fractal random fields: Topics by Science.gov

Sample records for fractal random fields

Fractal planetary rings: Energy inequalities and random field model

NASA Astrophysics Data System (ADS)

Malyarenko, Anatoliy; Ostoja-Starzewski, Martin

2017-12-01

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

PubMed

Xu, Jia; Li, Chao; Li, Yiran; Lim, Chee Wah; Zhu, Zhiwen

2018-05-04

In this paper, a kind of single-walled carbon nanotube nonlinear model is developed and the strongly nonlinear dynamic characteristics of such carbon nanotubes subjected to random magnetic field are studied. The nonlocal effect of the microstructure is considered based on Eringen’s differential constitutive model. The natural frequency of the strongly nonlinear dynamic system is obtained by the energy function method, the drift coefficient and the diffusion coefficient are verified. The stationary probability density function of the system dynamic response is given and the fractal boundary of the safe basin is provided. Theoretical analysis and numerical simulation show that stochastic resonance occurs when varying the random magnetic field intensity. The boundary of safe basin has fractal characteristics and the area of safe basin decreases when the intensity of the magnetic field permeability increases.
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
Simulating and mapping spatial complexity using multi-scale techniques

USGS Publications Warehouse

De Cola, L.

1994-01-01

A central problem in spatial analysis is the mapping of data for complex spatial fields using relatively simple data structures, such as those of a conventional GIS. This complexity can be measured using such indices as multi-scale variance, which reflects spatial autocorrelation, and multi-fractal dimension, which characterizes the values of fields. These indices are computed for three spatial processes: Gaussian noise, a simple mathematical function, and data for a random walk. Fractal analysis is then used to produce a vegetation map of the central region of California based on a satellite image. This analysis suggests that real world data lie on a continuum between the simple and the random, and that a major GIS challenge is the scientific representation and understanding of rapidly changing multi-scale fields. -Author
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.
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.
Skin cancer texture analysis of OCT images based on Haralick, fractal dimension, Markov random field features, and the complex directional field features

NASA Astrophysics Data System (ADS)

Raupov, Dmitry S.; Myakinin, Oleg O.; Bratchenko, Ivan A.; Zakharov, Valery P.; Khramov, Alexander G.

2016-10-01

In this paper, we propose a report about our examining of the validity of OCT in identifying changes using a skin cancer texture analysis compiled from Haralick texture features, fractal dimension, Markov random field method and the complex directional features from different tissues. Described features have been used to detect specific spatial characteristics, which can differentiate healthy tissue from diverse skin cancers in cross-section OCT images (B- and/or C-scans). In this work, we used an interval type-II fuzzy anisotropic diffusion algorithm for speckle noise reduction in OCT images. The Haralick texture features as contrast, correlation, energy, and homogeneity have been calculated in various directions. A box-counting method is performed to evaluate fractal dimension of skin probes. Markov random field have been used for the quality enhancing of the classifying. Additionally, we used the complex directional field calculated by the local gradient methodology to increase of the assessment quality of the diagnosis method. Our results demonstrate that these texture features may present helpful information to discriminate tumor from healthy tissue. The experimental data set contains 488 OCT-images with normal skin and tumors as Basal Cell Carcinoma (BCC), Malignant Melanoma (MM) and Nevus. All images were acquired from our laboratory SD-OCT setup based on broadband light source, delivering an output power of 20 mW at the central wavelength of 840 nm with a bandwidth of 25 nm. We obtained sensitivity about 97% and specificity about 73% for a task of discrimination between MM and Nevus.
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.
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
Diffusion, Dispersion, and Uncertainty in Anisotropic Fractal Porous Media

NASA Astrophysics Data System (ADS)

Monnig, N. D.; Benson, D. A.

2007-12-01

Motivated by field measurements of aquifer hydraulic conductivity (K), recent techniques were developed to construct anisotropic fractal random fields, in which the scaling, or self-similarity parameter, varies with direction and is defined by a matrix. Ensemble numerical results are analyzed for solute transport through these 2-D "operator-scaling" fractional Brownian motion (fBm) ln(K) fields. Contrary to some analytic stochastic theories for monofractal K fields, the plume growth rates never exceed Mercado's (1967) purely stratified aquifer growth rate of plume apparent dispersivity proportional to mean distance. Apparent super-stratified growth must be the result of other demonstrable factors, such as initial plume size. The addition of large local dispersion and diffusion does not significantly change the effective longitudinal dispersivity of the plumes. In the presence of significant local dispersion or diffusion, the concentration coefficient of variation CV={σc}/{\\langle c \\rangle} remains large at the leading edge of the plumes. This indicates that even with considerable mixing due to dispersion or diffusion, there is still substantial uncertainty in the leading edge of a plume moving in fractal porous media.
Analysis of stratocumulus cloud fields using LANDSAT imagery: Size distributions and spatial separations

NASA Technical Reports Server (NTRS)

Welch, R. M.; Sengupta, S. K.; Chen, D. W.

1990-01-01

Stratocumulus cloud fields in the FIRE IFO region are analyzed using LANDSAT Thematic Mapper imagery. Structural properties such as cloud cell size distribution, cell horizontal aspect ratio, fractional coverage and fractal dimension are determined. It is found that stratocumulus cloud number densities are represented by a power law. Cell horizontal aspect ratio has a tendency to increase at large cell sizes, and cells are bi-fractal in nature. Using LANDSAT Multispectral Scanner imagery for twelve selected stratocumulus scenes acquired during previous years, similar structural characteristics are obtained. Cloud field spatial organization also is analyzed. Nearest-neighbor spacings are fit with a number of functions, with Weibull and Gamma distributions providing the best fits. Poisson tests show that the spatial separations are not random. Second order statistics are used to examine clustering.
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.
Sierpinski triangles as a tool to introduce fractal geometry to children and their parents

NASA Astrophysics Data System (ADS)

Gires, Auguste; Schertzer, Daniel

2017-04-01

There are currently two somehow contradictory trends in the public debates involving scientific issues. On the one hand there is a need to address topics of increasing complexity, while on the other hand simple(istic) solutions are suggested by numerous people (including high level ones). Meanwhile there seems to be growing defiance towards science findings. Such problems are faced in numerous fields including geosciences where famous examples are the debates dealing with climate change, or water / air contamination. Such unfortunate trends means that the input of scientists in the society and public debates is strongly required. Although it not actually their job, scientists should get involved as a citizens. They should try to explain the complexity of the issues at stake, and take the necessary time to achieve this; not all problems can be explained with the help of a 140 characters tweet! Rather than hiding the uncertainties, they should try to explain this notion often not well understood, and admit the current limitations of knowledge. In the meantime it would be positive if this dialogue could help children and their parents to get familiarized with science and scientists, show that science is not obscure and actually present in everyday life. Scientists obviously also have the hope of fostering a desire for understanding, enhancing scientific culture and even promoting careers in this field. Fractals and fractal geometry are actually a rather good tool to achieve this. Indeed through numerous iterations of a simple process, one can easily obtain a rather complex shape, exhibiting some of the features observed in the nature. Fractal shapes are scale invariant, i.e. the more you zoom in, the more details you see; a portion of the shape is similar to the full one. This paper aims at presenting a series of activities presenting fractals to young people developed primarily around the famous Sierpinski triangles. Two types of activities were carefully designed: (i) Classroom introduction to fractals. The idea here is to use children rather than computers to carry out numerous iterations of a process (:-)), i.e. each child does a small part of a greater shape. Fractals are intrinsically build this way. Such activities were implemented in 4 class of children between 4 and 10, with means of drawing or collage according to their age. Activities were prepared in collaboration with the teachers. (ii) "Fract'art : randomness and geometry for all", an open workshop in the science museum "L'exploradôme" in Vitry. Target audience was 8-12 years children (and their parents were welcomed!). Randomness, a unfortunately much neglected notion, was introduced within the fractal shapes. The use of random fractals and colour gave an aesthetic aspect to the studied shapes. A user friendly software was created for this workshop so that everyone was able to create its own fractal shape starting from well known simple shapes (triangle, rectangle, segment, circle). After a very short introduction, people were able to plot their own shapes and print them. An exchange during the implementation phase lead to questions on how such shapes are used in geosciences. An evaluation quizz was distributed at the end of the two sessions of this workshop. This paper will discuss and analyse the preparation and outcome of these activities.
Describing soil surface microrelief by crossover length and fractal dimension

NASA Astrophysics Data System (ADS)

Vidal Vázquez, E.; Miranda, J. G. V.; Paz González, A.

2007-05-01

Accurate description of soil surface topography is essential because different tillage tools produce different soil surface roughness conditions, which in turn affects many processes across the soil surface boundary. Advantages of fractal analysis in soil microrelief assessment have been recognised but the use of fractal indices in practice remains challenging. There is also little information on how soil surface roughness decays under natural rainfall conditions. The objectives of this work were to investigate the decay of initial surface roughness induced by natural rainfall under different soil tillage systems and to compare the performances of a classical statistical index and fractal microrelief indices. Field experiments were performed on an Oxisol at Campinas, São Paulo State (Brazil). Six tillage treatments, namely, disc harrow, disc plow, chisel plow, disc harrow + disc level, disc plow + disc level and chisel plow + disc level were tested. Measurements were made four times, firstly just after tillage and subsequently with increasing amounts of natural rainfall. Duplicated measurements were taken per treatment and date, yielding a total of 48 experimental surfaces. The sampling scheme was a square grid with 25×25 mm point spacing and the plot size was 1350×1350 mm, so that each data set consisted of 3025 individual elevation points. Statistical and fractal indices were calculated both for oriented and random roughness conditions, i.e. after height reading have been corrected for slope and for slope and tillage tool marks. The main drawback of the standard statistical index random roughness, RR, lies in its no spatial nature. The fractal approach requires two indices, fractal dimension, D, which describes how roughness changes with scale, and crossover length, l, specifying the variance of surface microrelief at a reference scale. Fractal parameters D and l, were estimated by two independent self-affine models, semivariogram (SMV) and local root mean square (RMS). Both algorithms, SMV and RMS, gave equivalent results for D and l indices, irrespective of trend removal procedure, even if some bias was present which is in accordance with previous work. Treatments with two tillage operations had the greatest D values, irrespective of evolution stage under rainfall and trend removal procedure. Primary tillage had the greatest initial values of RR and l. Differences in D values between treatments with primary tillage and those with two successive tillage operations were significant for oriented but not for random conditions. The statistical index RR and the fractal indices l and D decreased with increasing cumulative rainfall following different patterns. The l and D decay from initial value was very sharp after the first 24.4 mm cumulative rainfall. For five out of six tillage treatments a significant relationship between D and l was found for the random microrelief conditions allowing a covariance analysis. It was concluded that using RR or l together with D best allow joint description of vertical and horizontal soil roughness variations.
Noteworthy fractal features and transport properties of Cantor tartans

NASA Astrophysics Data System (ADS)

Balankin, Alexander S.; Golmankhaneh, Alireza K.; Patiño-Ortiz, Julián; Patiño-Ortiz, Miguel

2018-06-01

This Letter is focused on the impact of fractal topology on the transport processes governed by different kinds of random walks on Cantor tartans. We establish that the spectral dimension of the infinitely ramified Cantor tartan ds is equal to its fractal (self-similarity) dimension D. Consequently, the random walk on the Cantor tartan leads to a normal diffusion. On the other hand, the fractal geometry of Cantor tartans allows for a natural definition of power-law distributions of the waiting times and step lengths of random walkers. These distributions are Lévy stable if D > 1.5. Accordingly, we found that the random walk with rests leads to sub-diffusion, whereas the Lévy walk leads to ballistic diffusion. The Lévy walk with rests leads to super-diffusion, if D >√{ 3 }, or sub-diffusion, if 1.5 < D <√{ 3 }.
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).
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.
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.
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

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.
Sequence Complexity of Chromosome 3 in Caenorhabditis elegans

PubMed Central

Pierro, Gaetano

2012-01-01

The nucleotide sequences complexity in chromosome 3 of Caenorhabditis elegans (C. elegans) is studied. The complexity of these sequences is compared with some random sequences. Moreover, by using some parameters related to complexity such as fractal dimension and frequency, indicator matrix is given a first classification of sequences of C. elegans. In particular, the sequences with highest and lowest fractal value are singled out. It is shown that the intrinsic nature of the low fractal dimension sequences has many common features with the random sequences. PMID:22919380
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.
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.
Universality of Critically Pinned Interfaces in Two-Dimensional Isotropic Random Media

NASA Astrophysics Data System (ADS)

Grassberger, Peter

2018-05-01

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

NASA Astrophysics Data System (ADS)

