000 km, which becomes better pronounced as the spatial resolution of data improves. Photospheric granulation measured with NST exhibits multi-fractal properties on very small scales of 50 - 600 km. While multi-fractal nature of solar active regions is well known, newly established multi-fractality of weakest magnetic fields on the solar surface, i.e., in CHs and QS, leads us to a conclusion that the entire variety of solar magnetic fields is generated by a unique nonlinear dynamical process.

Unity and diversity in mixing: Stretching, diffusion, breakup, and aggregation in chaotic flows

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

Ottino, J.M.

1991-05-01

Experiments and theory have produced a reasonably good qualitative understanding of the evolution of chaotic mixing of passive tracers, especially in two-dimensional time-periodic flow fields. Such an understanding forms a fabric for the evolution of breakup, aggregation, and diffusion-controlled reactions in more complex flows. These systems can be viewed as a population of microstructures'' whose behavior is dictated by iterations of a chaotic flow; microstructures break, diffuse, and aggregate, causing the population to evolve in space and time. This paper presents simple physical models for such processes. Self-similarity is common to all the problems; examples arise in the context ofmore » the distribution of stretchings within chaotic flows, in the asymptotic evolution of diffusion-reaction processes at striation thickness scales, in the equilibrium distribution of drop sizes generated upon mixing of immiscible fluids, in the equations describing mean-field kinetics of coagulation, in the sequence of actions necessary for the destruction of islands in two-dimensional flow, and in the fractal structure of clusters produced upon aggregation in chaotic flows.« less

How Important Is Connectivity for Surface Water Fluxes? A Generalized Expression for Flow Through Heterogeneous Landscapes

NASA Astrophysics Data System (ADS)

Larsen, Laurel G.; Ma, Jie; Kaplan, David

2017-10-01

How important is hydrologic connectivity for surface water fluxes through heterogeneous floodplains, deltas, and wetlands? While significant for management, this question remains poorly addressed. Here we adopt spatial resistance averaging, based on channel and patch configuration metrics quantifiable from aerial imagery, to produce an upscaled rate law for discharge. Our model suggests that patch coverage largely controls discharge sensitivity, with smaller effects from channel connectivity and vegetation patch fractal dimension. However, connectivity and patch configuration become increasingly important near the percolation threshold and at low water levels. These effects can establish positive feedbacks responsible for substantial flow change in evolving landscapes (14-36%, in our Everglades case study). Connectivity also interacts with other drivers; flow through poorly connected hydroscapes is less resilient to perturbations in other drivers. Finally, we found that flow through heterogeneous patches is alone sufficient to produce non-Manning flow-depth relationships commonly observed in wetlands but previously attributed to depth-varying roughness.

Fractal Patterns and Chaos Games

ERIC Educational Resources Information Center

Devaney, Robert L.

2004-01-01

Teachers incorporate the chaos game and the concept of a fractal into various areas of the algebra and geometry curriculum. The chaos game approach to fractals provides teachers with an opportunity to help students comprehend the geometry of affine transformations.

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.

Fractal astronomy.

NASA Astrophysics Data System (ADS)

Beech, M.

1989-02-01

The author discusses some of the more recent research on fractal astronomy and results presented in several astronomical studies. First, the large-scale structure of the universe is considered, while in another section one drops in scale to examine some of the smallest bodies in our solar system; the comets and meteoroids. The final section presents some thoughts on what influence the fractal ideology might have on astronomy, focusing particularly on the question recently raised by Kadanoff, "Fractals: where's the physics?"

Using Peano Curves to Construct Laplacians on Fractals

NASA Astrophysics Data System (ADS)

Molitor, Denali; Ott, Nadia; Strichartz, Robert

2015-12-01

We describe a new method to construct Laplacians on fractals using a Peano curve from the circle onto the fractal, extending an idea that has been used in the case of certain Julia sets. The Peano curve allows us to visualize eigenfunctions of the Laplacian by graphing the pullback to the circle. We study in detail three fractals: the pentagasket, the octagasket and the magic carpet. We also use the method for two nonfractal self-similar sets, the torus and the equilateral triangle, obtaining appealing new visualizations of eigenfunctions on the triangle. In contrast to the many familiar pictures of approximations to standard Peano curves, that do no show self-intersections, our descriptions of approximations to the Peano curves have self-intersections that play a vital role in constructing graph approximations to the fractal with explicit graph Laplacians that give the fractal Laplacian in the limit.

Emergence of fractal geometry on the surface of human cervical epithelial cells during progression towards cancer

NASA Astrophysics Data System (ADS)

Dokukin, M. E.; Guz, N. V.; Woodworth, C. D.; Sokolov, I.

2015-03-01

Despite considerable advances in understanding the molecular nature of cancer, many biophysical aspects of malignant development are still unclear. Here we study physical alterations of the surface of human cervical epithelial cells during stepwise in vitro development of cancer (from normal to immortal (premalignant), to malignant). We use atomic force microscopy to demonstrate that development of cancer is associated with emergence of simple fractal geometry on the cell surface. Contrary to the previously expected correlation between cancer and fractals, we find that fractal geometry occurs only at a limited period of development when immortal cells become cancerous; further cancer progression demonstrates deviation from fractal. Because of the connection between fractal behaviour and chaos (or far from equilibrium behaviour), these results suggest that chaotic behaviour coincides with the cancer transformation of the immortalization stage of cancer development, whereas further cancer progression recovers determinism of processes responsible for cell surface formation.

Multi-Scale Fractal Analysis of Image Texture and Pattern

NASA Technical Reports Server (NTRS)

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

1999-01-01

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

Surface Fractal Analysis for Estimating the Fracture Energy Absorption of Nanoparticle Reinforced Composites

PubMed Central

Pramanik, Brahmananda; Tadepalli, Tezeswi; Mantena, P. Raju

2012-01-01

In this study, the fractal dimensions of failure surfaces of vinyl ester based nanocomposites are estimated using two classical methods, Vertical Section Method (VSM) and Slit Island Method (SIM), based on the processing of 3D digital microscopic images. Self-affine fractal geometry has been observed in the experimentally obtained failure surfaces of graphite platelet reinforced nanocomposites subjected to quasi-static uniaxial tensile and low velocity punch-shear loading. Fracture energy and fracture toughness are estimated analytically from the surface fractal dimensionality. Sensitivity studies show an exponential dependency of fracture energy and fracture toughness on the fractal dimensionality. Contribution of fracture energy to the total energy absorption of these nanoparticle reinforced composites is demonstrated. For the graphite platelet reinforced nanocomposites investigated, surface fractal analysis has depicted the probable ductile or brittle fracture propagation mechanism, depending upon the rate of loading. PMID:28817017

Multi-Scale Fractal Analysis of Image Texture and Pattern

NASA Technical Reports Server (NTRS)

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

1999-01-01

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

Emerging of fractal geometry on surface of human cervical epithelial cells during progression towards cancer

PubMed Central

Dokukin, M. E.; Guz, N. V.; Woodworth, C.D.; Sokolov, I.

2015-01-01

Despite considerable advances in understanding the molecular nature of cancer, many biophysical aspects of malignant development are still unclear. Here we study physical alterations of the surface of human cervical epithelial cells during stepwise in vitro development of cancer (from normal to immortal (premalignant), to malignant). We use atomic force microscopy to demonstrate that development of cancer is associated with emergence of simple fractal geometry on the cell surface. Contrary to the previously expected correlation between cancer and fractals, we find that fractal geometry occurs only at a limited period of development when immortal cells become cancerous; further cancer progression demonstrates deviation from fractal. Because of the connection between fractal behaviour and chaos (or far from equilibrium behaviour), these results suggest that chaotic behaviour coincides with the cancer transformation of the immortalization stage of cancer development, whereas further cancer progression recovers determinism of processes responsible for cell surface formation. PMID:25844044

Fractal Analysis of Rock Joint Profiles

NASA Astrophysics Data System (ADS)

Audy, Ondřej; Ficker, Tomáš

2017-10-01

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

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.

Navigation performance in virtual environments varies with fractal dimension of landscape.

PubMed

Juliani, Arthur W; Bies, Alexander J; Boydston, Cooper R; Taylor, Richard P; Sereno, Margaret E

2016-09-01

Fractal geometry has been used to describe natural and built environments, but has yet to be studied in navigational research. In order to establish a relationship between the fractal dimension (D) of a natural environment and humans' ability to navigate such spaces, we conducted two experiments using virtual environments that simulate the fractal properties of nature. In Experiment 1, participants completed a goal-driven search task either with or without a map in landscapes that varied in D. In Experiment 2, participants completed a map-reading and location-judgment task in separate sets of fractal landscapes. In both experiments, task performance was highest at the low-to-mid range of D, which was previously reported as most preferred and discriminable in studies of fractal aesthetics and discrimination, respectively, supporting a theory of visual fluency. The applicability of these findings to architecture, urban planning, and the general design of constructed spaces is discussed.

Noninvasive fractal biomarker of clock neurotransmitter disturbance in humans with dementia

PubMed Central

Hu, Kun; Harper, David G.; Shea, Steven A.; Stopa, Edward G.; Scheer, Frank A. J. L.

2013-01-01

Human motor activity has a robust, intrinsic fractal structure with similar patterns from minutes to hours. The fractal activity patterns appear to be physiologically important because the patterns persist under different environmental conditions but are significantly altered/reduced with aging and Alzheimer's disease (AD). Here, we report that dementia patients, known to have disrupted circadian rhythmicity, also have disrupted fractal activity patterns and that the disruption is more pronounced in patients with more amyloid plaques (a marker of AD severity). Moreover, the degree of fractal activity disruption is strongly associated with vasopressinergic and neurotensinergic neurons (two major circadian neurotransmitters) in postmortem suprachiasmatic nucleus (SCN), and can better predict changes of the two neurotransmitters than traditional circadian measures. These findings suggest that the SCN impacts human activity regulation at multiple time scales and that disrupted fractal activity may serve as a non-invasive biomarker of SCN neurodegeneration in dementia. PMID:23863985

PIV measurements in a compact return diffuser under multi-conditions

NASA Astrophysics Data System (ADS)

Zhou, L.; Lu, W. G.; Shi, W. D.

2013-12-01

Due to the complex three-dimensional geometries of impellers and diffusers, their design is a delicate and difficult task. Slight change could lead to significant changes in hydraulic performance and internal flow structure. Conversely, the grasp of the pump's internal flow pattern could benefit from pump design improvement. The internal flow fields in a compact return diffuser have been investigated experimentally under multi-conditions. A special Particle Image Velocimetry (PIV) test rig is designed, and the two-dimensional PIV measurements are successfully conducted in the diffuser mid-plane to capture the complex flow patterns. The analysis of the obtained results has been focused on the flow structure in diffuser, especially under part-load conditions. The vortex and recirculation flow patterns in diffuser are captured and analysed accordingly. Strong flow separation and back flow appeared at the part-load flow rates. Under the design and over-load conditions, the flow fields in diffuser are uniform, and the flow separation and back flow appear at the part-load flow rates, strong back flow is captured at one diffuser passage under 0.2Qdes.

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.

Fractal fluctuations in spatiotemporal variables when walking on a self-paced treadmill.

PubMed

Choi, Jin-Seung; Kang, Dong-Won; Seo, Jeong-Woo; Tack, Gye-Rae

2017-12-08

This study investigated the fractal dynamic properties of stride time (ST), stride length (SL) and stride speed (SS) during walking on a self-paced treadmill (STM) in which the belt speed is automatically controlled by the walking speed. Twelve healthy young subjects participated in the study. The subjects walked at their preferred walking speed under four conditions: STM, STM with a metronome (STM+met), fixed-speed (conventional) treadmill (FTM), and FTM with a metronome (FTM+met). To compare the fractal dynamics between conditions, the mean, variability, and fractal dynamics of ST, SL, and SS were compared. Moreover, the relationship among the variables was examined under each walking condition using three types of surrogates. The mean values of all variables did not differ between the two treadmills, and the variability of all variables was generally larger for STM than for FTM. The use of a metronome resulted in a decrease in variability in ST and SS for all conditions. The fractal dynamic characteristics of SS were maintained with STM, in contrast to FTM, and only the fractal dynamic characteristics of ST disappeared when using a metronome. In addition, the fractal dynamic patterns of the cross-correlated surrogate results were identical to those of all variables for the two treadmills. In terms of the fractal dynamic properties, STM walking was generally closer to overground walking than FTM walking. Although further research is needed, the present results will be useful in research on gait fractal dynamics and rehabilitation. Copyright © 2017 Elsevier Ltd. All rights reserved.

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

PubMed

Risović, Dubravko; Pavlović, Zivko

2013-01-01

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

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

PubMed

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

2017-12-01

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

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

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.

Fractals and foods.

PubMed

Peleg, M

1993-01-01

Fractal geometry and related concepts have had only a very minor impact on food research. The very few reported food applications deal mainly with the characterization of the contours of agglomerated instant coffee particles, the surface morphology of treated starch particles, the microstructure of casein gels viewed as a product limited diffusion aggregation, and the jagged mechanical signatures of crunchy dry foods. Fractal geometry describes objects having morphological features that are scale invariant. A demonstration of the self-similarity of fractal objects can be found in the familiar morphology of cauliflower and broccoli, both foods. Processes regulated by nonlinear dynamics can exhibit a chaotic behavior that has fractal characteristics. Examples are mixing of viscous fluids, turbulence, crystallization, agglomeration, diffusion, and possibly food spoilage.

ELEMENTAL MERCURY CAPTURE BY ACTIVATED CARBON IN A FLOW REACTOR

EPA Science Inventory

The paper gives results of bench-scale experiments in a flow reactor to simulate the entrained-flow capture of elemental mercury (Hgo) using solid sorbents. Adsorption of Hgo by a lignite-based activated carbon (Calgon FGD) was examined at different carbon/mercury (C/Hg) rat...

26 CFR 1.475(a)-4 - Valuation safe harbor.

Code of Federal Regulations, 2011 CFR

2011-04-01

... achieved a predictable net cash flow (for example, a synthetic annuity) that reflects the captured bid-ask spread. This net cash flow is generally impervious to market fluctuations in the values on which the... cash flow attributable to the capture of these spreads. (3) Summary of paragraphs. Paragraph (b) of...

Effects of unidirectional flow shear stresses on the formation, fractal microstructure and rigidity of incipient whole blood clots and fibrin gels.

PubMed

Badiei, N; Sowedan, A M; Curtis, D J; Brown, M R; Lawrence, M J; Campbell, A I; Sabra, A; Evans, P A; Weisel, J W; Chernysh, I N; Nagaswami, C; Williams, P R; Hawkins, K

2015-01-01

Incipient clot formation in whole blood and fibrin gels was studied by the rheometric techniques of controlled stress parallel superposition (CSPS) and small amplitude oscillatory shear (SAOS). The effects of unidirectional shear stress on incipient clot microstructure, formation kinetics and elasticity are reported in terms of the fractal dimension (df) of the fibrin network, the gel network formation time (TGP) and the shear elastic modulus, respectively. The results of this first haemorheological application of CSPS reveal the marked sensitivity of incipient clot microstructure to physiologically relevant levels of shear stress, these being an order of magnitude lower than have previously been studied by SAOS. CSPS tests revealed that exposure of forming clots to increasing levels of shear stress produces a corresponding elevation in df, consistent with the formation of tighter, more compact clot microstructures under unidirectional flow. A corresponding increase in shear elasticity was recorded. The scaling relationship established between shear elasticity and df for fibrin clots and whole blood confirms the fibrin network as the dominant microstructural component of the incipient clot in terms of its response to imposed stress. Supplementary studies of fibrin clot formation by rheometry and microscopy revealed the substantial additional network mass required to increase df and provide evidence to support the hypothesis that microstructural changes in blood clotted under unidirectional shear may be attributed to flow enhanced thrombin generation and activation. CSPS also identified a threshold value of unidirectional shear stress above which no incipient clot formation could be detected. CSPS was shown to be a valuable haemorheological tool for the study of the effects of physiological and pathological levels of shear on clot properties.

Mechanical History Dependence in Carbon Black Suspensions for Flow Batteries: A Rheo-Impedance Study

PubMed Central

2017-01-01

We studied the effects of shear and its history on suspensions of carbon black (CB) in lithium ion battery electrolyte via simultaneous rheometry and electrical impedance spectroscopy. Ketjen black (KB) suspensions showed shear thinning and rheopexy and exhibited a yield stress. Shear step experiments revealed a two time scale response. The immediate effect of decreasing the shear rate is an increase in both viscosity and electronic conductivity. In a much slower secondary response, both quantities change in the opposite direction, leading to a reversal of the initial change in the conductivity. Stepwise increases in the shear rate lead to similar responses in the opposite direction. This remarkable behavior is consistent with a picture in which agglomerating KB particles can stick directly on contact, forming open structures, and then slowly interpenetrate and densify. The fact that spherical CB particles show the opposite slow response suggests that the fractal structure of the KB primary units plays an important role. A theoretical scheme was used to analyze the shear and time-dependent viscosity and conductivity. Describing the agglomerates as effective hard spheres with a fractal architecture and using an effective medium approximation for the conductivity, we found the changes in the derived suspension structure to be in agreement with our qualitative mechanistic picture. This behavior of KB in flow has consequences for the properties of the gel network that is formed immediately after the cessation of shear: both the yield stress and the electronic conductivity increase with the previously applied shear rate. Our findings thus have clear implications for the operation and filling strategies of semisolid flow batteries. PMID:28122184

Flocculation kinetics and aggregate structure of kaolinite mixtures in laminar tube flow.

PubMed

Vaezi G, Farid; Sanders, R Sean; Masliyah, Jacob H

2011-03-01

Flocculation is commonly used in various solid-liquid separation processes in chemical and mineral industries to separate desired products or to treat waste streams. This paper presents an experimental technique to study flocculation processes in laminar tube flow. This approach allows for more realistic estimation of the shear rate to which an aggregate is exposed, as compared to more complicated shear fields (e.g. stirred tanks). A direct sampling method is used to minimize the effect of sampling on the aggregate structure. A combination of aggregate settling velocity and image analysis was used to quantify the structure of the aggregate. Aggregate size, density, and fractal dimension were found to be the most important aggregate structural parameters. The two methods used to determine aggregate fractal dimension were in good agreement. The effects of advective flow through an aggregate's porous structure and transition-regime drag coefficient on the evaluation of aggregate density were considered. The technique was applied to investigate the flocculation kinetics and the evolution of the aggregate structure of kaolin particles with an anionic flocculant under conditions similar to those of oil sands fine tailings. Aggregates were formed using a well controlled two-stage aggregation process. Detailed statistical analysis was performed to investigate the establishment of dynamic equilibrium condition in terms of aggregate size and density evolution. An equilibrium steady state condition was obtained within 90 s of the start of flocculation; after which no further change in aggregate structure was observed. Although longer flocculation times inside the shear field could conceivably cause aggregate structure conformation, statistical analysis indicated that this did not occur for the studied conditions. The results show that the technique and experimental conditions employed here produce aggregates having a well-defined, reproducible structure. Copyright © 2011. Published by Elsevier Inc.

Multifractal spectrum of physiological signals: a mechanism-related approach

NASA Astrophysics Data System (ADS)

Pavlov, Alexey N.; Pavlova, Olga N.; Abdurashitov, Arkady S.; Arinushkin, Pavel A.; Runnova, Anastasiya E.; Semyachkina-Glushkovskaya, Oxana V.

2017-04-01

In this paper we discuss an approach for mechanism-related analysis of physiological signals performed with the wavelet-based multifractal formalism. This approach assumes estimation of the singularity spectrum for the band-pass filtered processes at different physiological conditions in order to provide explanation of the occurred changes in the Hölder exponents and the multi-fractality degree. We illustrate the considered approach using two examples, namely, the dynamics of the cerebral blood flow (CBF) and the electrical activity of the brain.

Surface areas of fractally rough particles studied by scattering

NASA Astrophysics Data System (ADS)

Hurd, Alan J.; Schaefer, Dale W.; Smith, Douglas M.; Ross, Steven B.; Le Méhauté, Alain; Spooner, Steven

1989-05-01

The small-angle scattering from fractally rough surfaces has the potential to give information on the surface area at a given resolution. By use of quantitative neutron and x-ray scattering, a direct comparison of surface areas of fractally rough powders was made between scattering and adsorption techniques. This study supports a recently proposed correction to the theory for scattering from fractal surfaces. In addition, the scattering data provide an independent calibration of molecular adsorbate areas.

Two-Dimensional Animal-Like Fractals in Thin Films

NASA Astrophysics Data System (ADS)

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

1996-02-01

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

Launching the chaotic realm of iso-fractals: A short remark

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

O'Schmidt, Nathan; Katebi, Reza; Corda, Christian

In this brief note, we introduce the new, emerging sub-discipline of iso-fractals by highlighting and discussing the preliminary results of recent works. First, we note the abundance of fractal, chaotic, non-linear, and self-similar structures in nature while emphasizing the importance of studying such systems because fractal geometry is the language of chaos. Second, we outline the iso-fractal generalization of the Mandelbrot set to exemplify the newly generated Mandelbrot iso-sets. Third, we present the cutting-edge notion of dynamic iso-spaces and explain how a mathematical space can be iso-topically lifted with iso-unit functions that (continuously or discretely) change; in the discrete casemore » examples, we mention that iteratively generated sequences like Fibonacci’s numbers and (the complex moduli of) Mandelbrot’s numbers can supply a deterministic chain of iso-units to construct an ordered series of (magnified and/or de-magnified) iso-spaces that are locally iso-morphic. Fourth, we consider the initiation of iso-fractals with Inopin’s holographic ring (IHR) topology and fractional statistics for 2D and 3D iso-spaces. In total, the reviewed iso-fractal results are a significant improvement over traditional fractals because the application of Santilli’s iso-mathematics arms us an extra degree of freedom for attacking problems in chaos. Finally, we conclude by proposing some questions and ideas for future research work.« less

Fractal dimension of turbulent black holes

NASA Astrophysics Data System (ADS)

Westernacher-Schneider, John Ryan

2017-11-01

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

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.

Asynchronous beating of cilia enhances particle capture rate

NASA Astrophysics Data System (ADS)

Ding, Yang; Kanso, Eva

2014-11-01

Many aquatic micro-organisms use beating cilia to generate feeding currents and capture particles in surrounding fluids. One of the capture strategies is to ``catch up'' with particles when a cilium is beating towards the overall flow direction (effective stroke) and intercept particles on the downstream side of the cilium. Here, we developed a 3D computational model of a cilia band with prescribed motion in a viscous fluid and calculated the trajectories of the particles with different sizes in the fluid. We found an optimal particle diameter that maximizes the capture rate. The flow field and particle motion indicate that the low capture rate of smaller particles is due to the laminar flow in the neighbor of the cilia, whereas larger particles have to move above the cilia tips to get advected downstream which decreases their capture rate. We then analyzed the effect of beating coordination between neighboring cilia on the capture rate. Interestingly, we found that asynchrony of the beating of the cilia can enhance the relative motion between a cilium and the particles near it and hence increase the capture rate.