Milliner, Christopher; Sammis, Charles; Allam, Amir; Dolan, James

2015-04-01

Co-seismic along-strike slip heterogeneity is widely observed for many surface-rupturing earthquakes as revealed by field and high-resolution geodetic methods. However, this co-seismic slip variability is currently a poorly understood phenomenon. Key unanswered questions include: What are the characteristics and underlying causes of along-strike slip variability? Do the properties of slip variability change from fault-to-fault, along-strike or at different scales? We cross-correlate optical, pre- and post-event air photos using the program COSI-Corr to measure the near-field, surface deformation pattern of the 1992 Mw 7.3 Landers and 1999 Mw 7.1 Hector Mine earthquakes in high-resolution. We produce the co-seismic slip profiles of both events from over 1,000 displacement measurements and observe consistent along-strike slip variability. Although the observed slip heterogeneity seems apparently complex and disordered, a spectral analysis reveals that the slip distributions are indeed self-affine fractal i.e., slip exhibits a consistent degree of irregularity at all observable length scales, with a 'short-memory' and is not random. We find a fractal dimension of 1.58 and 1.75 for the Landers and Hector Mine earthquakes, respectively, indicating that slip is more heterogeneous for the Hector Mine event. Fractal slip is consistent with both dynamic and quasi-static numerical simulations that use non-planar faults, which in turn causes heterogeneous along-strike stress, and we attribute the observed fractal slip to fault surfaces of fractal roughness. As fault surfaces are known to smooth over geologic time due to abrasional wear and fracturing, we also test whether the fractal properties of slip distributions alters between earthquakes from immature to mature fault systems. We will present results that test this hypothesis by using the optical image correlation technique to measure historic, co-seismic slip distributions of earthquakes from structurally mature, large cumulative displacement faults and compare these slip distributions to those from immature fault systems. Our results have fundamental implications for an understanding of slip heterogeneity and the behavior of the rupture process.
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
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.
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…
Thin film growth by 3D multi-particle diffusion limited aggregation model: Anomalous roughening and fractal analysis

NASA Astrophysics Data System (ADS)

Nasehnejad, Maryam; Nabiyouni, G.; Gholipour Shahraki, Mehran

2018-03-01

In this study a 3D multi-particle diffusion limited aggregation method is employed to simulate growth of rough surfaces with fractal behavior in electrodeposition process. A deposition model is used in which the radial motion of the particles with probability P, competes with random motions with probability 1 - P. Thin films growth is simulated for different values of probability P (related to the electric field) and thickness of the layer(related to the number of deposited particles). The influence of these parameters on morphology, kinetic of roughening and the fractal dimension of the simulated surfaces has been investigated. The results show that the surface roughness increases with increasing the deposition time and scaling exponents exhibit a complex behavior which is called as anomalous scaling. It seems that in electrodeposition process, radial motion of the particles toward the growing seeds may be an important mechanism leading to anomalous scaling. The results also indicate that the larger values of probability P, results in smoother topography with more densely packed structure. We have suggested a dynamic scaling ansatz for interface width has a function of deposition time, scan length and probability. Two different methods are employed to evaluate the fractal dimension of the simulated surfaces which are "cube counting" and "roughness" methods. The results of both methods show that by increasing the probability P or decreasing the deposition time, the fractal dimension of the simulated surfaces is increased. All gained values for fractal dimensions are close to 2.5 in the diffusion limited aggregation model.
Active tectonics on Deception Island (West-Antarctica): A new approach by using the fractal anisotropy of lineaments, fault slip measurements and the caldera collapse shape

USGS Publications Warehouse

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

2007-01-01

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

NASA Astrophysics Data System (ADS)

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

2009-10-01

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

NASA Astrophysics Data System (ADS)

Tokitani, M.; Kajita, S.; Masuzaki, S.; Hirahata, Y.; Ohno, N.; Tanabe, T.; LHD Experiment Group

2011-10-01

The tungsten nanostructure (W-fuzz) created in the linear divertor simulator (NAGDIS) was exposed to the Large Helical Device (LHD) divertor plasma for only 2 s (1 shot) to study exfoliation/erosion and microscopic modifications due to the high heat/particle loading under high magnetic field conditions. Very fine and randomly moved unipolar arc trails were clearly observed on about half of the W-fuzz area (6 × 10 mm2). The fuzzy surface was exfoliated by continuously moving arc spots even for the very short exposure time. This is the first observation of unipolar arcing and exfoliation of some areas of the W-fuzz structure itself in a large plasma confinement device with a high magnetic field. The typical width and depth of each arc trail were about 8 µm and 1 µm, respectively, and the arc spots moved randomly on the micrometre scale. The fractality of the arc trails was analysed using a box-counting method, and the fractal dimension (D) of the arc trails was estimated to be D ≈ 1.922. This value indicated that the arc spots moved in Brownian motion, and were scarcely influenced by the magnetic field. One should note that such a large scale exfoliation due to unipolar arcing may enhance the surface erosion of the tungsten armour and act as a serious impurity source for fusion plasmas.
A New Algorithm with Plane Waves and Wavelets for Random Velocity Fields with Many Spatial Scales

NASA Astrophysics Data System (ADS)

Elliott, Frank W.; Majda, Andrew J.

1995-03-01

A new Monte Carlo algorithm for constructing and sampling stationary isotropic Gaussian random fields with power-law energy spectrum, infrared divergence, and fractal self-similar scaling is developed here. The theoretical basis for this algorithm involves the fact that such a random field is well approximated by a superposition of random one-dimensional plane waves involving a fixed finite number of directions. In general each one-dimensional plane wave is the sum of a random shear layer and a random acoustical wave. These one-dimensional random plane waves are then simulated by a wavelet Monte Carlo method for a single space variable developed recently by the authors. The computational results reported in this paper demonstrate remarkable low variance and economical representation of such Gaussian random fields through this new algorithm. In particular, the velocity structure function for an imcorepressible isotropic Gaussian random field in two space dimensions with the Kolmogoroff spectrum can be simulated accurately over 12 decades with only 100 realizations of the algorithm with the scaling exponent accurate to 1.1% and the constant prefactor accurate to 6%; in fact, the exponent of the velocity structure function can be computed over 12 decades within 3.3% with only 10 realizations. Furthermore, only 46,592 active computational elements are utilized in each realization to achieve these results for 12 decades of scaling behavior.
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.
Selective modulation of cell response on engineered fractal silicon substrates

PubMed Central

Gentile, Francesco; Medda, Rebecca; Cheng, Ling; Battista, Edmondo; Scopelliti, Pasquale E.; Milani, Paolo; Cavalcanti-Adam, Elisabetta A.; Decuzzi, Paolo

2013-01-01

A plethora of work has been dedicated to the analysis of cell behavior on substrates with ordered topographical features. However, the natural cell microenvironment is characterized by biomechanical cues organized over multiple scales. Here, randomly rough, self-affinefractal surfaces are generated out of silicon,where roughness Ra and fractal dimension Df are independently controlled. The proliferation rates, the formation of adhesion structures, and the morphology of 3T3 murine fibroblasts are monitored over six different substrates. The proliferation rate is maximized on surfaces with moderate roughness (Ra ~ 40 nm) and large fractal dimension (Df ~ 2.4); whereas adhesion structures are wider and more stable on substrates with higher roughness (Ra ~ 50 nm) and lower fractal dimension (Df ~ 2.2). Higher proliferation occurson substrates exhibiting densely packed and sharp peaks, whereas more regular ridges favor adhesion. These results suggest that randomly roughtopographies can selectively modulate cell behavior. PMID:23492898
Nonlinear Dynamics Used to Classify Effects of Mild Traumatic Brain Injury

DTIC Science & Technology

2012-01-11

evaluate random fractal characteristics, and scale-dependent Lyapunov exponents (SDLE) to evaluate chaotic characteristics. Both Shannon and Renyi entropy...fluctuation analysis to evaluate random fractal characteristics, and scale-dependent Lyapunov exponents (SDLE) to evaluate chaotic characteristics. Both...often called the Hurst parameter [32]. When the scaling law described by Eq. (2) holds, the September 2011 I Volume 6 I Issue 9 I e24446 -Q.384

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

NASA Astrophysics Data System (ADS)

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

2001-12-01

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

NASA Astrophysics Data System (ADS)

Kolotev, Sergei; Malyutin, Aleksandr; Burovski, Evgeni; Krashakov, Sergei; Shchur, Lev

2018-06-01

We investigate critical properties of a spatial evolutionary game based on the Prisoner's Dilemma. Simulations demonstrate a jump in the component densities accompanied by drastic changes in average sizes of the component clusters. We argue that the cluster boundary is a random fractal. Our simulations are consistent with the fractal dimension of the boundary being equal to 2, and the cluster boundaries are hence asymptotically space filling as the system size increases.
Fat fractal scaling of drainage networks from a random spatial network model

USGS Publications Warehouse

Karlinger, Michael R.; Troutman, Brent M.

1992-01-01

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

NASA Technical Reports Server (NTRS)

Burlaga, L. F.; Klein, L. W.

1985-01-01

Under some conditions, time series of the interplanetary magnetic field strength and components have the properties of fractal curves. Magnetic field measurements made near 8.5 AU by Voyager 2 from June 5 to August 24, 1981 were self-similar over time scales from approximately 20 sec to approximately 3 x 100,000 sec, and the fractal dimension of the time series of the strength and components of the magnetic field was D = 5/3, corresponding to a power spectrum P(f) approximately f sup -5/3. Since the Kolmogorov spectrum for homogeneous, isotropic, stationary turbulence is also f sup -5/3, the Voyager 2 measurements are consistent with the observation of an inertial range of turbulence extending over approximately four decades in frequency. Interaction regions probably contributed most of the power in this interval. As an example, one interaction region is discussed in which the magnetic field had a fractal dimension D = 5/3.
Collisions of ideal gas molecules with a rough/fractal surface. A computational study.

PubMed

Panczyk, Tomasz

2007-02-01

The frequency of collisions of ideal gas molecules (argon) with a rough surface has been studied. The rough/fractal surface was created using random deposition technique. By applying various depositions, the roughness of the surface was controlled and, as a measure of the irregularity, the fractal dimensions of the surfaces were determined. The surfaces were next immersed in argon (under pressures 2 x 10(3) to 2 x 10(5) Pa) and the numbers of collisions with these surfaces were counted. The calculations were carried out using a simplified molecular dynamics simulation technique (only hard core repulsions were assumed). As a result, it was stated that the frequency of collisions is a linear function of pressure for all fractal dimensions studied (D = 2, ..., 2.5). The frequency per unit pressure is quite complex function of the fractal dimension; however, the changes of that frequency with the fractal dimension are not strong. It was found that the frequency of collisions is controlled by the number of weakly folded sites on the surfaces and there is some mapping between the shape of adsorption energy distribution functions and this number of weakly folded sites. The results for the rough/fractal surfaces were compared with the prediction given by the Langmuir-Hertz equation (valid for smooth surface), generally the departure from the Langmuir-Hertz equation is not higher than 48% for the studied systems (i.e. for the surfaces created using the random deposition technique).
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.
Random-fractal Ansatz for the configurations of two-dimensional critical systems

NASA Astrophysics Data System (ADS)

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

2016-12-01

Critical systems have always intrigued physicists and precipitated the development of new techniques. Recently, there has been renewed interest in the information contained in the configurations of classical critical systems, whose computation do not require full knowledge of the wave function. Inspired by holographic duality, we investigated the entanglement properties of the classical configurations (snapshots) of the Potts model by introducing an Ansatz ensemble of random fractal images. By virtue of the central limit theorem, our Ansatz accurately reproduces the entanglement spectra of actual Potts snapshots without any fine tuning of parameters or artificial restrictions on ensemble choice. It provides a microscopic interpretation of the results of previous studies, which established a relation between the scaling behavior of snapshot entropy and the critical exponent. More importantly, it elucidates the role of ensemble disorder in restoring conformal invariance, an aspect previously ignored. Away from criticality, the breakdown of scale invariance leads to a renormalization of the parameter Σ in the random fractal Ansatz, whose variation can be used as an alternative determination of the critical exponent. We conclude by providing a recipe for the explicit construction of fractal unit cells consistent with a given scaling exponent.
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.
Task 1, Fractal characteristics of drainage patterns observed in the Appalachian Valley and Ridge and Plateau provinces

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

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

1996-04-10

Drainage patterns observed in the Appalachian Valley and Ridge and Plateau provinces exhibit distinctly different patterns. The patterns appear to be controlled by varying influences of local structural and lithologic variability. Drainage patterns in the Valley and Ridge study area can be classified as a combination of dendritic and trellis arrangements. The patterns vary over short distances in both the strike and dip directions. In the Granny Creek area of the Appalachian Plateau drainage patterns are predominantly dendritic. The possibility that these drainage patterns have fractal characteristics was evaluated by box-counting. Results obtained from box counting do not yield amore » well defined fractal regime in either areas. In the Valley and Ridge a space-filling, or random regime (D=2) is observed for boxes with side-lengths of 300 meters and greater. Below 300 meters, large changes in D occur between consecutively smaller box sizes. From side lengths of 300 to 150m, 150 to 75m, and 75 to 38m, D is measured at 1.77, 1.39, and 1.08 respectively. For box sizes less than 38m the fractal dimension is 1 or less. While the l0g-log response of the box counting data is nonlinear and does not define a fractal regime, the curves offer the possibility of characterizing non-fractal patterns. The rate at which D drops outside the random regime correlates to drainage density. D in areas with a smaller density of drainage segments fell toward saturation (D=1) more abruptly. The break-away point from the random regime and the transition to the saturated regime may provide useful information about the relative lengths of stream segments.« less
Efficiency analysis of diffusion on T-fractals in the sense of random walks.