Suction feeding across fish life stages: flow dynamics from larvae to adults and implications for prey capture.

PubMed

Yaniv, Sarit; Elad, David; Holzman, Roi

2014-10-15

Suction feeding is thought to be the primary mode of prey capture in most larval fishes. Similar to adult suction feeders, larvae swim towards their prey while rapidly expanding their mouth cavity to generate an inward flow of water that draws the prey into the mouth. Although larvae are known to experience flows with lower Reynolds numbers than adults, it is unclear how the suction-induced flow field changes throughout ontogeny, and how such changes relate to prey capture performance. To address these questions, we determined mouth dimensions and opening speeds in Sparus aurata from first-feeding larvae to adults. We proceeded to develop a computational model of mouth expansion in order to analyze the scaling of suction flows under the observed parameters. Larval fish produced suction flows that were around two orders of magnitude slower than those of adults. Compared with adult fish, in which flow speed decays steeply with distance in front of the mouth, flow speed decayed more gradually in larval fish. This difference indicates that viscous forces in low Reynolds number flows modify the spatial distribution flow speed in front of the mouth. Consequently, simulated predator-prey encounters showed that larval fish could capture inert prey from a greater distance compared with adults. However, if prey attempted to escape then larval fish performed poorly: simulations inferred capture success in only weakly escaping prey immediately in front of the mouth. These ontogenetic changes in Reynolds number, suction-induced flow field and feeding performance could explain a widespread ontogenetic diet shift from passive prey at early life stages to evasive prey as larvae mature. © 2014. Published by The Company of Biologists Ltd.

Swimming and feeding of mixotrophic biflagellates

NASA Astrophysics Data System (ADS)

Dölger, Julia; Nielsen, Lasse Tor; Kiørboe, Thomas; Andersen, Anders

2017-01-01

Many unicellular flagellates are mixotrophic and access resources through both photosynthesis and prey capture. Their fitness depends on those processes as well as on swimming and predator avoidance. How does the flagellar arrangement and beat pattern of the flagellate affect swimming speed, predation risk due to flow-sensing predators, and prey capture? Here, we describe measured flows around two species of mixotrophic, biflagellated haptophytes with qualitatively different flagellar arrangements and beat patterns. We model the near cell flows using two symmetrically arranged point forces with variable position next to a no-slip sphere. Utilizing the observations and the model we find that puller force arrangements favour feeding, whereas equatorial force arrangements favour fast and quiet swimming. We determine the capture rates of both passive and motile prey, and we show that the flow facilitates transport of captured prey along the haptonema structure. We argue that prey capture alone cannot fulfil the energy needs of the observed species, and that the mixotrophic life strategy is essential for survival.

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.

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.

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.

A physically-based analytical model to describe effective excess charge for streaming potential generation in saturated porous media

NASA Astrophysics Data System (ADS)

Jougnot, D.; Guarracino, L.

2016-12-01

The self-potential (SP) method is considered by most researchers the only geophysical method that is directly sensitive to groundwater flow. One source of SP signals, the so-called streaming potential, results from the presence of an electrical double layer at the mineral-pore water interface. When water flows through the pore space, it gives rise to a streaming current and a resulting measurable electrical voltage. Different approaches have been proposed to predict streaming potentials in porous media. One approach is based on the excess charge which is effectively dragged in the medium by the water flow. Following a recent theoretical framework, we developed a physically-based analytical model to predict the effective excess charge in saturated porous media. In this study, the porous media is described by a bundle of capillary tubes with a fractal pore-size distribution. First, an analytical relationship is derived to determine the effective excess charge for a single capillary tube as a function of the pore water salinity. Then, this relationship is used to obtain both exact and approximated expressions for the effective excess charge at the Representative Elementary Volume (REV) scale. The resulting analytical relationship allows the determination of the effective excess charge as a function of pore water salinity, fractal dimension and hydraulic parameters like porosity and permeability, which are also obtained at the REV scale. This new model has been successfully tested against data from the literature of different sources. One of the main finding of this study is that it provides a mechanistic explanation to the empirical dependence between the effective excess charge and the permeability that has been found by various researchers. The proposed petrophysical relationship also contributes to understand the role of porosity and water salinity on effective excess charge and will help to push further the use of streaming potential to monitor groundwater flow.

Fractality of sensations and the brain health: the theory linking neurodegenerative disorder with distortion of spatial and temporal scale-invariance and fractal complexity of the visible world

PubMed Central

Zueva, Marina V.

2015-01-01

The theory that ties normal functioning and pathology of the brain and visual system with the spatial–temporal structure of the visual and other sensory stimuli is described for the first time in the present study. The deficit of fractal complexity of environmental influences can lead to the distortion of fractal complexity in the visual pathways of the brain and abnormalities of development or aging. The use of fractal light stimuli and fractal stimuli of other modalities can help to restore the functions of the brain, particularly in the elderly and in patients with neurodegenerative disorders or amblyopia. Non-linear dynamics of these physiological processes have a strong base of evidence, which is seen in the impaired fractal regulation of rhythmic activity in aged and diseased brains. From birth to old age, we live in a non-linear world, in which objects and processes with the properties of fractality and non-linearity surround us. Against this background, the evolution of man took place and all periods of life unfolded. Works of art created by man may also have fractal properties. The positive influence of music on cognitive functions is well-known. Insufficiency of sensory experience is believed to play a crucial role in the pathogenesis of amblyopia and age-dependent diseases. The brain is very plastic in its early development, and the plasticity decreases throughout life. However, several studies showed the possibility to reactivate the adult’s neuroplasticity in a variety of ways. We propose that a non-linear structure of sensory information on many spatial and temporal scales is crucial to the brain health and fractal regulation of physiological rhythms. Theoretical substantiation of the author’s theory is presented. Possible applications and the future research that can experimentally confirm or refute the theoretical concept are considered. PMID:26236232

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.

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.

A robust algorithm for optimisation and customisation of fractal dimensions of time series modified by nonlinearly scaling their time derivatives: mathematical theory and practical applications.

PubMed

Fuss, Franz Konstantin

2013-01-01

Standard methods for computing the fractal dimensions of time series are usually tested with continuous nowhere differentiable functions, but not benchmarked with actual signals. Therefore they can produce opposite results in extreme signals. These methods also use different scaling methods, that is, different amplitude multipliers, which makes it difficult to compare fractal dimensions obtained from different methods. The purpose of this research was to develop an optimisation method that computes the fractal dimension of a normalised (dimensionless) and modified time series signal with a robust algorithm and a running average method, and that maximises the difference between two fractal dimensions, for example, a minimum and a maximum one. The signal is modified by transforming its amplitude by a multiplier, which has a non-linear effect on the signal's time derivative. The optimisation method identifies the optimal multiplier of the normalised amplitude for targeted decision making based on fractal dimensions. The optimisation method provides an additional filter effect and makes the fractal dimensions less noisy. The method is exemplified by, and explained with, different signals, such as human movement, EEG, and acoustic signals.

A Robust Algorithm for Optimisation and Customisation of Fractal Dimensions of Time Series Modified by Nonlinearly Scaling Their Time Derivatives: Mathematical Theory and Practical Applications

PubMed Central

2013-01-01

Standard methods for computing the fractal dimensions of time series are usually tested with continuous nowhere differentiable functions, but not benchmarked with actual signals. Therefore they can produce opposite results in extreme signals. These methods also use different scaling methods, that is, different amplitude multipliers, which makes it difficult to compare fractal dimensions obtained from different methods. The purpose of this research was to develop an optimisation method that computes the fractal dimension of a normalised (dimensionless) and modified time series signal with a robust algorithm and a running average method, and that maximises the difference between two fractal dimensions, for example, a minimum and a maximum one. The signal is modified by transforming its amplitude by a multiplier, which has a non-linear effect on the signal's time derivative. The optimisation method identifies the optimal multiplier of the normalised amplitude for targeted decision making based on fractal dimensions. The optimisation method provides an additional filter effect and makes the fractal dimensions less noisy. The method is exemplified by, and explained with, different signals, such as human movement, EEG, and acoustic signals. PMID:24151522

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.

About Schrödinger Equation on Fractals Curves Imbedding in R 3

NASA Astrophysics Data System (ADS)

Golmankhaneh, Alireza Khalili; Golmankhaneh, Ali Khalili; Baleanu, Dumitru

2015-04-01

In this paper we introduced the quantum mechanics on fractal time-space. In a suggested formalism the time and space vary on Cantor-set and Von-Koch curve, respectively. Using Feynman path method in quantum mechanics and F α -calculus we find Schrëdinger equation on on fractal time-space. The Hamiltonian and momentum fractal operator has been indicated. More, the continuity equation and the probability density is given in view of F α -calculus.

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

NASA Astrophysics Data System (ADS)

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

2012-11-01

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

Fractal 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.

The fractal heart — embracing mathematics in the cardiology clinic

PubMed Central

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

2017-01-01

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

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

NASA Astrophysics Data System (ADS)

Su, Junying

2011-11-01

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

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.

Self-organized network of fractal-shaped components coupled through statistical interaction.

PubMed

Ugajin, R

2001-09-01

A dissipative dynamics is introduced to generate self-organized networks of interacting objects, which we call coupled-fractal networks. The growth model is constructed based on a growth hypothesis in which the growth rate of each object is a product of the probability of receiving source materials from faraway and the probability of receiving adhesives from other grown objects, where each object grows to be a random fractal if isolated, but connects with others if glued. The network is governed by the statistical interaction between fractal-shaped components, which can only be identified in a statistical manner over ensembles. This interaction is investigated using the degree of correlation between fractal-shaped components, enabling us to determine whether it is attractive or repulsive.

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.

Where Does the River Run? Lessons from a Semi-Arid River

NASA Astrophysics Data System (ADS)

Meixner, T.; Soto, C. D.; Richter, H.; Uhlman, K.

2009-12-01

Spatial data sets to assess the nature of stream groundwater interactions and the resulting power law/fractal structure of travel time distributions are rare. Spatial data sets can be collected using high technology or by use of a large number of field assistants. The labor intensive way is expensive unless the public can be enlisted as citizen scientists to gather large, robust, spatial data sets robustly and cheaply. Such an effort requires public interest and the ability of a few to organize such an effort at a basin if not regional scale. The San Pedro basin offers such an opportunity for citizen science due to the water resource restrictions of the basins semi-arid climate. Since 1999 The Nature Conservancy, in cooperation with the Upper San Pedro Partnership, the public at large and various university and federal science agency participants, has been mapping where the San Pedro River has water present versus where it is dry. This mapping has used an army of volunteers armed with GPS units, clipboards and their eyes to make the determination if a given 10m reach of the river is wet or dry. These wet/dry mapping data now exist for 11 different annual surveys. These data are unique and enable an investigation of the hydrologic connectedness of flowing waters within this system. Analysis of these data reveals several important findings. The total river area that is wet is strongly correlated with stream flow as observed at three USGS gauges. The correlation is strongest however for 90 day and 1 year average flows rather than more local in time observations such as the daily, 7 day or monthly mean flow at the gauges. This result indicates that where the river is flowing depends on long term hydrologic conditions. The length of river reach that is mapped as wet or dry is indicative of the travel distance and thus time that water travels in the surface (wet) and subsurface (dry) of the river system. The reach length that is mapped as wet follows a power law function (slope of ~ -0.64 approximately) indicating that the fractal travel time distributions observed by others for catchment (Kirchner et al 2001), local to regional scale flow patterns (Cardenas 2008) and for stream solute transport (Haggerty et al. 2005) may have their origin in the fundamental nature of stream groundwater interactions in flowing water systems.