PubMed

Peng, Junhao; Xu, Guoai

2014-04-07

Efficiently controlling the diffusion process is crucial in the study of diffusion problem in complex systems. In the sense of random walks with a single trap, mean trapping time (MTT) and mean diffusing time (MDT) are good measures of trapping efficiency and diffusion efficiency, respectively. They both vary with the location of the node. In this paper, we analyze the effects of node's location on trapping efficiency and diffusion efficiency of T-fractals measured by MTT and MDT. First, we provide methods to calculate the MTT for any target node and the MDT for any source node of T-fractals. The methods can also be used to calculate the mean first-passage time between any pair of nodes. Then, using the MTT and the MDT as the measure of trapping efficiency and diffusion efficiency, respectively, we compare the trapping efficiency and diffusion efficiency among all nodes of T-fractal and find the best (or worst) trapping sites and the best (or worst) diffusing sites. Our results show that the hub node of T-fractal is the best trapping site, but it is also the worst diffusing site; and that the three boundary nodes are the worst trapping sites, but they are also the best diffusing sites. Comparing the maximum of MTT and MDT with their minimums, we find that the maximum of MTT is almost 6 times of the minimum of MTT and the maximum of MDT is almost equal to the minimum for MDT. Thus, the location of target node has large effect on the trapping efficiency, but the location of source node almost has no effect on diffusion efficiency. We also simulate random walks on T-fractals, whose results are consistent with the derived results.
A model study of aggregates composed of spherical soot monomers with an acentric carbon shell

NASA Astrophysics Data System (ADS)

Luo, Jie; Zhang, Yongming; Zhang, Qixing

2018-01-01

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

NASA Astrophysics Data System (ADS)

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

2013-05-01

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

NASA Astrophysics Data System (ADS)

Banda-Barragan, Wladimir Eduardo; Federrath, Christoph; Crocker, Roland M.; Bicknell, Geoffrey Vincent; Parkin, Elliot Ross

2015-08-01

Using high-resolution three-dimensional simulations, we examine the formation and evolution of filamentary structures arising from magnetohydrodynamic interactions between supersonic winds and turbulent clumps in the interstellar medium. Previous numerical studies assumed homogenous density profiles, null velocity fields, and uniformly distributed magnetic fields as the initial conditions for interstellar clumps. Here, we have, for the first time, incorporated fractal clumps with log-normal density distributions, random velocity fields and turbulent magnetic fields (superimposed on top of a uniform background field). Disruptive processes, instigated by dynamical instabilities and akin to those observed in simulations with uniform media, lead to stripping of clump material and the subsequent formation of filamentary tails. The evolution of filaments in uniform and turbulent models is, however, radically different as evidenced by comparisons of global quantities in both scenarios. We show, for example, that turbulent clumps produce tails with higher velocity dispersions, increased gas mixing, greater kinetic energy, and lower plasma beta than their uniform counterparts. We attribute the observed differences to: 1) the turbulence-driven enhanced growth of dynamical instabilities (e.g. Kelvin-Helmholtz and Rayleigh-Taylor instabilities) at fluid interfaces, and 2) the localised amplification of magnetic fields caused by the stretching of field lines trapped in the numerous surface deformations of fractal clumps. We briefly discuss the implications of this work to the physics of the optical filaments observed in the starburst galaxy M82.
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.
Fractality and growth of He bubbles in metals

NASA Astrophysics Data System (ADS)

Kajita, Shin; Ito, Atsushi M.; Ohno, Noriyasu

2017-08-01

Pinholes are formed on surfaces of metals by the exposure to helium plasmas, and they are regarded as the initial process of the growth of fuzzy nanostructures. In this study, number density of the pinholes is investigated in detail from the scanning electron microscope (SEM) micrographs of tungsten and tantalum exposed to the helium plasmas. A power law relation was identified between the number density and the size of pinholes. From the slope and the region where the power law was satisfied, the fractal dimension D and smin, which characterize the SEM images, are deduced. Parametric dependences and material dependence of D and smin are revealed. To explain the fractality, simple Monte-Carlo simulations including random walks of He atoms and absorption on bubble was introduced. It is shown that the initial position of the random walk is one of the key factors to deduce the fractality. The results indicated that new nucleations of bubbles are necessary to reproduce the number-density distribution of bubbles.
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.

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 ...
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.
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.
Entropy Production of Entirely Diffusional Laplacian Transfer and the Possible Role of Fragmentation of the Boundaries

NASA Astrophysics Data System (ADS)

Karamanos, K.; Mistakidis, S. I.; Massart, T. J.; Mistakidis, I. S.

2015-06-01

The entropy production and the variational functional of a Laplacian diffusional field around the first four fractal iterations of a linear self-similar tree (von Koch curve) is studied analytically and detailed predictions are stated. In a next stage, these predictions are confronted with results from numerical resolution of the Laplace equation by means of Finite Elements computations. After a brief review of the existing results, the range of distances near the geometric irregularity, the so-called "Near Field", a situation never studied in the past, is treated exhaustively. We notice here that in the Near Field, the usual notion of the active zone approximation introduced by Sapoval et al. [M. Filoche and B. Sapoval, Transfer across random versus deterministic fractal interfaces, Phys. Rev. Lett. 84(25) (2000) 5776;1 B. Sapoval, M. Filoche, K. Karamanos and R. Brizzi, Can one hear the shape of an electrode? I. Numerical study of the active zone in Laplacian transfer, Eur. Phys. J. B. Condens. Matter Complex Syst. 9(4) (1999) 739-753.]2 is strictly inapplicable. The basic new result is that the validity of the active-zone approximation based on irreversible thermodynamics is confirmed in this limit, and this implies a new interpretation of this notion for Laplacian diffusional fields.
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.
Dual Fractal Dimension and Long-Range Correlation of Chinese Stock Prices

NASA Astrophysics Data System (ADS)

Chen, Chaoshi; Wang, Lei

2012-03-01

The recently developed modified inverse random midpoint displacement (mIRMD) and conventional detrended fluctuation analysis (DFA) algorithms are used to analyze the tick-by-tick high-frequency time series of Chinese A-share stock prices and indexes. A dual-fractal structure with a crossover at about 10 min is observed. The majority of the selected time series show visible persistence within this time threshold, but approach a random walk on a longer time scale. The phenomenon is found to be industry-dependent, i.e., the crossover is much more prominent for stocks belonging to cyclical industries than for those belonging to noncyclical (defensive) industries. We have also shown that the sign series show a similar dual-fractal structure, while like generally found, the magnitude series show a much longer time persistence.
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.
Unified Mie and fractal scattering by cells and experimental study on application in optical characterization of cellular and subcellular structures.

PubMed

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

2008-01-01

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

NASA Astrophysics Data System (ADS)

Gou, Xueqiang; Chen, Mingli; Zhang, Guangshu

2018-01-01

By using the data of lightning detection and ranging system at the Kennedy Space Center, the temporal fractal and correlation of interevent time series of lightning flash sequences in thunderstorms have been investigated with Allan factor (AF), Fano factor (FF), and detrended fluctuation analysis (DFA) methods. AF, FF, and DFA methods are powerful tools to detect the time-scaling structures and correlations in point processes. Totally 40 thunderstorms with distinguishing features of a single-cell storm and apparent increase and decrease in the total flash rate were selected for the analysis. It is found that the time-scaling exponents for AF (αAF) and FF (αFF) analyses are 1.62 and 0.95 in average, respectively, indicating a strong time correlation of the lightning flash sequences. DFA analysis shows that there is a crossover phenomenon—a crossover timescale (τc) ranging from 54 to 195 s with an average of 114 s. The occurrence of a lightning flash in a thunderstorm behaves randomly at timescales <τc but shows strong time correlation at scales >τc. Physically, these may imply that the establishment of an extensive strong electric field necessary for the occurrence of a lightning flash needs a timescale >τc, which behaves strongly time correlated. But the initiation of a lightning flash within a well-established extensive strong electric field may involve the heterogeneities of the electric field at a timescale <τc, which behave randomly.
Entanglement and area law with a fractal boundary in a topologically ordered phase

NASA Astrophysics Data System (ADS)

Hamma, Alioscia; Lidar, Daniel A.; Severini, Simone

2010-01-01

Quantum systems with short-range interactions are known to respect an area law for the entanglement entropy: The von Neumann entropy S associated to a bipartition scales with the boundary p between the two parts. Here we study the case in which the boundary is a fractal. We consider the topologically ordered phase of the toric code with a magnetic field. When the field vanishes it is possible to analytically compute the entanglement entropy for both regular and fractal bipartitions (A,B) of the system and this yields an upper bound for the entire topological phase. When the A-B boundary is regular we have S/p=1 for large p. When the boundary is a fractal of the Hausdorff dimension D, we show that the entanglement between the two parts scales as S/p=γ⩽1/D, and γ depends on the fractal considered.
Magnetic hierarchical deposition

NASA Astrophysics Data System (ADS)

Posazhennikova, Anna I.; Indekeu, Joseph O.

2014-11-01

We consider random deposition of debris or blocks on a line, with block sizes following a rigorous hierarchy: the linear size equals 1/λn in generation n, in terms of a rescaling factor λ. Without interactions between the blocks, this model is described by a logarithmic fractal, studied previously, which is characterized by a constant increment of the length, area or volume upon proliferation. We study to what extent the logarithmic fractality survives, if each block is equipped with an Ising (pseudo-)spin s=±1 and the interactions between those spins are switched on (ranging from antiferromagnetic to ferromagnetic). It turns out that the dependence of the surface topology on the interaction sign and strength is not trivial. For instance, deep in the ferromagnetic regime, our numerical experiments and analytical results reveal a sharp crossover from a Euclidean transient, consisting of aggregated domains of aligned spins, to an asymptotic logarithmic fractal growth. In contrast, deep into the antiferromagnetic regime the surface roughness is important and is shown analytically to be controlled by vacancies induced by frustrated spins. Finally, in the weak interaction regime, we demonstrate that the non-interacting model is extremal in the sense that the effect of the introduction of interactions is only quadratic in the magnetic coupling strength. In all regimes, we demonstrate the adequacy of a mean-field approximation whenever vacancies are rare. In sum, the logarithmic fractal character is robust with respect to the introduction of spatial correlations in the hierarchical deposition process.
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.
Disassortativity of random critical branching trees

NASA Astrophysics Data System (ADS)

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

2009-06-01

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

NASA Astrophysics Data System (ADS)

Iomin, A.

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

DTIC Science & Technology

2007-06-30

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

NASA Astrophysics Data System (ADS)

Monnig, Nathan D.; Benson, David A.; Meerschaert, Mark M.

2008-02-01

Motivated by field measurements of aquifer hydraulic conductivity (K), recent techniques were developed to construct anisotropic fractal random fields in which the scaling, or self-similarity parameter, varies with direction and is defined by a matrix. Ensemble numerical results are analyzed for solute transport through these two-dimensional "operator-scaling" fractional Brownian motion ln(K) fields. Both the longitudinal and transverse Hurst coefficients, as well as the "radius of isotropy" are important to both plume growth rates and the timing and duration of breakthrough. It is possible to create operator-scaling fractional Brownian motion fields that have more "continuity" or stratification in the direction of transport. The effects on a conservative solute plume are continually faster-than-Fickian growth rates, highly non-Gaussian shapes, and a heavier tail early in the breakthrough curve. Contrary to some analytic stochastic theories for monofractal K fields, the plume growth rates never exceed A. Mercado's (1967) purely stratified aquifer growth rate of plume apparent dispersivity proportional to mean distance. Apparent superstratified growth must be the result of other demonstrable factors, such as initial plume size.

Influence of Turbulent Flow and Fractal Scaling on Effective Permeability of Fracture Network

NASA Astrophysics Data System (ADS)

Zhu, J.

2017-12-01

A new approach is developed to calculate hydraulic gradient dependent effective permeability of a fractal fracture network where both laminar and turbulent flows may occur in individual fractures. A critical fracture length is used to distinguish flow characteristics in individual fractures. The developed new solutions can be used for the case of a general scaling relationship, an extension to the linear scaling. We examine the impact on the effective permeability of the network of fractal fracture network characteristics, which include the fractal scaling coefficient and exponent, fractal dimension, ratio of minimum over maximum fracture lengths. Results demonstrate that the developed solution can explain more variations of the effective permeability in relation to the fractal dimensions estimated from the field observations. At high hydraulic gradient the effective permeability decreases with the fractal scaling exponent, but increases with the fractal scaling exponent at low gradient. The effective permeability increases with the scaling coefficient, fractal dimension, fracture length ratio and maximum fracture length.
Metabolic networks are almost nonfractal: a comprehensive evaluation.

PubMed

Takemoto, Kazuhiro

2014-08-01

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

NASA Astrophysics Data System (ADS)

Abramov, Valeriy

2017-10-01

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

NASA Astrophysics Data System (ADS)

Chang, Longfei; Wu, Yucheng; Zhu, Zicai; Li, Heng

2016-04-01

Ionic Polymer-Metal Composite (IPMC) actuators have been attracting a growing interest in extensive applications, which consequently raises the demands on the accuracy of its theoretical modeling. For the last few years, rough landscape of the interface between the electrode and the ionic membrane of IPMC has been well-documented as one of the key elements to ensure a satisfied performance. However, in most of the available work, the interface morphology of IPMC was simplified with structural idealization, which lead to perplexity in the physical interpretation on its interface mechanism. In this paper, the quasi-random rough interface of IPMC was described with fractal dimension and scaling parameters. And the electro-chemical field was modeled by Poisson equation and a properly simplified Nernst-Planck equation set. Then, by simulation with Finite Element Method, a comprehensive analysis on he inner mass and charge transportation in IPMC actuators with different fractal interfaces was provided, which may be further adopted to instruct the performance-oriented interface design for ionic electro-active actuators. The results also verified that rough interface can impact the electrical and mechanical response of IPMC, not only from the respect of the real surface increase, but also from mass distribution difference caused by the complexity of the micro profile.
Fractal attractors and singular invariant measures in two-sector growth models with random factor shares

NASA Astrophysics Data System (ADS)

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

2018-05-01

We analyze a multi-sector growth model subject to random shocks affecting the two sector-specific production functions twofold: the evolution of both productivity and factor shares is the result of such exogenous shocks. We determine the optimal dynamics via Euler-Lagrange equations, and show how these dynamics can be described in terms of an iterated function system with probability. We also provide conditions that imply the singularity of the invariant measure associated with the fractal attractor. Numerical examples show how specific parameter configurations might generate distorted copies of the Barnsley's fern attractor.
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.
Resource Letter FR-1: Fractals

NASA Astrophysics Data System (ADS)

Hurd, Alan J.

1988-11-01

This Resource Letter provides a guide to the literature on fractals. Although ``fractal'' is a relatively new term in science, unifying many new ideas with established ones, its wide application and general popularity have made it one of the fastest growing fields in statistical physics. The letter E after an item indicates elementary level or material of general interest to persons becoming informed in the field; the letter I, for intermediate level, indicates material of somewhat more specialized nature; and the letter A indicates rather specialized or advanced material. An asterisk (*) indicates those articles to be included in an accompanying Reprint Book.
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 Note on the Fractal Behavior of Hydraulic Conductivity and Effective Porosity for Experimental Values in a Confined Aquifer

PubMed Central

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

2013-01-01

Hydraulic conductivity and effective porosity values for the confined sandy loam aquifer of the Montalto Uffugo (Italy) test field were obtained by laboratory and field measurements; the first ones were carried out on undisturbed soil samples and the others by slug and aquifer tests. A direct simple-scaling analysis was performed for the whole range of measurement and a comparison among the different types of fractal models describing the scale behavior was made. Some indications about the largest pore size to utilize in the fractal models were given. The results obtained for a sandy loam soil show that it is possible to obtain global indications on the behavior of the hydraulic conductivity versus the porosity utilizing a simple scaling relation and a fractal model in coupled manner. PMID:24385876
New 5-adic Cantor sets and fractal string.

PubMed

Kumar, Ashish; Rani, Mamta; Chugh, Renu

2013-01-01

In the year (1879-1884), George Cantor coined few problems and consequences in the field of set theory. One of them was the Cantor ternary set as a classical example of fractals. In this paper, 5-adic Cantor one-fifth set as an example of fractal string have been introduced. Moreover, the applications of 5-adic Cantor one-fifth set in string theory have also been studied.
Scaling laws of marine predator search behaviour.

PubMed

Sims, David W; Southall, Emily J; Humphries, Nicolas E; Hays, Graeme C; Bradshaw, Corey J A; Pitchford, Jonathan W; James, Alex; Ahmed, Mohammed Z; Brierley, Andrew S; Hindell, Mark A; Morritt, David; Musyl, Michael K; Righton, David; Shepard, Emily L C; Wearmouth, Victoria J; Wilson, Rory P; Witt, Matthew J; Metcalfe, Julian D

2008-02-28

Many free-ranging predators have to make foraging decisions with little, if any, knowledge of present resource distribution and availability. The optimal search strategy they should use to maximize encounter rates with prey in heterogeneous natural environments remains a largely unresolved issue in ecology. Lévy walks are specialized random walks giving rise to fractal movement trajectories that may represent an optimal solution for searching complex landscapes. However, the adaptive significance of this putative strategy in response to natural prey distributions remains untested. Here we analyse over a million movement displacements recorded from animal-attached electronic tags to show that diverse marine predators-sharks, bony fishes, sea turtles and penguins-exhibit Lévy-walk-like behaviour close to a theoretical optimum. Prey density distributions also display Lévy-like fractal patterns, suggesting response movements by predators to prey distributions. Simulations show that predators have higher encounter rates when adopting Lévy-type foraging in natural-like prey fields compared with purely random landscapes. This is consistent with the hypothesis that observed search patterns are adapted to observed statistical patterns of the landscape. This may explain why Lévy-like behaviour seems to be widespread among diverse organisms, from microbes to humans, as a 'rule' that evolved in response to patchy resource distributions.
Nonlinear stochastic interacting dynamics and complexity of financial gasket fractal-like lattice percolation

NASA Astrophysics Data System (ADS)

Zhang, Wei; Wang, Jun

2018-05-01

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

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

Mandelbrot, B.B.

1991-03-01

The following statements are obviously quite wrong: oil fields are circular; they are the same size and are distributed uniformly throughout the world; soil is of uniform porosity and permeability; after water has been pumped into a field it seeps through as an underground sphere. The preceding statements are so grossly incorrect that they do not even provide useful first approximations that one could improve upon by adding so-called corrective terms. For example, one gains little by starting with the notion of a uniform distribution of oil fields and then assuming it is perturbed by small Gaussian scatter. The flowmore » of water in a porous medium often fingers out in a pattern so diffuse that a sphere is not a useful point of departure in describing it. In summary, even the simplest data underlying petroleum geology exhibit very gross irregularity and unevenness. Fractal geometry is the proper geometry of manageable irregularity, fragmentation, and unevenness. It is the only workable alternative between the excessive order of the Euclidean geometry and unmanageable disorder. The main features of fractal geometry will be described and several techniques will be pointed out that show promise for the petroleum geologist.« less
Soil variability in engineering applications

NASA Astrophysics Data System (ADS)

Vessia, Giovanna

2014-05-01

Natural geomaterials, as soils and rocks, show spatial variability and heterogeneity of physical and mechanical properties. They can be measured by in field and laboratory testing. The heterogeneity concerns different values of litho-technical parameters pertaining similar lithological units placed close to each other. On the contrary, the variability is inherent to the formation and evolution processes experienced by each geological units (homogeneous geomaterials on average) and captured as a spatial structure of fluctuation of physical property values about their mean trend, e.g. the unit weight, the hydraulic permeability, the friction angle, the cohesion, among others. The preceding spatial variations shall be managed by engineering models to accomplish reliable designing of structures and infrastructures. Materon (1962) introduced the Geostatistics as the most comprehensive tool to manage spatial correlation of parameter measures used in a wide range of earth science applications. In the field of the engineering geology, Vanmarcke (1977) developed the first pioneering attempts to describe and manage the inherent variability in geomaterials although Terzaghi (1943) already highlighted that spatial fluctuations of physical and mechanical parameters used in geotechnical designing cannot be neglected. A few years later, Mandelbrot (1983) and Turcotte (1986) interpreted the internal arrangement of geomaterial according to Fractal Theory. In the same years, Vanmarcke (1983) proposed the Random Field Theory providing mathematical tools to deal with inherent variability of each geological units or stratigraphic succession that can be resembled as one material. In this approach, measurement fluctuations of physical parameters are interpreted through the spatial variability structure consisting in the correlation function and the scale of fluctuation. Fenton and Griffiths (1992) combined random field simulation with the finite element method to produce the Random Finite Element Method (RFEM). This method has been used to investigate the random behavior of soils in the context of a variety of classical geotechnical problems. Afterward, some following studies collected the worldwide variability values of many technical parameters of soils (Phoon and Kulhawy 1999a) and their spatial correlation functions (Phoon and Kulhawy 1999b). In Italy, Cherubini et al. (2007) calculated the spatial variability structure of sandy and clayey soils from the standard cone penetration test readings. The large extent of the worldwide measured spatial variability of soils and rocks heavily affects the reliability of geotechnical designing as well as other uncertainties introduced by testing devices and engineering models. So far, several methods have been provided to deal with the preceding sources of uncertainties in engineering designing models (e.g. First Order Reliability Method, Second Order Reliability Method, Response Surface Method, High Dimensional Model Representation, etc.). Nowadays, the efforts in this field have been focusing on (1) measuring spatial variability of different rocks and soils and (2) developing numerical models that take into account the spatial variability as additional physical variable. References Cherubini C., Vessia G. and Pula W. 2007. Statistical soil characterization of Italian sites for reliability analyses. Proc. 2nd Int. Workshop. on Characterization and Engineering Properties of Natural Soils, 3-4: 2681-2706. Griffiths D.V. and Fenton G.A. 1993. Seepage beneath water retaining structures founded on spatially random soil, Géotechnique, 43(6): 577-587. Mandelbrot B.B. 1983. The Fractal Geometry of Nature. San Francisco: W H Freeman. Matheron G. 1962. Traité de Géostatistique appliquée. Tome 1, Editions Technip, Paris, 334 p. Phoon K.K. and Kulhawy F.H. 1999a. Characterization of geotechnical variability. Can Geotech J, 36(4): 612-624. Phoon K.K. and Kulhawy F.H. 1999b. Evaluation of geotechnical property variability. Can Geotech J, 36(4): 625-639. Terzaghi K. 1943. Theoretical Soil Mechanics. New York: John Wiley and Sons. Turcotte D.L. 1986. Fractals and fragmentation. J Geophys Res, 91: 1921-1926. Vanmarcke E.H. 1977. Probabilistic modeling of soil profiles. J Geotech Eng Div, ASCE, 103: 1227-1246. Vanmarcke E.H. 1983. Random fields: analysis and synthesis. MIT Press, Cambridge.
Anomalous relaxation in fractal structures

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

Fujiwara, S.; Yonezawa, F.

1995-03-01

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

Fractal 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.
Fractal patterns of fracture in sandwich composite materials under biaxial tension

NASA Astrophysics Data System (ADS)

Fang, Jing; Yao, Xuefeng; Qi, Jia

1996-04-01

The paper presents a successful experiment to generate a fractal pattern of branching cracks in a brittle material sandwiched in ductile plates. A glass sheet bonded between two polycarbonate plates was heated at different levels of temperatures and the stress field due to the difference of thermal coefficients of the materials was solved by combining the results from isochromatic fringes and thermal stress analysis. At a critical degree of temperature, a crack was initiated at a point and soon produced crack branches to release the stored energy. A tree—like fractal patterns of the branch cracks was then developed with the growth of the branches that subsequently produced more branches on their ways of propagation. The fractal dimension of the fracture pattern was evaluated and the mechanism of the fragmentation was analyzed with the help of the residual stress field of isochromatic and isoclinic patterns.
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.
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.
Electronic shot noise in fractal conductors.

PubMed

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

2008-05-02

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

PubMed

Sharma, Vijay

2009-09-10

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

PubMed Central

Sharma, Vijay

2009-01-01

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

NASA Astrophysics Data System (ADS)

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

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

NASA Astrophysics Data System (ADS)

Cao, Wenzhuo; Lei, Qinghua

2018-01-01

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

NASA Astrophysics Data System (ADS)

Ulyanov, Alexander S.; Lyapina, Anna M.; Ulianova, Onega V.; Feodorova, Valentina A.

2010-10-01

New field of application of fractal dimensions is proposed. A technique, based on the calculation of fractal dimension, was used for express-diagnostics and identification of bacteria of the vaccine strain Yersinia pestis EV line NIIEG. Purpose of this study was the experimental investigation of properties of speckle patterns, formed under laser illumination of a single colony of the strain that was grown on different agars.
Influence of condition of growth of bacterial colonies on fractal dimension of bacterial speckle patterns

NASA Astrophysics Data System (ADS)

Ulyanov, Alexander S.; Lyapina, Anna M.; Ulianova, Onega V.; Feodorova, Valentina A.

2011-03-01

New field of application of fractal dimensions is proposed. A technique, based on the calculation of fractal dimension, was used for express-diagnostics and identification of bacteria of the vaccine strain Yersinia pestis EV line NIIEG. Purpose of this study was the experimental investigation of properties of speckle patterns, formed under laser illumination of a single colony of the strain that was grown on different agars.
From Mathematical Monsters to Generalized Scale Invariance in Geophysics: Highlights of the Multifractal Saga

NASA Astrophysics Data System (ADS)

Schertzer, D. J.; Tchiguirinskaia, I.; Lovejoy, S.

2013-12-01

Fractals and multifractals are very illustrative of the profound synergies between mathematics and geophysics. The book ';Fractal Geometry of Nature' (Mandelbrot, 1982) brilliantly demonstrated the genericity in geophysics of geometric forms like Cantor set, Peano curve and Koch snowflake, which were once considered as mathematical monsters. However, to tame the geophysical monsters (e.g. extreme weather, floods, earthquakes), it was required to go beyond geometry and a unique fractal dimension. The concept of multifractal was coined in the course of rather theoretical debates on intermittency in hydrodynamic turbulence, sometimes with direct links to atmospheric dynamics. The latter required a generalized notion of scale in order to deal both with scale symmetries and strong anisotropies (e.g. time vs. space, vertical vs. horizontal). It was thus possible to show that the consequences of intermittency are of first order, not just 'corrections' with respect to the classical non-intermittent modeling. This was in fact a radical paradigm shift for geophysics: the extreme variability of geophysical fields over wide ranges of scale, which had long been so often acknowledged and deplored, suddenly became handy. Recent illustrations are the possibility to track down in large date sets the Higgs boson of intermittence, i.e. a first order multifractal phase transition leading to self-organized criticality, and to simulate intermittent vector fields with the help of Lie cascades, based for instance on random Clifford algebra. It is rather significant that this revolution is no longer limited to fundamental and theoretical problems of geophysics, but now touches many applications including environmental management, in particular for urban management and resilience. These applications are particularly stimulating when taken in their full complexity.
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.
Use of wavelet-packet transforms to develop an engineering model for multifractal characterization of mutation dynamics in pathological and nonpathological gene sequences

NASA Astrophysics Data System (ADS)

Walker, David Lee

1999-12-01

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

NASA Astrophysics Data System (ADS)

Cao, Ting; Yang, Nan; Wang, Fengping; Gao, Ting; Wang, Weixing

2017-11-01

With the development of computer vision technology, crack detection based on digital image segmentation method arouses global attentions among researchers and transportation ministries. Since the crack always exhibits the random shape and complex texture, it is still a challenge to accomplish reliable crack detection results. Therefore, a novel crack image segmentation method based on fractal DBC (differential box counting) is introduced in this paper. The proposed method can estimate every pixel fractal feature based on neighborhood information which can consider the contribution from all possible direction in the related block. The block moves just one pixel every time so that it could cover all the pixels in the crack image. Unlike the classic DBC method which only describes fractal feature for the related region, this novel method can effectively achieve crack image segmentation according to the fractal feature of every pixel. The experiment proves the proposed method can achieve satisfactory results in crack detection.
Analysis of regional deformation and strain accumulation data adjacent to the San Andreas fault

NASA Technical Reports Server (NTRS)

Turcotte, Donald L.