Containment of groundwater contamination plumes: minimizing drawdown by aligning capture wells parallel to regional flow

NASA Astrophysics Data System (ADS)

Christ, John A.; Goltz, Mark N.

2004-01-01

Pump-and-treat systems that are installed to contain contaminated groundwater migration typically involve placement of extraction wells perpendicular to the regional groundwater flow direction at the down gradient edge of a contaminant plume. These wells capture contaminated water for above ground treatment and disposal, thereby preventing further migration of contaminated water down gradient. In this work, examining two-, three-, and four-well systems, we compare well configurations that are parallel and perpendicular to the regional groundwater flow direction. We show that orienting extraction wells co-linearly, parallel to regional flow, results in (1) a larger area of aquifer influenced by the wells at a given total well flow rate, (2) a center and ultimate capture zone width equal to the perpendicular configuration, and (3) more flexibility with regard to minimizing drawdown. Although not suited for some scenarios, we found orienting extraction wells parallel to regional flow along a plume centerline, when compared to a perpendicular configuration, reduces drawdown by up to 7% and minimizes the fraction of uncontaminated water captured.

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

PubMed

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

2014-05-01

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

Characterization of branch complexity by fractal analyses

USGS Publications Warehouse

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

1999-01-01

The comparison between complexity in the sense of space occupancy (box-counting fractal dimension D(c) and information dimension D1) and heterogeneity in the sense of space distribution (average evenness index f and evenness variation coefficient J(cv)) were investigated in mathematical fractal objects and natural branch structures. In general, increased fractal dimension was paired with low heterogeneity. Comparisons between branch architecture in Anthyllis cytisoides under different slope exposure and grazing impact revealed that branches were more complex and more homogeneously distributed for plants on northern exposures than southern, while grazing had no impact during a wet year. Developmental instability was also investigated by the statistical noise of the allometric relation between internode length and node order. In conclusion, our study demonstrated that fractal dimension of branch structure can be used to analyze the structural organization of plants, especially if we consider not only fractal dimension but also shoot distribution within the canopy (lacunarity). These indexes together with developmental instability analyses are good indicators of growth responses to the environment.

Characterization of branch complexity by fractal analyses and detect plant functional adaptations

USGS Publications Warehouse

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

1999-01-01

The comparison between complexity in the sense of space occupancy (box-counting fractal dimension Dc and information dimension DI ) and heterogeneity in the sense of space distribution (average evenness index and evenness variation coefficient JCV) were investigated in mathematical fractal objects and natural branch ¯ J structures. In general, increased fractal dimension was paired with low heterogeneity. Comparisons between branch architecture in Anthyllis cytisoides under different slope exposure and grazing impact revealed that branches were more complex and more homogeneously distributed for plants on northern exposures than southern, while grazing had no impact during a wet year. Developmental instability was also investigated by the statistical noise of the allometric relation between internode length and node order. In conclusion, our study demonstrated that fractal dimension of branch structure can be used to analyze the structural organization of plants, especially if we consider not only fractal dimension but also shoot distribution within the canopy (lacunarity). These indexes together with developmental instability analyses are good indicators of growth responses to the environment.

H-fractal seismic metamaterial with broadband low-frequency bandgaps

NASA Astrophysics Data System (ADS)

Du, Qiujiao; Zeng, Yi; Xu, Yang; Yang, Hongwu; Zeng, Zuoxun

2018-03-01

The application of metamaterial in civil engineering to achieve isolation of a building by controlling the propagation of seismic waves is a substantial challenge because seismic waves, a superposition of longitudinal and shear waves, are more complex than electromagnetic and acoustic waves. In this paper, we design a broadband seismic metamaterial based on H-shaped fractal pillars and report numerical simulation of band structures for seismic surface waves propagating. Comparative study on the band structures of H-fractal seismic metamaterials with different levels shows that a new level of fractal structure creates new band gap, widens the total band gaps and shifts the same band gap towards lower frequencies. Moreover, the vibration modes for H-fractal seismic metamaterials are computed and analyzed to clarify the mechanism of widening band gaps. A numerical investigation of seismic surface waves propagation on a 2D array of fractal unit cells on the surface of semi-infinite substrate is proposed to show the efficiency of earthquake shielding in multiple complete band gaps.

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

NASA Astrophysics Data System (ADS)

Reza Namazi, H.

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

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

NASA Astrophysics Data System (ADS)

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

2016-11-01

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

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.

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

NASA Astrophysics Data System (ADS)

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

2008-09-01

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

Effects of reservoir heterogeneity on scaling of effective mass transfer coefficient for solute transport

NASA Astrophysics Data System (ADS)

Leung, Juliana Y.; Srinivasan, Sanjay

2016-09-01

Modeling transport process at large scale requires proper scale-up of subsurface heterogeneity and an understanding of its interaction with the underlying transport mechanisms. A technique based on volume averaging is applied to quantitatively assess the scaling characteristics of effective mass transfer coefficient in heterogeneous reservoir models. The effective mass transfer coefficient represents the combined contribution from diffusion and dispersion to the transport of non-reactive solute particles within a fluid phase. Although treatment of transport problems with the volume averaging technique has been published in the past, application to geological systems exhibiting realistic spatial variability remains a challenge. Previously, the authors developed a new procedure where results from a fine-scale numerical flow simulation reflecting the full physics of the transport process albeit over a sub-volume of the reservoir are integrated with the volume averaging technique to provide effective description of transport properties. The procedure is extended such that spatial averaging is performed at the local-heterogeneity scale. In this paper, the transport of a passive (non-reactive) solute is simulated on multiple reservoir models exhibiting different patterns of heterogeneities, and the scaling behavior of effective mass transfer coefficient (Keff) is examined and compared. One such set of models exhibit power-law (fractal) characteristics, and the variability of dispersion and Keff with scale is in good agreement with analytical expressions described in the literature. This work offers an insight into the impacts of heterogeneity on the scaling of effective transport parameters. A key finding is that spatial heterogeneity models with similar univariate and bivariate statistics may exhibit different scaling characteristics because of the influence of higher order statistics. More mixing is observed in the channelized models with higher-order continuity. It reinforces the notion that the flow response is influenced by the higher-order statistical description of heterogeneity. An important implication is that when scaling-up transport response from lab-scale results to the field scale, it is necessary to account for the scale-up of heterogeneity. Since the characteristics of higher-order multivariate distributions and large-scale heterogeneity are typically not captured in small-scale experiments, a reservoir modeling framework that captures the uncertainty in heterogeneity description should be adopted.

Persistent fluctuations in stride intervals under fractal auditory stimulation.

PubMed

Marmelat, Vivien; Torre, Kjerstin; Beek, Peter J; Daffertshofer, Andreas

2014-01-01

Stride sequences of healthy gait are characterized by persistent long-range correlations, which become anti-persistent in the presence of an isochronous metronome. The latter phenomenon is of particular interest because auditory cueing is generally considered to reduce stride variability and may hence be beneficial for stabilizing gait. Complex systems tend to match their correlation structure when synchronizing. In gait training, can one capitalize on this tendency by using a fractal metronome rather than an isochronous one? We examined whether auditory cues with fractal variations in inter-beat intervals yield similar fractal inter-stride interval variability as isochronous auditory cueing in two complementary experiments. In Experiment 1, participants walked on a treadmill while being paced by either an isochronous or a fractal metronome with different variation strengths between beats in order to test whether participants managed to synchronize with a fractal metronome and to determine the necessary amount of variability for participants to switch from anti-persistent to persistent inter-stride intervals. Participants did synchronize with the metronome despite its fractal randomness. The corresponding coefficient of variation of inter-beat intervals was fixed in Experiment 2, in which participants walked on a treadmill while being paced by non-isochronous metronomes with different scaling exponents. As expected, inter-stride intervals showed persistent correlations similar to self-paced walking only when cueing contained persistent correlations. Our results open up a new window to optimize rhythmic auditory cueing for gait stabilization by integrating fractal fluctuations in the inter-beat intervals.

Persistent Fluctuations in Stride Intervals under Fractal Auditory Stimulation

PubMed Central

Marmelat, Vivien; Torre, Kjerstin; Beek, Peter J.; Daffertshofer, Andreas

2014-01-01

Stride sequences of healthy gait are characterized by persistent long-range correlations, which become anti-persistent in the presence of an isochronous metronome. The latter phenomenon is of particular interest because auditory cueing is generally considered to reduce stride variability and may hence be beneficial for stabilizing gait. Complex systems tend to match their correlation structure when synchronizing. In gait training, can one capitalize on this tendency by using a fractal metronome rather than an isochronous one? We examined whether auditory cues with fractal variations in inter-beat intervals yield similar fractal inter-stride interval variability as isochronous auditory cueing in two complementary experiments. In Experiment 1, participants walked on a treadmill while being paced by either an isochronous or a fractal metronome with different variation strengths between beats in order to test whether participants managed to synchronize with a fractal metronome and to determine the necessary amount of variability for participants to switch from anti-persistent to persistent inter-stride intervals. Participants did synchronize with the metronome despite its fractal randomness. The corresponding coefficient of variation of inter-beat intervals was fixed in Experiment 2, in which participants walked on a treadmill while being paced by non-isochronous metronomes with different scaling exponents. As expected, inter-stride intervals showed persistent correlations similar to self-paced walking only when cueing contained persistent correlations. Our results open up a new window to optimize rhythmic auditory cueing for gait stabilization by integrating fractal fluctuations in the inter-beat intervals. PMID:24651455

The generalized 20/80 law using probabilistic fractals applied to petroleum field size

USGS Publications Warehouse

Crovelli, R.A.

1995-01-01

Fractal properties of the Pareto probability distribution are used to generalize "the 20/80 law." The 20/80 law is a heuristic law that has evolved over the years into the following rule of thumb for many populations: 20 percent of the population accounts for 80 percent of the total value. The general p100/q100 law in probabilistic form is defined with q as a function of p, where p is the population proportion and q is the proportion of total value. Using the Pareto distribution, the p100/q100 law in fractal form is derived with the parameter q being a fractal, where q unexpectedly possesses the scale invariance property. The 20/80 law is a special case of the p100/q100 law in fractal form. The p100/q100 law in fractal form is applied to petroleum fieldsize data to obtain p and q such that p100% of the oil fields greater than any specified scale or size in a geologic play account for q100% of the total oil of the fields. The theoretical percentages of total resources of oil using the fractal q are extremely close to the empirical percentages from the data using the statistic q. Also, the empirical scale invariance property of the statistic q for the petroleum fieldsize data is in excellent agreement with the theoretical scale invariance property of the fractal q. ?? 1995 Oxford University Press.

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

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

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

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

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.