1991-01-01

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

PubMed

Kopelman, R

1988-09-23

Classical reaction kinetics has been found to be unsatisfactory when the reactants are spatially constrained on the microscopic level by either walls, phase boundaries, or force fields. Recently discovered theories of heterogeneous reaction kinetics have dramatic consequences, such as fractal orders for elementary reactions, self-ordering and self-unmixing of reactants, and rate coefficients with temporal "memories." The new theories were needed to explain the results of experiments and supercomputer simulations of reactions that were confined to low dimensions or fractal dimensions or both. Among the practical examples of "fractal-like kinetics" are chemical reactions in pores of membranes, excitation trapping in molecular aggregates, exciton fusion in composite materials, and charge recombination in colloids and clouds.
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.

Fractality Evidence and Long-Range Dependence on Capital Markets: a Hurst Exponent Evaluation

NASA Astrophysics Data System (ADS)

Oprean, Camelia; Tănăsescu, Cristina

2014-07-01

Since the existence of market memory could implicate the rejection of the efficient market hypothesis, the aim of this paper is to find any evidence that selected emergent capital markets (eight European and BRIC markets, namely Hungary, Romania, Estonia, Czech Republic, Brazil, Russia, India and China) evince long-range dependence or the random walk hypothesis. In this paper, the Hurst exponent as calculated by R/S fractal analysis and Detrended Fluctuation Analysis is our measure of long-range dependence in the series. The results reinforce our previous findings and suggest that if stock returns present long-range dependence, the random walk hypothesis is not valid anymore and neither is the market efficiency hypothesis.
Anomalous diffusion on a random comblike structure

NASA Astrophysics Data System (ADS)

Havlin, Shlomo; Kiefer, James E.; Weiss, George H.

1987-08-01

We have recently studied a random walk on a comblike structure as an analog of diffusion on a fractal structure. In our earlier work, the comb was assumed to have a deterministic structure, the comb having teeth of infinite length. In the present paper we study diffusion on a one-dimensional random comb, the length of whose teeth are random variables with an asymptotic stable law distribution φ(L)~L-(1+γ) where 0<γ<=1. Two mean-field methods are used for the analysis, one based on the continuous-time random walk, and the second a self-consistent scaling theory. Both lead to the same conclusions. We find that the diffusion exponent characterizing the mean-square displacement along the backbone of the comb is dw=4/(1+γ) for γ<1 and dw=2 for γ>=1. The probability of being at the origin at time t is P0(t)~t-ds/2 for large t with ds=(3-γ)/2 for γ<1 and ds=1 for γ>1. When a field is applied along the backbone of the comb the diffusion exponent is dw=2/(1+γ) for γ<1 and dw=1 for γ>=1. The theoretical results are confirmed using the exact enumeration method.
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.
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).
Buried mine detection using fractal geometry analysis to the LWIR successive line scan data image

NASA Astrophysics Data System (ADS)

Araki, Kan

2012-06-01

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

NASA Astrophysics Data System (ADS)

Hausdorff, J. M.

1998-03-01

The complex, hierarchical locomotor system normally does a remarkable job of controlling an inherently unstable, multi-joint system. Nevertheless, the stride interval --- the duration of a gait cycle --- fluctuates from one stride to the next, even under stationary conditions. We used random walk analysis to study the dynamical properties of these fluctuations under normal conditions and how they change with disease and aging. Random walk analysis of the stride-to-stride fluctuations of healthy, young adult men surprisingly reveals a self-similar pattern: fluctuations at one time scale are statistically similar to those at multiple other time scales (Hausdorff et al, J Appl Phsyiol, 1995). To study the stability of this fractal property, we analyzed data obtained from healthy subjects who walked for 1 hour at their usual pace, as well as at slower and faster speeds. The stride interval fluctuations exhibited long-range correlations with power-law decay for up to a thousand strides at all three walking rates. In contrast, during metronomically-paced walking, these long-range correlations disappeared; variations in the stride interval were uncorrelated and non-fractal (Hausdorff et al, J Appl Phsyiol, 1996). To gain insight into the mechanism(s) responsible for this fractal property, we examined the effects of aging and neurological impairment. Using detrended fluctuation analysis (DFA), we computed α, a measure of the degree to which one stride interval is correlated with previous and subsequent intervals over different time scales. α was significantly lower in healthy elderly subjects compared to young adults (p < .003) and in subjects with Huntington's disease, a neuro-degenerative disorder of the central nervous system, compared to disease-free controls (p < 0.005) (Hausdorff et al, J Appl Phsyiol, 1997). α was also significantly related to degree of functional impairment in subjects with Huntington's disease (r=0.78). Recently, we have observed that just as there are changes with α during aging, there also changes with development. Apparently, the fractal scaling of walking does not become mature until children are eleven years old. Conclusions: The fractal dynamics of spontaneous stride interval fluctuations are normally quite robust and are apparently intrinsic to the healthy adult locomotor system. However, alterations in this fractal scaling property are associated with impairment in central nervous system control, aging and neural development.
Fractals for Geoengineering

NASA Astrophysics Data System (ADS)

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

2016-04-01

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

NASA Astrophysics Data System (ADS)

Dean, Cory

2015-03-01

In 1976, Douglas Hofstadter predicted that in the presence of both a strong magnetic field, and a spatially varying periodic potential, Bloch electrons confined to a 2D quantum well exhibit a self-similar fractal energy spectrum known as the ``Hofstadter's Butterfly.'' In subsequent years, experimental discovery of the quantum Hall effect gave birth to an expansive field of research into 2D electronic systems in the presence of a magnetic field, however, direct confirmation of the fractal spectrum remained elusive. Recently we demonstrated that graphene, in which Bloch electrons can be described by Dirac fermions, provides a new opportunity to investigate this nearly 40 year old problem. In this talk I will discuss the experimental realization of Hofstader's butterfly by exploiting nano-scale interfacial effects between graphene and hexagonal boron nitride substrates, together with application of extremely high magnetic fields. Utilizing newly developed techniques to fabricate ultra-clean graphene devices, I will additionally demonstrate the capability to probe for the first time the effect of strong electron interactions within the fractal Hofstadter spectrum.
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).
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.
Infrared small target detection in heavy sky scene clutter based on sparse representation

NASA Astrophysics Data System (ADS)

Liu, Depeng; Li, Zhengzhou; Liu, Bing; Chen, Wenhao; Liu, Tianmei; Cao, Lei

2017-09-01

A novel infrared small target detection method based on sky clutter and target sparse representation is proposed in this paper to cope with the representing uncertainty of clutter and target. The sky scene background clutter is described by fractal random field, and it is perceived and eliminated via the sparse representation on fractal background over-complete dictionary (FBOD). The infrared small target signal is simulated by generalized Gaussian intensity model, and it is expressed by the generalized Gaussian target over-complete dictionary (GGTOD), which could describe small target more efficiently than traditional structured dictionaries. Infrared image is decomposed on the union of FBOD and GGTOD, and the sparse representation energy that target signal and background clutter decomposed on GGTOD differ so distinctly that it is adopted to distinguish target from clutter. Some experiments are induced and the experimental results show that the proposed approach could improve the small target detection performance especially under heavy clutter for background clutter could be efficiently perceived and suppressed by FBOD and the changing target could also be represented accurately by GGTOD.
Implementation for wideband applications using UWB fractal patch antenna

NASA Astrophysics Data System (ADS)

Kumar, D. Naresh

2018-04-01

This paper defines in detail about the diverse fractal patch antenna. Microstrip patch antennas has evolved in the field of research and development extending its impact across wide range of applications. A combination of patch antenna with fractal patterns has become a tryout to outspread it further. Because of its low profile nature patch antennas have added to a lot of prominence. Apart from have this property it can also be renovated further for wide bandwidth (2929 MHz) applications, as it exhibits self-analogous property. This antenna is premeditated on a patch using Sierpinski(4.040 GHz, 6.566 GHz) and Koch fractal geometries respectively. The antenna is designed using HFSS software.
Isolation and Connectivity in Random Geometric Graphs with Self-similar Intensity Measures

NASA Astrophysics Data System (ADS)

Dettmann, Carl P.

2018-05-01

Random geometric graphs consist of randomly distributed nodes (points), with pairs of nodes within a given mutual distance linked. In the usual model the distribution of nodes is uniform on a square, and in the limit of infinitely many nodes and shrinking linking range, the number of isolated nodes is Poisson distributed, and the probability of no isolated nodes is equal to the probability the whole graph is connected. Here we examine these properties for several self-similar node distributions, including smooth and fractal, uniform and nonuniform, and finitely ramified or otherwise. We show that nonuniformity can break the Poisson distribution property, but it strengthens the link between isolation and connectivity. It also stretches out the connectivity transition. Finite ramification is another mechanism for lack of connectivity. The same considerations apply to fractal distributions as smooth, with some technical differences in evaluation of the integrals and analytical arguments.
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.
Cluster-cluster correlations and constraints on the correlation hierarchy

NASA Technical Reports Server (NTRS)

Hamilton, A. J. S.; Gott, J. R., III

1988-01-01

The hypothesis that galaxies cluster around clusters at least as strongly as they cluster around galaxies imposes constraints on the hierarchy of correlation amplitudes in hierachical clustering models. The distributions which saturate these constraints are the Rayleigh-Levy random walk fractals proposed by Mandelbrot; for these fractal distributions cluster-cluster correlations are all identically equal to galaxy-galaxy correlations. If correlation amplitudes exceed the constraints, as is observed, then cluster-cluster correlations must exceed galaxy-galaxy correlations, as is observed.
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.
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.
Zn-metalloprotease sequences in extremophiles

NASA Astrophysics Data System (ADS)

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

2010-09-01

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

PubMed

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

2013-08-01

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

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.
Nonlinear Field Equations and Solitons as Particles

NASA Astrophysics Data System (ADS)

Maccari, Attilio

2006-05-01

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

NASA Astrophysics Data System (ADS)

Deems, J. S.

2017-12-01

Knowledge of spatial patterns of snow accumulation is required for understanding the hydrology, climatology, and ecology of mountain regions. Spatial structure in snow accumulation patterns changes with the scale of observation, a feature that has been characterized using fractal dimensions calculated from lidar-derived snow depth maps: fractal scaling structure at short length scales, with a `scale break' transition to more stochastic patterns at longer separation distances. Previous work has shown that this fractal structure of snow depth distributions differs between sites with different vegetation and terrain characteristics. Forested areas showed a transition to a nearly random spatial distribution at a much shorter lag distance than do unforested sites, enabling a statistical characterization. Alpine areas, however, showed strong spatial structure for a much wider scale range, and were the source of the dominant spatial pattern observable over a wider area. These spatial structure characteristics suggest that the choice of measurement or model resolution (satellite sensor, DEM, field survey point spacing, etc.) will strongly affect the estimates of snow volume or mass, as well as the magnitude of spatial variability. These prior efforts used data sets that were high resolution ( 1 m laser point spacing) but of limited extent ( 1 km2), constraining detection of scale features such as fractal dimension or scale breaks to areas of relatively similar characteristics and to lag distances of under 500 m. New datasets available from the NASA JPL Airborne Snow Observatory (ASO) provide similar resolution but over large areas, enabling assessment of snow spatial structure across an entire watershed, or in similar vegetation or physiography but in different parts of the basin. Additionally, the multi-year ASO time series allows an investigation into the temporal stability of these scale characteristics, within a single snow season and between seasons of strongly varying accumulation totals and patterns. This presentation will explore initial results from this study, using data from the Tuolumne River Basin in California, USA. Fractal scaling characteristics derived from ASO lidar snow depth measurements are examined at the basin scale, as well as in varying topographic and forest cover environments.
Chaotic electron transport in semiconductor devices

NASA Astrophysics Data System (ADS)

Scannell, William Christian

The field of quantum chaos investigates the quantum mechanical behavior of classically chaotic systems. This dissertation begins by describing an experiment conducted on an apparatus constructed to represent a three dimensional analog of a classically chaotic system. Patterns of reflected light are shown to produce fractals, and the behavior of the fractal dimension D F is shown to depend on the light's ability to escape the apparatus. The classically chaotic system is then used to investigate the conductance properties of semiconductor heterostructures engineered to produce a conducting plane relatively free of impurities and defects. Introducing walls that inhibit conduction to partition off sections considerably smaller than the mean distance between impurities defines devices called 'billiards'. Cooling to low temperatures enables the electrons traveling through the billiard to maintain quantum mechanical phase. Exposure to a changing electric or magnetic field alters the electron's phase, leading to fluctuations in the conductance through the billiard. Magnetoconductance fluctuations in billiards have previously been shown to be fractal. This behavior has been charted using an empirical parameter, Q, that is a measure of the resolution of the energy levels within the billiard. The relationship with Q is shown to extend beyond the ballistic regime into the 'quasi-ballistic' and 'diffusive' regimes, characterized by having defects within the conduction plane. A model analogous to the classically chaotic system is proposed as the origin of the fractal conductance fluctuations. This model is shown to be consistent with experiment and to account for changes of fine scale features in MCF known to occur when a billiard is brought to room temperature between low temperature measurements. An experiment is conducted in which fractal conductance fluctuations (FCF) are produced by exposing a billiard to a changing electric field. Comparison of DF values of FCF produced by electric fields is made to FCF produced by magnetic fields. FCF with high DF values are shown to de-correlate at smaller increments of field than the FCF with lower DF values. This indicates that FCF may be used as a novel sensor of external fields, so the response of FCF to high bias voltages is investigated.
Fractal Analyses of High-Resolution Cloud Droplet Measurements.