Evaluation of bias associated with capture maps derived from nonlinear groundwater flow models

USGS Publications Warehouse

Nadler, Cara; Allander, Kip K.; Pohll, Greg; Morway, Eric D.; Naranjo, Ramon C.; Huntington, Justin

2018-01-01

The impact of groundwater withdrawal on surface water is a concern of water users and water managers, particularly in the arid western United States. Capture maps are useful tools to spatially assess the impact of groundwater pumping on water sources (e.g., streamflow depletion) and are being used more frequently for conjunctive management of surface water and groundwater. Capture maps have been derived using linear groundwater flow models and rely on the principle of superposition to demonstrate the effects of pumping in various locations on resources of interest. However, nonlinear models are often necessary to simulate head-dependent boundary conditions and unconfined aquifers. Capture maps developed using nonlinear models with the principle of superposition may over- or underestimate capture magnitude and spatial extent. This paper presents new methods for generating capture difference maps, which assess spatial effects of model nonlinearity on capture fraction sensitivity to pumping rate, and for calculating the bias associated with capture maps. The sensitivity of capture map bias to selected parameters related to model design and conceptualization for the arid western United States is explored. This study finds that the simulation of stream continuity, pumping rates, stream incision, well proximity to capture sources, aquifer hydraulic conductivity, and groundwater evapotranspiration extinction depth substantially affect capture map bias. Capture difference maps demonstrate that regions with large capture fraction differences are indicative of greater potential capture map bias. Understanding both spatial and temporal bias in capture maps derived from nonlinear groundwater flow models improves their utility and defensibility as conjunctive-use management tools.

Structure-Property Relationships of Architectural Coatings by Neutron Methods

NASA Astrophysics Data System (ADS)

Nakatani, Alan

2015-03-01

Architectural coatings formulations are multi-component mixtures containing latex polymer binder, pigment, rheology modifiers, surfactants, and colorants. In order to achieve the desired flow properties for these formulations, measures of the underlying structure of the components as a function of shear rate and the impact of formulation variables on the structure is necessary. We have conducted detailed measurements to understand the evolution under shear of local microstructure and larger scale mesostructure in model architectural coatings formulations by small angle neutron scattering (SANS) and ultra small angle neutron scattering (USANS), respectively. The SANS results show an adsorbed layer of rheology modifier molecules exist on the surface of the latex particles. However, the additional hydrodynamic volume occupied by the adsorbed surface layer is insufficient to account for the observed viscosity by standard hard sphere suspension models (Krieger-Dougherty). The USANS results show the presence of latex aggregates, which are fractal in nature. These fractal aggregates are the primary structures responsible for coatings formulation viscosity. Based on these results, a new model for the viscosity of coatings formulations has been developed, which is capable of reproducing the observed viscosity behavior.

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.

Undergraduate Experiment with Fractal Diffraction Gratings

ERIC Educational Resources Information Center

Monsoriu, Juan A.; Furlan, Walter D.; Pons, Amparo; Barreiro, Juan C.; Gimenez, Marcos H.

2011-01-01

We present a simple diffraction experiment with fractal gratings based on the triadic Cantor set. Diffraction by fractals is proposed as a motivating strategy for students of optics in the potential applications of optical processing. Fraunhofer diffraction patterns are obtained using standard equipment present in most undergraduate physics…

A Double-Minded Fractal

ERIC Educational Resources Information Center

Simoson, Andrew J.

2009-01-01

This article presents a fun activity of generating a double-minded fractal image for a linear algebra class once the idea of rotation and scaling matrices are introduced. In particular the fractal flip-flops between two words, depending on the level at which the image is viewed. (Contains 5 figures.)

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

DTIC Science & Technology

2001-10-25

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

Complex Convective Thermal Fluxes and Vorticity Structure

NASA Astrophysics Data System (ADS)

Redondo, Jose M.; Tellez, Jackson; Sotillos, Laura; Lopez Gonzalez-Nieto, Pilar; Sanchez, Jesus M.; Furmanek, Petr; Diez, Margarita

2015-04-01

Local Diffusion and the topological structure of vorticity and velocity fields is measured in the transition from a homogeneous linearly stratified fluid to a cellular or layered structure by means of convective cooling and/or heating[1,2]. Patterns arise by setting up a convective flow generated by an array of Thermoelectric devices (Peltier/Seebeck cells) these are controlled by thermal PID generating a buoyant heat flux [2]. The experiments described here investigate high Prandtl number mixing using brine and fresh water in order to form density interfaces and low Prandtl number mixing with temperature gradients. The set of dimensionless parameters define conditions of numeric and small scale laboratory modeling of environmental flows. Fields of velocity, density and their gradients were computed and visualized [3,4]. When convective heating and cooling takes place the combination of internal waves and buoyant turbulence is much more complicated if the Rayleigh and Reynolds numbers are high in order to study entrainment and mixing. Using ESS and selfsimilarity structures in the velocity and vorticity fieds and intermittency [3,5] that forms in the non-homogeneous flow is related to mixing and stiring. The evolution of the mixing fronts are compared and the topological characteristics of the merging of plumes and jets in different configurations presenting detailed comparison of the evolution of RM and RT, Jets and Plumes in overall mixing. The relation between structure functions, fractal analysis and spectral analysis can be very useful to determine the evolution of scales. Experimental and numerical results on the advance of a mixing or nonmixing front occurring at a density interface due to body forces [6]and gravitational acceleration are analyzed considering the fractal and spectral structure of the fronts like in removable plate experiments for Rayleigh-Taylor flows. The evolution of the turbulent mixing layer and its complex configuration is studied taking into account the dependence on the initial modes at the early stages and its spectral, self-similar information [3,7-9]. Spectral and Fractal analysis on the images has been used in order to estimate dominant mixing structures as well as the dispersion relations of basic instabilities [4,8. Comparison of the range of entrainment values from laboratory experiments with those ocurring in nature, both in the atmosphere and ocean or in Astrophysics shows the importance of modeling correctly the integral lengthscales of the turbulence. The Entrainment may actually be related to the ratio of the flux to gradient Richardson numbers as well as the Turbulent Schmidt or Prandtl number [6,8] and their structure functions [5]. Turbulent mixing diagnostics are based on schlieren and shadowgraph visualization, planar laser sheet, laser Doppler velocimetry (LDV) and particle image velocimetry (PIV). We are interested by the influence of initial conditions [9](flux gradients of various sizes) on the transition to turbulent mixing, the influence of subsequent vortices and waves, initially in a one dimensional or plane configuration and furthermore in a two-three dimensional configuration with the interface oblique with respect to the horizontal. [1] Redondo J.M. (1992) Termodinámica de los procesos irreversibles, efectos termoeléctricos Rev. Termoelectricidad 2, 16-29.AIT.Pamplona. [2] Redondo J.M., Sanchez J.M. Pascual I. Noriega,G.F.(1995).Thermoelectric regulation for electric cabinets. XVI International Conference in Thermoelectrics, 02-G20. Ed. V. Vedernikov. 456-468. St. Petersburg, Russia. [3] Nicolleau, F.C.G.A.; Cambon, C.; Redondo, J.M.; Vassilicos, J.C.; Reeks, M.; Nowakowski, A.F. (Eds.)(2012) New Approaches in Modeling Multiphase Flows and Dispersion in Turbulence, Fractal Methods and Synthetic Turbulence. ERCOFTAC Series. [4] Redondo J M, Sanchez M A and Cantalapiedra I R (1995). Turbulent Mechanisms in Stratified Flows, Dynamics of Atmospheres and Oceans, 23, 454-462. [5] Mahjoub O.B., Redondo J.M. and Babiano A.(2000) Hyerarchy flux in nonhomogeneous flows in Turbulent diffusion in the environment Eds. Redondo J.M. and Babiano A. 249-260. [6] Matulka A., Redondo J.M. and Carrillo A.(2008) Experiments in stratified and rotating decaying 2D flows, Il Nuovo Cimento 31, 5-6, 757-770. 2008. [7]Fraunie P., Berreba S. Chashechkin Yu.D., Velasco D. and Redondo J.M. (2008) Large eddy simulation and laboratory experiments on the decay of grid wakes in strongly stratified flows. Il Nuovo Cimento C 31, 909-930. [8]Matulka, A., López, P., Redondo, J. M., and Tarquis, A.(2014) On the entrainment coefficient in a forced plume: quantitative effects of source parameters, Nonlin. Processes Geophys., 21, 269-278. [9] Castilla R., Oñate E. and Redondo J.M. (2007) Models, Experiments and Computations in Turbulence. CIMNE, Barcelona, 255.

Geostatistics and Bayesian updating for transmissivity estimation in a multiaquifer system in Manitoba, Canada.

PubMed

Kennedy, Paula L; Woodbury, Allan D

2002-01-01

In ground water flow and transport modeling, the heterogeneous nature of porous media has a considerable effect on the resulting flow and solute transport. Some method of generating the heterogeneous field from a limited dataset of uncertain measurements is required. Bayesian updating is one method that interpolates from an uncertain dataset using the statistics of the underlying probability distribution function. In this paper, Bayesian updating was used to determine the heterogeneous natural log transmissivity field for a carbonate and a sandstone aquifer in southern Manitoba. It was determined that the transmissivity in m2/sec followed a natural log normal distribution for both aquifers with a mean of -7.2 and - 8.0 for the carbonate and sandstone aquifers, respectively. The variograms were calculated using an estimator developed by Li and Lake (1994). Fractal nature was not evident in the variogram from either aquifer. The Bayesian updating heterogeneous field provided good results even in cases where little data was available. A large transmissivity zone in the sandstone aquifer was created by the Bayesian procedure, which is not a reflection of any deterministic consideration, but is a natural outcome of updating a prior probability distribution function with observations. The statistical model returns a result that is very reasonable; that is homogeneous in regions where little or no information is available to alter an initial state. No long range correlation trends or fractal behavior of the log-transmissivity field was observed in either aquifer over a distance of about 300 km.

Using Disney's "Frozen" to Motivate Mathematics: Bringing Fractals into the Classroom

ERIC Educational Resources Information Center

Piatek-Jimenez, Katrina; Phelps, Christine M.

2016-01-01

The movie "Frozen" took the world by storm and this global popularity of the movie and its music can be harnessed by teachers of mathematics. This article builds on the "frozen fractal" lyric from "Let It Go" to incorporate fractal geometry into primary mathematics classrooms.

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 ...

Curriculum Forms: On the Assumed Shapes of Knowing and Knowledge.

ERIC Educational Resources Information Center

Davis, Brent; Sumara, Dennis J.

2000-01-01

Draws on the new field of mathematical study called fractal geometry. Illustrates the pervasiveness and constraining tendencies of classical geometries. Suggests that fractal geometry is a mathematical analogue to fields such as post-modernism, post-structuralism, and ecological theory. Examines how fractal geometry can complement other emergent…

Texture, microstructure, and fractal features of the low-cycle fatigue failure of the metal in pipeline welded joints

NASA Astrophysics Data System (ADS)

Usov, V. V.; Gopkalo, E. E.; Shkatulyak, N. M.; Gopkalo, A. P.; Cherneva, T. S.

2015-09-01

Crystallographic texture and fracture features are studied after low-cycle fatigue tests of laboratory specimens cut from the base metal and the characteristic zones of a welded joint in a pipeline after its longterm operation. The fractal dimensions of fracture surfaces are determined. The fractal dimension is shown to increase during the transition from ductile to quasi-brittle fracture, and a relation between the fractal dimension of a fracture surface and the fatigue life of the specimen is found.

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

NASA Astrophysics Data System (ADS)

Slyamov, Azat

2017-12-01

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

Surface and mass fractals in vapor-phase aggregates

NASA Astrophysics Data System (ADS)

Hurd, Alan J.; Schaefer, Dale W.; Martin, James E.