NASA Astrophysics Data System (ADS)

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

1994-02-01

Fractal analyses of individual cloud droplet distributions using aircraft measurements along one-dimensional horizontal cross sections through clouds are performed. Box counting and cluster analyses are used to determine spatial scales of inhomogeneity of cloud droplet spacing. These analyses reveal that droplet spatial distributions do not exhibit a fractal behavior. A high variability in local droplet concentration in cloud volumes undergoing mixing was found. In these regions, thin filaments of cloudy air with droplet concentration close to those observed in cloud cores were found. Results suggest that these filaments may be anisotropic. Additional box counting analyses performed for various classes of cloud droplet diameters indicate that large and small droplets are similarly distributed, except for the larger characteristic spacing of large droplets.A cloud-clear air interface defined by a certain threshold of total droplet count (TDC) was investigated. There are indications that this interface is a convoluted surface of a fractal nature, at least in actively developing cumuliform clouds. In contrast, TDC in the cloud interior does not have fractal or multifractal properties. Finally a random Cantor set (RCS) was introduced as a model of a fractal process with an ill-defined internal scale. A uniform measure associated with the RCS after several generations was introduced to simulate the TDC records. Comparison of the model with real TDC records indicates similar properties of both types of data series.
Fractal 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.
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).
SU-E-T-418: Explore the Sensitive of the Planar Quality Assurance to the MLC Error with Different Beam Complexity in Intensity-Modulate Radiation Therapy

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

Wang, J; Peng, J; Xie, J

2015-06-15

Purpose: The purpose of this study is to investigate the sensitivity of the planar quality assurance to MLC errors with different beam complexities in intensity-modulate radiation therapy. Methods: sixteen patients’ planar quality assurance (QA) plans in our institution were enrolled in this study, including 10 dynamic MLC (DMLC) IMRT plans measured by Portal Dosimetry and 6 static MLC (SMLC) IMRT plans measured by Mapcheck. The gamma pass rate was calculated using vender’s software. The field numbers were 74 and 40 for DMLC and SMLC, respectively. A random error was generated and introduced to these fields. The modified gamma pass ratemore » was calculated by comparing the original measured fluence and modified fields’ fluence. A decreasing gamma pass rate was acquired using the original gamma pass rate minus the modified gamma pass rate. Eight complexity scores were calculated in MATLAB based on the fluence and MLC sequence of these fields. The complexity scores include fractal dimension, monitor unit of field, modulation index, fluence map complexity, weighted average of field area, weighted average of field perimeter, and small aperture ratio ( <5cm{sup 2} and <50cm{sup 2}). The Spearman’s rank correlation coefficient was implemented to analyze the correlation between these scores and decreasing gamma rate. Results: The relation between the decreasing gamma pass rate and field complexity was insignificant for most complexity scores. The most significant complexity score was fluence map complexity for SMLC, which have ρ =0.4274 (p-value=0.0063). For DMLC, the most significant complex score was fractal dimension, which have ρ=−0.3068 (p-value=0.0081). Conclusions: According to the primarily Result of this study, the sensitivity gamma pass rate was not strongly relate to the field complexity.« less
A shift to randomness of brain oscillations in people with autism.

PubMed

Lai, Meng-Chuan; Lombardo, Michael V; Chakrabarti, Bhismadev; Sadek, Susan A; Pasco, Greg; Wheelwright, Sally J; Bullmore, Edward T; Baron-Cohen, Simon; Suckling, John

2010-12-15

Resting-state functional magnetic resonance imaging (fMRI) enables investigation of the intrinsic functional organization of the brain. Fractal parameters such as the Hurst exponent, H, describe the complexity of endogenous low-frequency fMRI time series on a continuum from random (H = .5) to ordered (H = 1). Shifts in fractal scaling of physiological time series have been associated with neurological and cardiac conditions. Resting-state fMRI time series were recorded in 30 male adults with an autism spectrum condition (ASC) and 33 age- and IQ-matched male volunteers. The Hurst exponent was estimated in the wavelet domain and between-group differences were investigated at global and voxel level and in regions known to be involved in autism. Complex fractal scaling of fMRI time series was found in both groups but globally there was a significant shift to randomness in the ASC (mean H = .758, SD = .045) compared with neurotypical volunteers (mean H = .788, SD = .047). Between-group differences in H, which was always reduced in the ASC group, were seen in most regions previously reported to be involved in autism, including cortical midline structures, medial temporal structures, lateral temporal and parietal structures, insula, amygdala, basal ganglia, thalamus, and inferior frontal gyrus. Severity of autistic symptoms was negatively correlated with H in retrosplenial and right anterior insular cortex. Autism is associated with a small but significant shift to randomness of endogenous brain oscillations. Complexity measures may provide physiological indicators for autism as they have done for other medical conditions. Copyright © 2010 Society of Biological Psychiatry. Published by Elsevier Inc. All rights reserved.
Towards thermomechanics of fractal media

NASA Astrophysics Data System (ADS)

Ostoja-Starzewski, Martin

2007-11-01

Hans Ziegler’s thermomechanics [1,2,3], established half a century ago, is extended to fractal media on the basis of a recently introduced continuum mechanics due to Tarasov [14,15]. Employing the concept of internal (kinematic) variables and internal stresses, as well as the quasiconservative and dissipative stresses, a field form of the second law of thermodynamics is derived. In contradistinction to the conventional Clausius Duhem inequality, it involves generalized rates of strain and internal variables. Upon introducing a dissipation function and postulating the thermodynamic orthogonality on any lengthscale, constitutive laws of elastic-dissipative fractal media naturally involving generalized derivatives of strain and stress can then be derived. This is illustrated on a model viscoelastic material. Also generalized to fractal bodies is the Hill condition necessary for homogenization of their constitutive responses.
Fractal growth mechanism of sp3-bonded 5H-BN microcones by plasma-assisted pulsed-laser chemical vapor deposition

NASA Astrophysics Data System (ADS)

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

2006-08-01

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

PubMed

Wang, Lifen; Wen, Jianguo; Sheng, Huaping; Miller, Dean J

2016-10-06

Fractals are commonly observed in nature and elucidating the mechanisms of fractal-related growth is a compelling issue for both fundamental science and technology. Here we report an in situ electron microscopy study of dynamic fractal growth of platinum during electrodeposition in a miniaturized electrochemical cell at varying growth conditions. Highly dendritic growth - either dense branching or ramified islands - are formed at the solid-electrolyte interface. We show how the diffusion length of ions in the electrolyte influences morphology selection and how instability induced by initial surface roughness, combined with local enhancement of electric field, gives rise to non-uniform branched deposition as a result of nucleation/growth at preferred locations. Comparing the growth behavior under these different conditions provides new insight into the fundamental mechanisms of platinum nucleation.
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
Microstructure of cotton fibrous assemblies based on computed tomography

NASA Astrophysics Data System (ADS)

Jing, Hui; Yu, Weidong

2017-12-01

This paper describes for the first time the analysis of inner microstructure of cotton fibrous assemblies using computed tomography. Microstructure parameters such as packing density, fractal dimension as well as porosity including open porosity, closed porosity and total porosity are calculated based on 2D data from computed tomography. Values of packing density and fractal dimension are stable in random oriented fibrous assemblies, and there exists a satisfactory approximate linear relationship between them. Moreover, poles analysis indicates that porosity represents the tightness of fibrous assemblies and open poles are main existence.
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
On the fractal characterization of Paretian Poisson processes

NASA Astrophysics Data System (ADS)

Eliazar, Iddo I.; Sokolov, Igor M.

2012-06-01

Paretian Poisson processes are Poisson processes which are defined on the positive half-line, have maximal points, and are quantified by power-law intensities. Paretian Poisson processes are elemental in statistical physics, and are the bedrock of a host of power-law statistics ranging from Pareto's law to anomalous diffusion. In this paper we establish evenness-based fractal characterizations of Paretian Poisson processes. Considering an array of socioeconomic evenness-based measures of statistical heterogeneity, we show that: amongst the realm of Poisson processes which are defined on the positive half-line, and have maximal points, Paretian Poisson processes are the unique class of 'fractal processes' exhibiting scale-invariance. The results established in this paper are diametric to previous results asserting that the scale-invariance of Poisson processes-with respect to physical randomness-based measures of statistical heterogeneity-is characterized by exponential Poissonian intensities.
Minimal spanning trees at the percolation threshold: A numerical calculation

NASA Astrophysics Data System (ADS)

Sweeney, Sean M.; Middleton, A. Alan

2013-09-01

The fractal dimension of minimal spanning trees on percolation clusters is estimated for dimensions d up to d=5. A robust analysis technique is developed for correlated data, as seen in such trees. This should be a robust method suitable for analyzing a wide array of randomly generated fractal structures. The trees analyzed using these techniques are built using a combination of Prim's and Kruskal's algorithms for finding minimal spanning trees. This combination reduces memory usage and allows for simulation of larger systems than would otherwise be possible. The path length fractal dimension ds of MSTs on critical percolation clusters is found to be compatible with the predictions of the perturbation expansion developed by T. S. Jackson and N. Read [Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.81.021131 81, 021131 (2010)].
Random-field Ising model on isometric lattices: Ground states and non-Porod scattering

NASA Astrophysics Data System (ADS)

Bupathy, Arunkumar; Banerjee, Varsha; Puri, Sanjay

2016-01-01

We use a computationally efficient graph cut method to obtain ground state morphologies of the random-field Ising model (RFIM) on (i) simple cubic (SC), (ii) body-centered cubic (BCC), and (iii) face-centered cubic (FCC) lattices. We determine the critical disorder strength Δc at zero temperature with high accuracy. For the SC lattice, our estimate (Δc=2.278 ±0.002 ) is consistent with earlier reports. For the BCC and FCC lattices, Δc=3.316 ±0.002 and 5.160 ±0.002 , respectively, which are the most accurate estimates in the literature to date. The small-r behavior of the correlation function exhibits a cusp regime characterized by a cusp exponent α signifying fractal interfaces. In the paramagnetic phase, α =0.5 ±0.01 for all three lattices. In the ferromagnetic phase, the cusp exponent shows small variations due to the lattice structure. Consequently, the interfacial energy Ei(L ) for an interface of size L is significantly different for the three lattices. This has important implications for nonequilibrium properties.
A Complex Story: Universal Preference vs. Individual Differences Shaping Aesthetic Response to Fractals Patterns.

PubMed

Street, Nichola; Forsythe, Alexandra M; Reilly, Ronan; Taylor, Richard; Helmy, Mai S

2016-01-01

Fractal patterns offer one way to represent the rough complexity of the natural world. Whilst they dominate many of our visual experiences in nature, little large-scale perceptual research has been done to explore how we respond aesthetically to these patterns. Previous research (Taylor et al., 2011) suggests that the fractal patterns with mid-range fractal dimensions (FDs) have universal aesthetic appeal. Perceptual and aesthetic responses to visual complexity have been more varied with findings suggesting both linear (Forsythe et al., 2011) and curvilinear (Berlyne, 1970) relationships. Individual differences have been found to account for many of the differences we see in aesthetic responses but some, such as culture, have received little attention within the fractal and complexity research fields. This two-study article aims to test preference responses to FD and visual complexity, using a large cohort (N = 443) of participants from around the world to allow universality claims to be tested. It explores the extent to which age, culture and gender can predict our preferences for fractally complex patterns. Following exploratory analysis that found strong correlations between FD and visual complexity, a series of linear mixed-effect models were implemented to explore if each of the individual variables could predict preference. The first tested a linear complexity model (likelihood of selecting the more complex image from the pair of images) and the second a mid-range FD model (likelihood of selecting an image within mid-range). Results show that individual differences can reliably predict preferences for complexity across culture, gender and age. However, in fitting with current findings the mid-range models show greater consistency in preference not mediated by gender, age or culture. This article supports the established theory that the mid-range fractal patterns appear to be a universal construct underlying preference but also highlights the fragility of universal claims by demonstrating individual differences in preference for the interrelated concept of visual complexity. This highlights a current stalemate in the field of empirical aesthetics.
DETECTION OF SMALL-SCALE GRANULAR STRUCTURES IN THE QUIET SUN WITH THE NEW SOLAR TELESCOPE

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

Abramenko, V. I.; Yurchyshyn, V. B.; Goode, P. R.