1987-03-01

Several types of fumed-silica aggregates with differing surface areas were studied over a wide range of spatial resolution by employing both light and neutron scattering. At intermediate length scales, between 100 and 1000 Å, the aggregates are mass fractals with Dm~=1.7-2.0, in basic agreement with simulations of aggregating clusters. At short length scales below 100 Å where the nature of the surfaces of the primary particles dominates the scattering, some of the samples appear to be fractally rough. In particular, a higher surface area seems to be correlated not with smaller primary particles in the aggregates, as previously assumed, but with fractally rough surfaces having Ds as high as 2.5. These may be the first materials discovered to have both mass and surface fractal structure.

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.

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.

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

NASA Astrophysics Data System (ADS)

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

2016-08-01

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

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

PubMed

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

2004-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2010-09-01

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

Assessment of disintegrant efficacy with fractal dimensions from real-time MRI.

PubMed

Quodbach, Julian; Moussavi, Amir; Tammer, Roland; Frahm, Jens; Kleinebudde, Peter

2014-11-20

An efficient disintegrant is capable of breaking up a tablet in the smallest possible particles in the shortest time. Until now, comparative data on the efficacy of different disintegrants is based on dissolution studies or the disintegration time. Extending these approaches, this study introduces a method, which defines the evolution of fractal dimensions of tablets as surrogate parameter for the available surface area. Fractal dimensions are a measure for the tortuosity of a line, in this case the upper surface of a disintegrating tablet. High-resolution real-time MRI was used to record videos of disintegrating tablets. The acquired video images were processed to depict the upper surface of the tablets and a box-counting algorithm was used to estimate the fractal dimensions. The influence of six different disintegrants, of different relative tablet density, and increasing disintegrant concentration was investigated to evaluate the performance of the novel method. Changing relative densities hardly affect the progression of fractal dimensions, whereas an increase in disintegrant concentration causes increasing fractal dimensions during disintegration, which are also reached quicker. Different disintegrants display only minor differences in the maximal fractal dimension, yet the kinetic in which the maximum is reached allows a differentiation and classification of disintegrants. Copyright © 2014 Elsevier B.V. All rights reserved.

A modified abstraction of Sierpiński fractals towards enhanced sensitivity of a cross-coupled bow-tie nanostructure

NASA Astrophysics Data System (ADS)

Hasan, Dihan; Lee, Chengkuo

2018-06-01

We experimentally demonstrate a modified abstraction of a fractal geometry (up to order M = 2), namely the Sierpiński fractal, with intrinsic self-similarity for a multitude of infrared sensing applications. The modification particularly strengthens the dipolar resonance and enables optical magnetism at longer wavelengths on a relatively miniaturized footprint. In contrast to the conventional resonant sensing, we harness the broadband electric field enhancement of the modified fractal patterns originating from the lightning rod effect in the non-resonant regime. We demonstrate strong enhancement of molecular absorption at mid-IR by the fractal patterns in the non-resonant regime even under extreme thermal broadening. Finally, we extend the work towards the functional study of the molecular fingerprint of ultra-thin film (∼5 nm) on a non-complementary metamaterial platform in the non-resonant regime. With the help of the solid state chemical dewetting of the monolayer, we also successfully demonstrate a new type of cross-coupling mediated sensitivity of the multispectral and mutually coupled fractal patterns. The research clearly indicates the usefulness of broadband electric field enhancement by the second order fractal pattern for on chip, complete profiling of mid-IR fingerprints of biological elements, i.e. cell, and protein monolayer on a limited footprint and under versatile morphological states.

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

PubMed

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

2018-04-01

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

QUANTITATIVE METHODS FOR RESERVOIR CHARACTERIZATION AND IMPROVED RECOVERY: APPLICATION TO HEAVY OIL SANDS

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

James W. Castle; Fred J. Molz; Ronald W. Falta

2002-10-30

Improved prediction of interwell reservoir heterogeneity has the potential to increase productivity and to reduce recovery cost for California's heavy oil sands, which contain approximately 2.3 billion barrels of remaining reserves in the Temblor Formation and in other formations of the San Joaquin Valley. This investigation involves application of advanced analytical property-distribution methods conditioned to continuous outcrop control for improved reservoir characterization and simulation, particularly in heavy oil sands. The investigation was performed in collaboration with Chevron Production Company U.S.A. as an industrial partner, and incorporates data from the Temblor Formation in Chevron's West Coalinga Field. Observations of lateral variabilitymore » and vertical sequences observed in Temblor Formation outcrops has led to a better understanding of reservoir geology in West Coalinga Field. Based on the characteristics of stratigraphic bounding surfaces in the outcrops, these surfaces were identified in the subsurface using cores and logs. The bounding surfaces were mapped and then used as reference horizons in the reservoir modeling. Facies groups and facies tracts were recognized from outcrops and cores of the Temblor Formation and were applied to defining the stratigraphic framework and facies architecture for building 3D geological models. The following facies tracts were recognized: incised valley, estuarine, tide- to wave-dominated shoreline, diatomite, and subtidal. A new minipermeameter probe, which has important advantages over previous methods of measuring outcrop permeability, was developed during this project. The device, which measures permeability at the distal end of a small drillhole, avoids surface weathering effects and provides a superior seal compared with previous methods for measuring outcrop permeability. The new probe was used successfully for obtaining a high-quality permeability data set from an outcrop in southern Utah. Results obtained from analyzing the fractal structure of permeability data collected from the southern Utah outcrop and from core permeability data provided by Chevron from West Coalinga Field were used in distributing permeability values in 3D reservoir models. Spectral analyses and the Double Trace Moment method (Lavallee et al., 1991) were used to analyze the scaling and multifractality of permeability data from cores from West Coalinga Field. T2VOC, which is a numerical flow simulator capable of modeling multiphase, multi-component, nonisothermal flow, was used to model steam injection and oil production for a portion of section 36D in West Coalinga Field. The layer structure and permeability distributions of different models, including facies group, facies tract, and fractal permeability models, were incorporated into the numerical flow simulator. The injection and production histories of wells in the study area were modeled, including shutdowns and the occasional conversion of production wells to steam injection wells. The framework provided by facies groups provides a more realistic representation of the reservoir conditions than facies tracts, which is revealed by a comparison of the history-matching for the oil production. Permeability distributions obtained using the fractal results predict the high degree of heterogeneity within the reservoir sands of West Coalinga Field. The modeling results indicate that predictions of oil production are strongly influenced by the geologic framework and by the boundary conditions. The permeability data collected from the southern Utah outcrop, support a new concept for representing natural heterogeneity, which is called the fractal/facies concept. This hypothesis is one of the few potentially simplifying concepts to emerge from recent studies of geological heterogeneity. Further investigation of this concept should be done to more fully apply fractal analysis to reservoir modeling and simulation. Additional outcrop permeability data sets and further analysis of the data from distinct facies will be needed in order to fully develop this new concept.« less

Chord length distributions interpretation using a polydispersed population: Modeling and experiments

NASA Astrophysics Data System (ADS)

Cameirao, A.; Le Ba, H.; Darbouret, M.; Herri, J.-M.; Peytavy, J.-L.; Glénat, P.

2012-03-01

Chord length distributions were measured during the crystallization of gas hydrates in a flow loop. The conditions on the flow loop were similar with the conditions in the marine pipelines. The flow loop was filled with water in oil emulsion and pressurized with methane (7 MPa) at low temperature (277 K). During crystallization water droplets crystallize and agglomerate. The CLD measures were interpreted in a preceding work [Le Ba et al., 2010] [1] by constructing random aggregates with known geometrical proprieties from a monodispersed population of droplets and calculating their CLD. Comparing calculated CLD with CLD from the experiment, the geometrical parameters: number of primary particles and fractal dimension of experimental aggregates are identified. However some differences remained between the experiment and the calculated CLD. In the present work the droplets population was considered polydispersed improving the comparison between the model and the experiment.

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.

Non-stationary dynamics in the bouncing ball: A wavelet perspective

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

Behera, Abhinna K., E-mail: abhinna@iiserkol.ac.in; Panigrahi, Prasanta K., E-mail: pprasanta@iiserkol.ac.in; Sekar Iyengar, A. N., E-mail: ansekar.iyengar@saha.ac.in

2014-12-01

The non-stationary dynamics of a bouncing ball, comprising both periodic as well as chaotic behavior, is studied through wavelet transform. The multi-scale characterization of the time series displays clear signatures of self-similarity, complex scaling behavior, and periodicity. Self-similar behavior is quantified by the generalized Hurst exponent, obtained through both wavelet based multi-fractal detrended fluctuation analysis and Fourier methods. The scale dependent variable window size of the wavelets aptly captures both the transients and non-stationary periodic behavior, including the phase synchronization of different modes. The optimal time-frequency localization of the continuous Morlet wavelet is found to delineate the scales corresponding tomore » neutral turbulence, viscous dissipation regions, and different time varying periodic modulations.« less

X-ray Vision for Aerosol Scientists: LCLS Snapshots of Soot (Narrated)

ScienceCinema

None

2018-01-26

This short conceptual animation depicts how scientists can now simultaneously capture fractal morphology (structure), chemical composition and nanoscale imagery of individual aerosol particles in flight. These particles, known as "PM2.5" because they are smaller than 2.5 microns in diameter, affect climate by interacting with sunlight and impact human health by entering the lungs. The single LCLS laser pulses travel to the Atomic, Molecular and Optical Sciences (AMO) laboratory in the Near Experimental Hall. As we zoom in, we see deep inside a simplified aerosol inlet, where the complex fractal structure of the soot particles, each one completely unique, is shown. Individual soot particles are then delivered into the pulses of the LCLS beam, which destroys them. X-rays are scattered to the detector before the particle is destroyed, giving information about the morphology of the particle. Ion fragments released in the explosion are sent into a mass spectrometer, which measures their mass-to-charge ratio -- giving scientists information about the chemical composition of the particle. Many different particles are analyzed in this manner, allowing scientists to probe variations in the particles due to changes in their environment before being sent through the aerosol inlet. The final visual of aerosols emitted from a factory is representative of the goal that such LCLS aerosol dynamics experiments can provide critical feedback into modeling and understanding combustion, aerosol processes in manufacturing or aerosol effects on climate change.

Developing trading strategies based on fractal finance: An application of MF-DFA in the context of Islamic equities

NASA Astrophysics Data System (ADS)

Dewandaru, Ginanjar; Masih, Rumi; Bacha, Obiyathulla Ismath; Masih, A. Mansur. M.

2015-11-01

We provide a new contribution to trading strategies by using multi-fractal de-trended fluctuation analysis (MF-DFA), imported from econophysics, to complement various momentum strategies. The method provides a single measure that can capture both persistency and anti-persistency in stock prices, accounting for multifractality. This study uses a sample of Islamic stocks listed in the U.S. Dow Jones Islamic market for a sample period covering 16 years starting in 1996. The findings show that the MF-DFA strategy produces monthly excess returns of 6.12%, outperforming other various momentum strategies. Even though the risk of the MF-DFA strategy may be relatively higher, it can still produce a Sharpe ratio of 0.164, which is substantially higher than that of the other strategies. When we control for the MF-DFA factor with the other factors, its pure factor return is still able to yield a monthly excess return of 1.35%. Finally, we combine the momentum and MF-DFA strategies, with the proportions of 90/10, 80/20, and 70/30 and by doing so we demonstrate that the MF-DFA measure can boost the total monthly excess returns as well as Sharpe ratio. The value added is non-linear which implies that the additional returns are associated with lower incremental risk.

Morphological texture assessment of oral bone as a screening tool for osteoporosis

NASA Astrophysics Data System (ADS)

Analoui, Mostafa; Eggertsson, Hafsteinn; Eckert, George

2001-07-01

Three classes of texture analysis approaches have been employed to assess the textural characteristic of oral bone. A set of linear structuring elements was used to compute granulometric features of trabecular bone. Multifractal analysis was also used to compute the fractal dimension of the corresponding tissues. In addition, some statistical features and histomorphometric parameters were computed. To assess the proposed approach we acquired digital intraoral radiographs of 47 subjects (14 males and 33 females). All radiographs were captured at 12 bits/pixel. Images were converted to binary form through a sliding locally adaptive thresholding approach. Each subject was scanned by DEXA for bone dosimetry. Subject were classified into one of the following three categories according World Health Organization (WHO) standard (1) healthy, (2) with osteopenia and (3) osteoporosis. In this study fractal dimension showed very low correlation with bone mineral density (BMD) measurements, which did not reach a level of statistical significance (p<0.5). However, entropy of pattern spectrum (EPS), along with statistical features and histomorphometric parameters, has shown correlation coefficients ranging from low to high, with statistical significance for both males and females. The results of this study indicate the utility of this approach for bone texture analysis. It is conjectured that designing a 2-D structuring element, specially tuned to trabecular bone texture, will increase the efficacy of the proposed method.

[Fractal features of soil particle size in the process of desertification in desert grassland of Ningxia, China].

PubMed

Yan, Xin; An, Hui

2017-10-01

The variation of soil properties, the fractal dimension of soil particle size, and the relationships between fractal dimension of soil particle size and soil properties in the process of desertification in desert grassland of Ningxia were discussed. The results showed that the fractal dimension (D) at different desertification stages in desert grassland varied greatly, the value of D was between 1.69 and 2.62. Except for the 10-20 cm soil layer, the value of D gradually declined with increa sing desertification of desert grassland at 0-30 cm soil layer. In the process of desertification in de-sert grassland, the grassland had the highest values of D , the volume percentage of clay and silt, and the lowest values of the volume percentage of very fine sand and fine sand. However, the mobile dunes had the lowest value of D , the volume percentage of clay and silt, and the highest value of the volume percentage of very fine sand and fine sand. There was a significant positive correlation between the soil fractal dimension value and the volume percentage of soil particles <50 μm, and a significant negative correlation between the soil fractal dimension value and the volume percentage of soil particles >50 μm. The grain size of 50 μm was the critical value for deciding the relationship between the soil particle fractal dimension and the volume percentage. Soil organic matter (SOM) and total nitrogen (TN) decreased gradually with increasing desertification of desert grassland, but soil bulk density increased gradually. Qualitative change from fixed dunes to semi fixed dunes with the rapid decrease of the volume percentage of clay and silt, SOM, TN and the rapid increase of volume percentage of very fine sand and fine sand, soil bulk density. Fractal dimension was significantly correlated to SOM, TN and soil bulk density. Fractal dimension 2.58 was a critical value of fixed dunes and semi fixed dunes. So, the fractal dimension of 2.58 could be taken as the desertification indicator of desert grassland.

[Soil particle size distribution and its fractal dimension among degradation sequences of the alpine meadow in the source region of the Yangtze and Yellow River, Qinghai-Tibetan Plateau, China].

PubMed

Wei, Mao-Hong; Lin, Hui-Long

2014-03-01

The alpine meadow in the source region of the Yangtze and Yellow River is suffering serious deterioration. Though great efforts have been put into, the restoration for the degraded grassland is far from being effective, mainly due to poor understanding of the degradation mechanism of alpine meadow in this region. In order to clarify the formation mechanism of degradation grassland and provide the new ideas for restoration, degradation sequences of the alpine meadow in the source region of the Yangtze and Yellow River were taken as target systems to analyze the soil particle size distribution, the fractal dimension of the soil particle size, and the relationship between soil erosion modulus and fractal dimension. The results showed that, with increasing grassland degradation, the percentage contents of clay increased while the percentage contents of silt sand and very fine sand showed a decreasing trend. The fractal dimension presented a positive correlation with clay among the degradation sequences while negative correlations were found with very fine sand and silt sand. The curvilinear regression of fractal dimension and erosion modulus fitted a quadratic function. Judged by the function, fractal dimension 2.81 was the threshold value of soil erosion. The threshold value has an indicative meaning on predicting the breakout of grazing-induced erosion and on restoration of the degraded grassland. Taking fractal dimension of 2.81 as the restoration indicator, adoption of corresponding measures to make fractal dimension less than 2.81, would an effective way to restore the degradation grassland.

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).

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

Burkholder, Michael B.; Litster, Shawn, E-mail: litster@andrew.cmu.edu

In this study, we analyze the stability of two-phase flow regimes and their transitions using chaotic and fractal statistics, and we report new measurements of dynamic two-phase pressure drop hysteresis that is related to flow regime stability and channel water content. Two-phase flow dynamics are relevant to a variety of real-world systems, and quantifying transient two-phase flow phenomena is important for efficient design. We recorded two-phase (air and water) pressure drops and flow images in a microchannel under both steady and transient conditions. Using Lyapunov exponents and Hurst exponents to characterize the steady-state pressure fluctuations, we develop a new, measurablemore » regime identification criteria based on the dynamic stability of the two-phase pressure signal. We also applied a new experimental technique by continuously cycling the air flow rate to study dynamic hysteresis in two-phase pressure drops, which is separate from steady-state hysteresis and can be used to understand two-phase flow development time scales. Using recorded images of the two-phase flow, we show that the capacitive dynamic hysteresis is related to channel water content and flow regime stability. The mixed-wettability microchannel and in-channel water introduction used in this study simulate a polymer electrolyte fuel cell cathode air flow channel.« less

A comparison of the fractal and JPEG algorithms

NASA Technical Reports Server (NTRS)

Cheung, K.-M.; Shahshahani, M.

1991-01-01

A proprietary fractal image compression algorithm and the Joint Photographic Experts Group (JPEG) industry standard algorithm for image compression are compared. In every case, the JPEG algorithm was superior to the fractal method at a given compression ratio according to a root mean square criterion and a peak signal to noise criterion.

Fractal Music: The Mathematics Behind "Techno" Music

ERIC Educational Resources Information Center

Padula, Janice

2005-01-01

This article describes sound waves, their basis in the sine curve, Fourier's theorem of infinite series, the fractal equation and its application to the composition of music, together with algorithms (such as those employed by meteorologist Edward Lorenz in his discovery of chaos theory) that are now being used to compose fractal music on…

Fractal Simulations of African Design in Pre-College Computing Education

ERIC Educational Resources Information Center

Eglash, Ron; Krishnamoorthy, Mukkai; Sanchez, Jason; Woodbridge, Andrew

2011-01-01

This article describes the use of fractal simulations of African design in a high school computing class. Fractal patterns--repetitions of shape at multiple scales--are a common feature in many aspects of African design. In African architecture we often see circular houses grouped in circular complexes, or rectangular houses in rectangular…

Aqueous synthesis of LiFePO4 with Fractal Granularity.

PubMed

Cabán-Huertas, Zahilia; Ayyad, Omar; Dubal, Deepak P; Gómez-Romero, Pedro

2016-06-03

Lithium iron phosphate (LiFePO4) electrodes with fractal granularity are reported. They were made from a starting material prepared in water by a low cost, easy and environmentally friendly hydrothermal method, thus avoiding the use of organic solvents. Our method leads to pure olivine phase, free of the impurities commonly found after other water-based syntheses. The fractal structures consisted of nanoparticles grown into larger micro-sized formations which in turn agglomerate leading to high tap density electrodes, which is beneficial for energy density. These intricate structures could be easily and effectively coated with a thin and uniform carbon layer for increased conductivity, as it is well established for simpler microstructures. Materials and electrodes were studied by means of XRD, SEM, TEM, SAED, XPS, Raman and TGA. Last but not least, lithium transport through fractal LiFePO4 electrodes was investigated based upon fractal theory. These water-made fractal electrodes lead to high-performance lithium cells (even at high rates) tested by CV and galvanostatic charge-discharge, their performance is comparable to state of the art (but less environmentally friendly) electrodes.

Aqueous synthesis of LiFePO4 with Fractal Granularity

PubMed Central

Cabán-Huertas, Zahilia; Ayyad, Omar; Dubal, Deepak P.; Gómez-Romero, Pedro

2016-01-01

Lithium iron phosphate (LiFePO4) electrodes with fractal granularity are reported. They were made from a starting material prepared in water by a low cost, easy and environmentally friendly hydrothermal method, thus avoiding the use of organic solvents. Our method leads to pure olivine phase, free of the impurities commonly found after other water-based syntheses. The fractal structures consisted of nanoparticles grown into larger micro-sized formations which in turn agglomerate leading to high tap density electrodes, which is beneficial for energy density. These intricate structures could be easily and effectively coated with a thin and uniform carbon layer for increased conductivity, as it is well established for simpler microstructures. Materials and electrodes were studied by means of XRD, SEM, TEM, SAED, XPS, Raman and TGA. Last but not least, lithium transport through fractal LiFePO4 electrodes was investigated based upon fractal theory. These water-made fractal electrodes lead to high-performance lithium cells (even at high rates) tested by CV and galvanostatic charge-discharge, their performance is comparable to state of the art (but less environmentally friendly) electrodes. PMID:27256504

Aqueous synthesis of LiFePO4 with Fractal Granularity

NASA Astrophysics Data System (ADS)

Cabán-Huertas, Zahilia; Ayyad, Omar; Dubal, Deepak P.; Gómez-Romero, Pedro

2016-06-01

Lithium iron phosphate (LiFePO4) electrodes with fractal granularity are reported. They were made from a starting material prepared in water by a low cost, easy and environmentally friendly hydrothermal method, thus avoiding the use of organic solvents. Our method leads to pure olivine phase, free of the impurities commonly found after other water-based syntheses. The fractal structures consisted of nanoparticles grown into larger micro-sized formations which in turn agglomerate leading to high tap density electrodes, which is beneficial for energy density. These intricate structures could be easily and effectively coated with a thin and uniform carbon layer for increased conductivity, as it is well established for simpler microstructures. Materials and electrodes were studied by means of XRD, SEM, TEM, SAED, XPS, Raman and TGA. Last but not least, lithium transport through fractal LiFePO4 electrodes was investigated based upon fractal theory. These water-made fractal electrodes lead to high-performance lithium cells (even at high rates) tested by CV and galvanostatic charge-discharge, their performance is comparable to state of the art (but less environmentally friendly) electrodes.

Fractal Dimensions of Umbral and Penumbral Regions of Sunspots

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

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.

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.

Fractal Signals & Space-Time Cartoons

NASA Astrophysics Data System (ADS)

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

2016-03-01

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

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

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

PubMed

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

2014-08-01

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

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

PubMed Central

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

2012-01-01

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

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

PubMed

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

2016-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

Process for applying control variables having fractal structures

DOEpatents

Bullock, IV, Jonathan S.; Lawson, Roger L.

1996-01-01

A process and apparatus for the application of a control variable having a fractal structure to a body or process. The process of the present invention comprises the steps of generating a control variable having a fractal structure and applying the control variable to a body or process reacting in accordance with the control variable. The process is applicable to electroforming where first, second and successive pulsed-currents are applied to cause the deposition of material onto a substrate, such that the first pulsed-current, the second pulsed-current, and successive pulsed currents form a fractal pulsed-current waveform.

Process for applying control variables having fractal structures

DOEpatents

Bullock, J.S. IV; Lawson, R.L.