2012-09-10

Results of a statistical analysis of solar granulation are presented. A data set of 36 images of a quiet-Sun area on the solar disk center was used. The data were obtained with the 1.6 m clear aperture New Solar Telescope at Big Bear Solar Observatory and with a broadband filter centered at the TiO (705.7 nm) spectral line. The very high spatial resolution of the data (diffraction limit of 77 km and pixel scale of 0.''0375) augmented by the very high image contrast (15.5% {+-} 0.6%) allowed us to detect for the first time a distinct subpopulation of mini-granular structures.more » These structures are dominant on spatial scales below 600 km. Their size is distributed as a power law with an index of -1.8 (which is close to the Kolmogorov's -5/3 law) and no predominant scale. The regular granules display a Gaussian (normal) size distribution with a mean diameter of 1050 km. Mini-granular structures contribute significantly to the total granular area. They are predominantly confined to the wide dark lanes between regular granules and often form chains and clusters, but different from magnetic bright points. A multi-fractality test reveals that the structures smaller than 600 km represent a multi-fractal, whereas on larger scales the granulation pattern shows no multi-fractality and can be considered as a Gaussian random field. The origin, properties, and role of the population of mini-granular structures in the solar magnetoconvection are yet to be explored.« less

Characterizing spatial heterogeneity based on the b-value and fractal analyses of the 2015 Nepal earthquake sequence

NASA Astrophysics Data System (ADS)

Nampally, Subhadra; Padhy, Simanchal; Dimri, Vijay P.

2018-01-01

The nature of spatial distribution of heterogeneities in the source area of the 2015 Nepal earthquake is characterized based on the seismic b-value and fractal analysis of its aftershocks. The earthquake size distribution of aftershocks gives a b-value of 1.11 ± 0.08, possibly representing the highly heterogeneous and low stress state of the region. The aftershocks exhibit a fractal structure characterized by a spectrum of generalized dimensions, Dq varying from D2 = 1.66 to D22 = 0.11. The existence of a fractal structure suggests that the spatial distribution of aftershocks is not a random phenomenon, but it self-organizes into a critical state, exhibiting a scale-independent structure governed by a power-law scaling, where a small perturbation in stress is sufficient enough to trigger aftershocks. In order to obtain the bias in fractal dimensions resulting from finite data size, we compared the multifractal spectrum for the real data and random simulations. On comparison, we found that the lower limit of bias in D2 is 0.44. The similarity in their multifractal spectra suggests the lack of long-range correlation in the data, with an only weakly multifractal or a monofractal with a single correlation dimension D2 characterizing the data. The minimum number of events required for a multifractal process with an acceptable error is discussed. We also tested for a possible correlation between changes in D2 and energy released during the earthquakes. The values of D2 rise during the two largest earthquakes (M > 7.0) in the sequence. The b- and D2 values are related by D2 = 1.45 b that corresponds to the intermediate to large earthquakes. Our results provide useful constraints on the spatial distribution of b- and D2-values, which are useful for seismic hazard assessment in the aftershock area of a large earthquake.
Shape characteristics of equilibrium and non-equilibrium fractal clusters.

PubMed

Mansfield, Marc L; Douglas, Jack F

2013-07-28

It is often difficult in practice to discriminate between equilibrium and non-equilibrium nanoparticle or colloidal-particle clusters that form through aggregation in gas or solution phases. Scattering studies often permit the determination of an apparent fractal dimension, but both equilibrium and non-equilibrium clusters in three dimensions frequently have fractal dimensions near 2, so that it is often not possible to discriminate on the basis of this geometrical property. A survey of the anisotropy of a wide variety of polymeric structures (linear and ring random and self-avoiding random walks, percolation clusters, lattice animals, diffusion-limited aggregates, and Eden clusters) based on the principal components of both the radius of gyration and electric polarizability tensor indicates, perhaps counter-intuitively, that self-similar equilibrium clusters tend to be intrinsically anisotropic at all sizes, while non-equilibrium processes such as diffusion-limited aggregation or Eden growth tend to be isotropic in the large-mass limit, providing a potential means of discriminating these clusters experimentally if anisotropy could be determined along with the fractal dimension. Equilibrium polymer structures, such as flexible polymer chains, are normally self-similar due to the existence of only a single relevant length scale, and are thus anisotropic at all length scales, while non-equilibrium polymer structures that grow irreversibly in time eventually become isotropic if there is no difference in the average growth rates in different directions. There is apparently no proof of these general trends and little theoretical insight into what controls the universal anisotropy in equilibrium polymer structures of various kinds. This is an obvious topic of theoretical investigation, as well as a matter of practical interest. To address this general problem, we consider two experimentally accessible ratios, one between the hydrodynamic and gyration radii, the other between the viscosity and hydrodynamic radii, as potential measures of shape anisotropy. We also find a strong correlation between anisotropy and effective fractal dimension. These observations should provide new practical methods for quantifying the nature of particle clustering in diverse contexts.
Origins and applications of the Montroll-Weiss continuous time random walk

NASA Astrophysics Data System (ADS)

Shlesinger, Michael F.

2017-05-01

The Continuous Time Random Walk (CTRW) was introduced by Montroll and Weiss in 1965 in a purely mathematical paper. Its antecedents and later applications beginning in 1973 are discussed, especially for the case of fractal time where the mean waiting time between jumps is infinite. Contribution to the Topical Issue: "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.
Quantitative characterization of the regressive ecological succession by fractal analysis of plant spatial patterns

USGS Publications Warehouse

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

2003-01-01

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

PubMed

Kearns, William D; Scott, Steven; Fozard, James L; Dillahunt-Aspillaga, Christina; Jasiewicz, Jan M

2016-01-01

To determine if movement path tortuosity in everyday ambulation decreases in Veterans being treated in a residential setting for traumatic brain injury. Elevated path tortuosity is observed in assisted living facility residents with cognitive impairment and at risk for falls, and tortuosity may decrease over the course of cognitive rehabilitation received by the Veterans. If observed, decreased tortuosity may be linked to improved clinical outcomes. Longitudinal observational study without random assignment. Veterans Affairs Medical Center inpatient residential polytrauma treatment facility. Twenty-two Veterans enrolled in a postacute predischarge residential polytrauma treatment facility. None, observation-only. Mayo-Portland Adaptability Index-4, and movement path tortuosity measured by Fractal Dimension (Fractal D). Fractal D was obtained continuously from an indoor movement tracking system primarily used to provide machine-generated prompts and reminders to facilitate activities of daily living. Patients were deemed "responders" (N = 10) if a significant linear decline in Fractal D occurred over the course of treatment, or nonresponders (N = 12) if no significant decline was observed. Responders had lower discharge Mayo-Portland Adaptability Inventory scores (mean = 32.6, SD = 9.53) than non-responders (mean = 39.5, SD = 6.02) (F = 2.07, df = 20, P = .05). Responders and nonresponders did not differ on initial injury severity or other demographic measures. Fractal D, a relatively simple measure of movement path tortuosity can be linked to functional recovery from traumatic brain injury.
Fractal serpentine-shaped design for stretchable wireless strain sensors

NASA Astrophysics Data System (ADS)

Dong, Wentao; Cheng, Xiao; Wang, Xiaoming; Zhang, Hailiang

2018-07-01

Stretchable sensors have been widely applied to biological fields due to their unique capacity to integrate with soft materials and curvilinear surfaces. The article presents the fractal serpentine-shaped design for stretchable wireless strain sensor which is operating around 1.6 GHz. The wireless passive LC sensor is formed by a fractal serpentine-shaped inductor coil and a concentric coplanar capacitor. The inductance of the fractal serpentine-shaped coil varies with the deformation of the wireless sensor, and the resonance frequency also varies with the applied strain of the wireless sensor embedded in soft substrate. The 40% stretchability of wireless sensor is verified by finite element analysis (FEA). Strain response of the stretchable wireless sensor has been characterized by experiments and demonstrates high strain responsivity about 6.74 MHz/1%. The stretchable wireless sensor has the potential to be used in biological and wearable applications.
Random-walk diffusion and drying of porous materials

NASA Astrophysics Data System (ADS)

Mehrafarin, M.; Faghihi, M.

2001-12-01

Based on random-walk diffusion, a microscopic model for drying is proposed to explain the characteristic features of the drying-rate curve of porous materials. The constant drying-rate period is considered as a normal diffusion process. The transition to the falling-rate regime is attributed to the fractal nature of porous materials which results in crossover to anomalous diffusion.
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).
A complexity theory model in science education problem solving: random walks for working memory and mental capacity.

PubMed

Stamovlasis, Dimitrios; Tsaparlis, Georgios

2003-07-01

The present study examines the role of limited human channel capacity from a science education perspective. A model of science problem solving has been previously validated by applying concepts and tools of complexity theory (the working memory, random walk method). The method correlated the subjects' rank-order achievement scores in organic-synthesis chemistry problems with the subjects' working memory capacity. In this work, we apply the same nonlinear approach to a different data set, taken from chemical-equilibrium problem solving. In contrast to the organic-synthesis problems, these problems are algorithmic, require numerical calculations, and have a complex logical structure. As a result, these problems cause deviations from the model, and affect the pattern observed with the nonlinear method. In addition to Baddeley's working memory capacity, the Pascual-Leone's mental (M-) capacity is examined by the same random-walk method. As the complexity of the problem increases, the fractal dimension of the working memory random walk demonstrates a sudden drop, while the fractal dimension of the M-capacity random walk decreases in a linear fashion. A review of the basic features of the two capacities and their relation is included. The method and findings have consequences for problem solving not only in chemistry and science education, but also in other disciplines.
Unsupervised segmentation of lung fields in chest radiographs using multiresolution fractal feature vector and deformable models.

PubMed

Lee, Wen-Li; Chang, Koyin; Hsieh, Kai-Sheng

2016-09-01

Segmenting lung fields in a chest radiograph is essential for automatically analyzing an image. We present an unsupervised method based on multiresolution fractal feature vector. The feature vector characterizes the lung field region effectively. A fuzzy c-means clustering algorithm is then applied to obtain a satisfactory initial contour. The final contour is obtained by deformable models. The results show the feasibility and high performance of the proposed method. Furthermore, based on the segmentation of lung fields, the cardiothoracic ratio (CTR) can be measured. The CTR is a simple index for evaluating cardiac hypertrophy. After identifying a suspicious symptom based on the estimated CTR, a physician can suggest that the patient undergoes additional extensive tests before a treatment plan is finalized.
Scattering by inhomogeneous systems with rough internal surfaces: Porous solids and random-field Ising systems

NASA Astrophysics Data System (ADS)

Wong, Po-Zen

1985-12-01

For a two-component inhomogeneous system consisting of compact domains of characteristic size R, I show that if the domain walls are ``rough'' and their root-mean-square fluctuation w over a distance r obeys a power law w=b(r/a)x (a is the lattice constant and x>0), then the geometrical correlation function γ(r) has leading terms proportional to rx and r for r<>R-1, where d is the dimension of the system. Two possible applications of this result are discussed. (i) In granular porous solids which have a minimum grain size Rmin, the above result implies that surface roughness can cause I(q) to fall off like 1/qα for q>>Rmin-1, where α=3+x>3 for d=3. In particular, when x>1, the surface becomes a fractal with dimension D=1+x=α-2, which can be extracted from the scattering data. On the other hand, if the grains are smooth and their size distribution obeys a power law dN(R)/dR~R-β over a range Rmin
An observationally-driven kinetic approach to coronal heating

NASA Astrophysics Data System (ADS)

Moraitis, K.; Toutountzi, A.; Isliker, H.; Georgoulis, M.; Vlahos, L.; Chintzoglou, G.

2016-11-01

Aims: Coronal heating through the explosive release of magnetic energy remains an open problem in solar physics. Recent hydrodynamical models attempt an investigation by placing swarms of "nanoflares" at random sites and times in modeled one-dimensional coronal loops. We investigate the problem in three dimensions, using extrapolated coronal magnetic fields of observed solar active regions. Methods: We applied a nonlinear force-free field extrapolation above an observed photospheric magnetogram of NOAA active region (AR) 11 158. We then determined the locations, energy contents, and volumes of "unstable" areas, namely areas prone to releasing magnetic energy due to locally accumulated electric current density. Statistical distributions of these volumes and their fractal dimension are inferred, investigating also their dependence on spatial resolution. Further adopting a simple resistivity model, we inferred the properties of the fractally distributed electric fields in these volumes. Next, we monitored the evolution of 105 particles (electrons and ions) obeying an initial Maxwellian distribution with a temperature of 10 eV, by following their trajectories and energization when subjected to the resulting electric fields. For computational convenience, the length element of the magnetic-field extrapolation is 1 arcsec, or 725 km, much coarser than the particles' collisional mean free path in the low corona (0.1-1 km). Results: The presence of collisions traps the bulk of the plasma around the unstable volumes, or current sheets (UCS), with only a tail of the distribution gaining substantial energy. Assuming that the distance between UCS is similar to the collisional mean free path we find that the low active-region corona is heated to 100-200 eV, corresponding to temperatures exceeding 2 MK, within tens of seconds for electrons and thousands of seconds for ions. Conclusions: Fractally distributed, nanoflare-triggening fragmented UCS in the active-region corona can heat electrons and ions with minor enhancements of the local resistivity. This statistical result is independent from the nature of the extrapolation and the spatial resolution of the modeled active-region corona. This finding should be coupled with a complete plasma treatment to determine whether a quasi-steady temperature similar to that of the ambient corona can be maintained, either via a kinetic or via a hybrid, kinetic and fluid, plasma treatment. The finding can also be extended to the quiet solar corona, provided that the currently undetected nanoflares are frequent enough to account for the lower (compared to active regions) energy losses in this case.
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.
Pulse regime in formation of fractal fibers