1996-01-23

A process and apparatus are disclosed for the application of a control variable having a fractal structure to a body or process. The process of the present invention comprises the steps of generating a control variable having a fractal structure and applying the control variable to a body or process reacting in accordance with the control variable. The process is applicable to electroforming where first, second and successive pulsed-currents are applied to cause the deposition of material onto a substrate, such that the first pulsed-current, the second pulsed-current, and successive pulsed currents form a fractal pulsed-current waveform. 3 figs.

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

NASA Astrophysics Data System (ADS)

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

2011-04-01

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

Fractal-based wideband invisibility cloak

NASA Astrophysics Data System (ADS)

Cohen, Nathan; Okoro, Obinna; Earle, Dan; Salkind, Phil; Unger, Barry; Yen, Sean; McHugh, Daniel; Polterzycki, Stefan; Shelman-Cohen, A. J.

2015-03-01

A wideband invisibility cloak (IC) at microwave frequencies is described. Using fractal resonators in closely spaced (sub wavelength) arrays as a minimal number of cylindrical layers (rings), the IC demonstrates that it is physically possible to attain a `see through' cloaking device with: (a) wideband coverage; (b) simple and attainable fabrication; (c) high fidelity emulation of the free path; (d) minimal side scattering; (d) a near absence of shadowing in the scattering. Although not a practical device, this fractal-enabled technology demonstrator opens up new opportunities for diverted-image (DI) technology and use of fractals in wideband optical, infrared, and microwave applications.

Vasomotor tone does not affect perfusion heterogeneity and gas exchange in normal primate lungs during normoxia

NASA Technical Reports Server (NTRS)

Glenny, R. W.; Robertson, H. T.; Hlastala, M. P.

2000-01-01

To determine whether vasoregulation is an important cause of pulmonary perfusion heterogeneity, we measured regional blood flow and gas exchange before and after giving prostacyclin (PGI(2)) to baboons. Four animals were anesthetized with ketamine and mechanically ventilated. Fluorescent microspheres were used to mark regional perfusion before and after PGI(2) infusion. The lungs were subsequently excised, dried inflated, and diced into approximately 2-cm(3) pieces (n = 1,208-1,629 per animal) with the spatial coordinates recorded for each piece. Blood flow to each piece was determined for each condition from the fluorescent signals. Blood flow heterogeneity did not change with PGI(2) infusion. Two other measures of spatial blood flow distribution, the fractal dimension and the spatial correlation, did not change with PGI(2) infusion. Alveolar-arterial O(2) differences did not change with PGI(2) infusion. We conclude that, in normal primate lungs during normoxia, vasomotor tone is not a significant cause of perfusion heterogeneity. Despite the heterogeneous distribution of blood flow, active regulation of regional perfusion is not required for efficient gas exchange.

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.

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.

A scale-entropy diffusion equation to describe the multi-scale features of turbulent flames near a wall

NASA Astrophysics Data System (ADS)

Queiros-Conde, D.; Foucher, F.; Mounaïm-Rousselle, C.; Kassem, H.; Feidt, M.

2008-12-01

Multi-scale features of turbulent flames near a wall display two kinds of scale-dependent fractal features. In scale-space, an unique fractal dimension cannot be defined and the fractal dimension of the front is scale-dependent. Moreover, when the front approaches the wall, this dependency changes: fractal dimension also depends on the wall-distance. Our aim here is to propose a general geometrical framework that provides the possibility to integrate these two cases, in order to describe the multi-scale structure of turbulent flames interacting with a wall. Based on the scale-entropy quantity, which is simply linked to the roughness of the front, we thus introduce a general scale-entropy diffusion equation. We define the notion of “scale-evolutivity” which characterises the deviation of a multi-scale system from the pure fractal behaviour. The specific case of a constant “scale-evolutivity” over the scale-range is studied. In this case, called “parabolic scaling”, the fractal dimension is a linear function of the logarithm of scale. The case of a constant scale-evolutivity in the wall-distance space implies that the fractal dimension depends linearly on the logarithm of the wall-distance. We then verified experimentally, that parabolic scaling represents a good approximation of the real multi-scale features of turbulent flames near a wall.

Polymer Self-Assembly into Unique Fractal Nanostructures in Solution by a One-Shot Synthetic Procedure.

PubMed

Shin, Suyong; Gu, Ming-Long; Yu, Chin-Yang; Jeon, Jongseol; Lee, Eunji; Choi, Tae-Lim

2018-01-10

A fractal nanostructure having a high surface area is potentially useful in sensors, catalysts, functional coatings, and biomedical and electronic applications. Preparation of fractal nanostructures on solid substrates has been reported using various inorganic or organic compounds. However, achieving such a process using polymers in solution has been extremely challenging. Here, we report a simple one-shot preparation of polymer fractal nanostructures in solution via an unprecedented assembly mechanism controlled by polymerization and self-assembly kinetics. This was possible only because one monomer was significantly more reactive than the other, thereby easily forming a diblock copolymer microstructure. Then, the second insoluble block containing poly(p-phenylenevinylene) (PPV) without any side chains spontaneously underwent self-assembly during polymerization by an in situ nanoparticlization of conjugated polymers (INCP) method. The formation of fractal structures in solution was confirmed by various imaging techniques such as atomic force microscopy, transmission electron microscopy (TEM), and cryogenic TEM. The diffusion-limited aggregation theory was adopted to explain the branching patterns of the fractal nanostructures according to the changes in polymerization conditions such as the monomer concentration and the presence of additives. Finally, after detailed kinetic analyses, we proposed a plausible mechanism for the formation of unique fractal nanostructures, where the gradual formation and continuous growth of micelles in a chain-growth-like manner were accounted for.

Numerical analysis of scalar dissipation length-scales and their scaling properties

NASA Astrophysics Data System (ADS)

Vaishnavi, Pankaj; Kronenburg, Andreas

2006-11-01

Scalar dissipation rate, χ, is fundamental to the description of scalar-mixing in turbulent non-premixed combustion. Most contributions to the statistics for χ come from the finest turbulent mixing-scales and thus its adequate characterisation requires good resolution. Reliable χ-measurement is complicated by the trade-off between higher resolution and greater signal-to-noise ratio. Thus, the present numerical study utilises the error-free mixture fraction, Z, and fluid mechanical data from the turbulent reacting jet DNS of Pantano (2004). The aim is to quantify the resolution requirements for χ-measurement in terms of easily measurable properties of the flow like the integral-scale Reynolds number, Reδ, using spectral and spatial-filtering [cf. Barlow and Karpetis (2005)] analyses. Analysis of the 1-D cross-stream dissipation spectra enables the estimation of the dissipation length scales. It is shown that these spectrally-computed scales follow the expected Kolmogorov scaling with Reδ-0.75 . The work also involves local smoothening of the instantaneous χ-field over a non-overlapping spatial-interval (filter-width, wf), to study the smoothened χ-value as a function of wf, as wf is extrapolated to the smallest scale of interest. The dissipation length-scales thus captured show a stringent Reδ-1 scaling, compared to the usual Kolmogorov-type. This concurs with the criterion of 'resolution adequacy' of the DNS, as set out by Sreenivasan (2004) using the theory of multi-fractals.

An Assessment of Stream Confluence Flow Dynamics using Large Scale Particle Image Velocimetry Captured from Unmanned Aerial Systems

NASA Astrophysics Data System (ADS)

Lewis, Q. W.; Rhoads, B. L.

2017-12-01

The merging of rivers at confluences results in complex three-dimensional flow patterns that influence sediment transport, bed morphology, downstream mixing, and physical habitat conditions. The capacity to characterize comprehensively flow at confluences using traditional sensors, such as acoustic Doppler velocimeters and profiles, is limited by the restricted spatial resolution of these sensors and difficulties in measuring velocities simultaneously at many locations within a confluence. This study assesses two-dimensional surficial patterns of flow structure at a small stream confluence in Illinois, USA, using large scale particle image velocimetry (LSPIV) derived from videos captured by unmanned aerial systems (UAS). The method captures surface velocity patterns at high spatial and temporal resolution over multiple scales, ranging from the entire confluence to details of flow within the confluence mixing interface. Flow patterns at high momentum ratio are compared to flow patterns when the two incoming flows have nearly equal momentum flux. Mean surface flow patterns during the two types of events provide details on mean patterns of surface flow in different hydrodynamic regions of the confluence and on changes in these patterns with changing momentum flux ratio. LSPIV data derived from the highest resolution imagery also reveal general characteristics of large-scale vortices that form along the shear layer between the flows during the high-momentum ratio event. The results indicate that the use of LSPIV and UAS is well-suited for capturing in detail mean surface patterns of flow at small confluences, but that characterization of evolving turbulent structures is limited by scale considerations related to structure size, image resolution, and camera instability. Complementary methods, including camera platforms mounted at fixed positions close to the water surface, provide opportunities to accurately characterize evolving turbulent flow structures in confluences.

Evolutionary and Cognitive Motivations for Fractal Art in Art and Design Education

ERIC Educational Resources Information Center

Joye, Yannick

2005-01-01

Humans are endowed with cognitive modules specialised in processing information about the class of natural things. Due to their naturalness, fractal art and design can contribute to developing these modules, and trigger affective responses that are associated with certain natural objects. It is argued that exposure to fractals in an art and design…

An application of geostatistics and fractal geometry for reservoir characterization

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

Aasum, Y.; Kelkar, M.G.; Gupta, S.P.

1991-03-01

This paper presents an application of geostatistics and fractal geometry concepts for 2D characterization of rock properties (k and {phi}) in a dolomitic, layered-cake reservoir. The results indicate that lack of closely spaced data yield effectively random distributions of properties. Further, incorporation of geology reduces uncertainties in fractal interpolation of wellbore properties.

Definition of a temporal distribution index for high temporal resolution precipitation data over Peninsular Spain and the Balearic Islands: the fractal dimension; and its synoptic implications

NASA Astrophysics Data System (ADS)

Meseguer-Ruiz, Oliver; Osborn, Timothy J.; Sarricolea, Pablo; Jones, Philip D.; Cantos, Jorge Olcina; Serrano-Notivoli, Roberto; Martin-Vide, Javier

2018-03-01

Precipitation on the Spanish mainland and in the Balearic archipelago exhibits a high degree of spatial and temporal variability, regardless of the temporal resolution of the data considered. The fractal dimension indicates the property of self-similarity, and in the case of this study, wherein it is applied to the temporal behaviour of rainfall at a fine (10-min) resolution from a total of 48 observatories, it provides insights into its more or less convective nature. The methodology of Jenkinson & Collison which automatically classifies synoptic situations at the surface, as well as an adaptation of this methodology at 500 hPa, was applied in order to gain insights into the synoptic implications of extreme values of the fractal dimension. The highest fractal dimension values in the study area were observed in places with precipitation that has a more random behaviour over time with generally high totals. Four different regions in which the atmospheric mechanisms giving rise to precipitation at the surface differ from the corresponding above-ground mechanisms have been identified in the study area based on the fractal dimension. In the north of the Iberian Peninsula, high fractal dimension values are linked to a lower frequency of anticyclonic situations, whereas the opposite occurs in the central region. In the Mediterranean, higher fractal dimension values are associated with a higher frequency of the anticyclonic type and a lower frequency of the advective type from the east. In the south, lower fractal dimension values indicate higher frequency with respect to the anticyclonic type from the east and lower frequency with respect to the cyclonic type.

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

PubMed Central

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

2013-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2012-07-01

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

On the fractal morphology of combustion-generated soot aggregates

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

Koylu, U.O.

1995-12-31

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