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

Smirnov, B. M., E-mail: bmsmirnov@gmail.com

The pulse regime of vaporization of a bulk metal located in a buffer gas is analyzed as a method of generation of metal atoms under the action of a plasma torch or a laser beam. Subsequently these atoms are transformed into solid nanoclusters, fractal aggregates and then into fractal fibers if the growth process proceeds in an external electric field. We are guided by metals in which transitions between s and d-electrons of their atoms are possible, since these metals are used as catalysts and filters in interaction with gas flows. The resistance of metal fractal structures to a gasmore » flow is evaluated that allows one to find optimal parameters of a fractal structure for gas flow propagation through it. The thermal regime of interaction between a plasma pulse or a laser beam and a metal surface is analyzed. It is shown that the basic energy from an external source is consumed on a bulk metal heating, and the efficiency of atom evaporation from the metal surface, that is the ratio of energy fluxes for vaporization and heating, is 10{sup –3}–10{sup –4} for transient metals under consideration. A typical energy flux (~10{sup 6} W/cm{sup 2}), a typical surface temperature (~3000 K), and a typical pulse duration (~1 μs) provide a sufficient amount of evaporated atoms to generate fractal fibers such that each molecule of a gas flow collides with the skeleton of fractal fibers many times.« less
Minimal spanning trees at the percolation threshold: a numerical calculation

NASA Astrophysics Data System (ADS)

Sweeney, Sean; Middleton, A. Alan

2013-03-01

Through computer simulations on a hypercubic lattice, we grow minimal spanning trees (MSTs) in up to five dimensions and examine their fractal dimensions. Understanding MSTs is imporant for studying systems with quenched disorder such as spin glasses. We implement a combination of Prim's and Kruskal's algorithms for finding MSTs in order to reduce memory usage and allow for simulation of larger systems than would otherwise be possible. These fractal objects are analyzed in an attempt to numerically verify predictions of the perturbation expansion developed by T. S. Jackson and N. Read for the pathlength fractal dimension ds of MSTs on percolation clusters at criticality [T. S. Jackson and N. Read, Phys. Rev. E 81, 021131 (2010)]. Examining these trees also sparked the development of an analysis technique for dealing with correlated data that could be easily generalized to other systems and should be a robust method for analyzing a wide array of randomly generated fractal structures. This work was made possible in part by NSF Grant No. DMR-1006731 and by the Syracuse University Gravitation and Relativity computing cluster, which is supported in part by NSF Grant No. PHY-0600953.
Theory and discretization of ideal magnetohydrodynamic equilibria with fractal pressure profiles

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

PubMed Central

Street, Nichola; Forsythe, Alexandra M.; Reilly, Ronan; Taylor, Richard; Helmy, Mai S.

2016-01-01

Fractal patterns offer one way to represent the rough complexity of the natural world. Whilst they dominate many of our visual experiences in nature, little large-scale perceptual research has been done to explore how we respond aesthetically to these patterns. Previous research (Taylor et al., 2011) suggests that the fractal patterns with mid-range fractal dimensions (FDs) have universal aesthetic appeal. Perceptual and aesthetic responses to visual complexity have been more varied with findings suggesting both linear (Forsythe et al., 2011) and curvilinear (Berlyne, 1970) relationships. Individual differences have been found to account for many of the differences we see in aesthetic responses but some, such as culture, have received little attention within the fractal and complexity research fields. This two-study article aims to test preference responses to FD and visual complexity, using a large cohort (N = 443) of participants from around the world to allow universality claims to be tested. It explores the extent to which age, culture and gender can predict our preferences for fractally complex patterns. Following exploratory analysis that found strong correlations between FD and visual complexity, a series of linear mixed-effect models were implemented to explore if each of the individual variables could predict preference. The first tested a linear complexity model (likelihood of selecting the more complex image from the pair of images) and the second a mid-range FD model (likelihood of selecting an image within mid-range). Results show that individual differences can reliably predict preferences for complexity across culture, gender and age. However, in fitting with current findings the mid-range models show greater consistency in preference not mediated by gender, age or culture. This article supports the established theory that the mid-range fractal patterns appear to be a universal construct underlying preference but also highlights the fragility of universal claims by demonstrating individual differences in preference for the interrelated concept of visual complexity. This highlights a current stalemate in the field of empirical aesthetics. PMID:27252634
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.
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 on the Distribution of Geological Hazards Based on Fractal Characteristics - a Case Study of Dachuan District

NASA Astrophysics Data System (ADS)

Wang, X.; Liu, H.; Yao, K.; Wei, Y.

2018-04-01

It is a complicated process to analyze the cause of geological hazard. Through the analysis function of GIS software, 250 landslides were randomly selected from 395 landslide hazards in the study area, superimposed with the types of landforms, annual rainfall and vegetation coverage respectively. It used box dimension method of fractal dimension theory to study the fractal characteristics of spatial distribution of landslide disasters in Dachuan district, and analyse the statistical results. Research findings showed that the The fractal dimension of the landslides in the Dachuan area is 0.9114, the correlation coefficient is 0.9627, and it has high autocorrelation. Zoning statistics according to various natural factors, the fractal dimension between landslide hazard points and deep hill, middle hill area is strong as well as the area whose average annual rainfall is 1050 mm-1250 mm and vegetation coverage is 30 %-60 %. Superposition of the potential hazard distribution map of single influence factors to get the potential hazard zoning of landslides in the area. Verifying the potential hazard zoning map of the potential landslides with 145 remaining disaster points, among them, there are 74 landslide hazard points in high risk area, accounting for 51.03 % of the total. There are 59 landslides in the middle risk area, accounting for 40.69 % of the total, and 12 in the low risk area, accounting for 8.28 % of the total. The matching degree of the verifying result and the potential hazard zoning is high. Therefore, the fractal dimension value divided the degree of geological disaster susceptibility can be described the influence degree of each influence factor to geological disaster point more intuitively, it also can divide potential disaster risk areas and provide visual data support for effective management of geological disasters.
Trabecular morphometry by fractal signature analysis is a novel marker of osteoarthritis progression.

PubMed

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

2009-12-01

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

DOE PAGES

Xi, Bin; Luo, Meng -Bo; Vinokur, Valerii M.; ...

2015-09-14

Here, we report first principle numerical study of domain wall (DW) depinning in two-dimensional magnetic film, which is modeled by 2D random-field Ising system with the dipole-dipole interaction. We observe non-conventional activation-type motion of DW and reveal the fractal structure of DW near the depinning transition. We determine scaling functions describing critical dynamics near the transition and obtain universal exponents establishing connection between thermal softening of pinning potential and critical dynamics. In addition, we observe that tuning the strength of the dipole-dipole interaction switches DW dynamics between two different universality classes, corresponding to two distinct dynamic regimes characterized by non-Arrheniusmore » and conventional Arrhenius-type DW motions.« less
FDTD simulations of localization and enhancements on fractal plasmonics nanostructures.

PubMed

Buil, Stéphanie; Laverdant, Julien; Berini, Bruno; Maso, Pierre; Hermier, Jean-Pierre; Quélin, Xavier

2012-05-21

A parallelized 3D FDTD (Finite-Difference Time-Domain) solver has been used to study the near-field electromagnetic intensity upon plasmonics nanostructures. The studied structures are obtained from AFM (Atomic Force Microscopy) topography measured on real disordered gold layers deposited by thermal evaporation under ultra-high vacuum. The simulation results obtained with these 3D metallic nanostructures are in good agreement with previous experimental results: the localization of the electromagnetic intensity in subwavelength areas ("hot spots") is demonstrated; the spectral and polarization dependences of the position of these "hot spots" are also satisfactory; the enhancement factors obtained are realistic compared to the experimental ones. These results could be useful to further our understanding of the electromagnetic behavior of random metal layers.
Beauty and the beholder: the role of visual sensitivity in visual preference

PubMed Central

Spehar, Branka; Wong, Solomon; van de Klundert, Sarah; Lui, Jessie; Clifford, Colin W. G.; Taylor, Richard P.

2015-01-01

For centuries, the essence of aesthetic experience has remained one of the most intriguing mysteries for philosophers, artists, art historians and scientists alike. Recently, views emphasizing the link between aesthetics, perception and brain function have become increasingly prevalent (Ramachandran and Hirstein, 1999; Zeki, 1999; Livingstone, 2002; Ishizu and Zeki, 2013). The link between art and the fractal-like structure of natural images has also been highlighted (Spehar et al., 2003; Graham and Field, 2007; Graham and Redies, 2010). Motivated by these claims and our previous findings that humans display a consistent preference across various images with fractal-like statistics, here we explore the possibility that observers’ preference for visual patterns might be related to their sensitivity for such patterns. We measure sensitivity to simple visual patterns (sine-wave gratings varying in spatial frequency and random textures with varying scaling exponent) and find that they are highly correlated with visual preferences exhibited by the same observers. Although we do not attempt to offer a comprehensive neural model of aesthetic experience, we demonstrate a strong relationship between visual sensitivity and preference for simple visual patterns. Broadly speaking, our results support assertions that there is a close relationship between aesthetic experience and the sensory coding of natural stimuli. PMID:26441611
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
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.
The cyclic and fractal seismic series preceding an mb 4.8 earthquake on 1980 February 14 near the Virgin Islands

USGS Publications Warehouse

Varnes, D.J.; Bufe, C.G.

1996-01-01

Seismic activity in the 10 months preceding the 1980 February 14, mb 4.8 earthquake in the Virgin Islands, reported on by Frankel in 1982, consisted of four principal cycles. Each cycle began with a relatively large event or series of closely spaced events, and the duration of the cycles progressively shortened by a factor of about 3/4. Had this regular shortening of the cycles been recognized prior to the earthquake, the time of the next episode of setsmicity (the main shock) might have been closely estimated 41 days in advance. That this event could be much larger than the previous events is indicated from time-to-failure analysis of the accelerating rise in released seismic energy, using a non-linear time- and slip-predictable foreshock model. Examination of the timing of all events in the sequence shows an even higher degree of order. Rates of seismicity, measured by consecutive interevent times, when plotted on an iteration diagram of a rate versus the succeeding rate, form a triangular circulating trajectory. The trajectory becomes an ascending helix if extended in a third dimension, time. This construction reveals additional and precise relations among the time intervals between times of relatively high or relatively low rates of seismic activity, including period halving and doubling. The set of 666 time intervals between all possible pairs of the 37 recorded events appears to be a fractal; the set of time points that define the intervals has a finite, non-integer correlation dimension of 0.70. In contrast, the average correlation dimension of 50 random sequences of 37 events is significantly higher, dose to 1.0. In a similar analysis, the set of distances between pairs of epicentres has a fractal correlation dimension of 1.52. Well-defined cycles, numerous precise ratios among time intervals, and a non-random temporal fractal dimension suggest that the seismic series is not a random process, but rather the product of a deterministic dynamic system.
Synthesis of Polyferrocenylsilane Block Copolymers and their Crystallization-Driven Self-Assembly in Protic Solvents

NASA Astrophysics Data System (ADS)

Zhou, Hang

Quantum walks are the quantum mechanical analogue of classical random walks. Discrete-time quantum walks have been introduced and studied mostly on the line Z or higher dimensional space Zd but rarely defined on graphs with fractal dimensions because the coin operator depends on the position and the Fourier transform on the fractals is not defined. Inspired by its nature of classical walks, different quantum walks will be defined by choosing different shift and coin operators. When the coin operator is uniform, the results of classical walks will be obtained upon measurement at each step. Moreover, with measurement at each step, our results reveal more information about the classical random walks. In this dissertation, two graphs with fractal dimensions will be considered. The first one is Sierpinski gasket, a degree-4 regular graph with Hausdorff dimension of df = ln 3/ ln 2. The second is the Cantor graph derived like Cantor set, with Hausdorff dimension of df = ln 2/ ln 3. The definitions and amplitude functions of the quantum walks will be introduced. The main part of this dissertation is to derive a recursive formula to compute the amplitude Green function. The exiting probability will be computed and compared with the classical results. When the generation of graphs goes to infinity, the recursion of the walks will be investigated and the convergence rates will be obtained and compared with the classical counterparts.
Theory and discretization of ideal magnetohydrodynamic equilibria with fractal pressure profiles

DOE PAGES

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

2017-09-29

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

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

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

In three-dimensional ideal magnetohydrodynamics, closed flux surfaces cannot maintain both rational rotational-transform and pressure gradients, as these features together produce unphysical, infinite currents. A proposed set of equilibria nullifies these currents by flattening the pressure on sufficiently wide intervals around each rational surface. Such rational surfaces exist at every scale, which characterizes the pressure profile as self-similar and thus fractal. The pressure profile is approximated numerically by considering a finite number of rational regions and analyzed mathematically by classifying the irrational numbers that support gradients into subsets. As a result, applying these results to a given rotational-transform profile in cylindricalmore » geometry, we find magnetic field and current density profiles compatible with the fractal pressure.« less
Special issue of selected papers from the second UK-Japan bilateral Workshop and First ERCOFTAC Workshop on Turbulent Flows Generated/Designed in Multiscale/Fractal Ways, London, March 2012

NASA Astrophysics Data System (ADS)

Laizet, Sylvain; Sakai, Yasuhiko; Christos Vassilicos, J.

2013-12-01

This special issue of Fluid Dynamics Research includes nine papers which are based on nine of the presentations at the Second UK-Japan bilateral Workshop and First ERCOFTAC Workshop on 'Turbulent flows generated/designed in multiscale/fractal ways: fundamentals and applications' held from 26 to 27 March 2012 at Imperial College London, UK. The research area of fractal-generated turbulent flows started with a chapter published in 2001 in one of the conference proceedings which came out of the 1999 Isaac Newton Institute 6 month Programme on Turbulence in Cambridge (UK). However, the first results which formed the basis of much of the work reported in this special issue started appearing from 2007 onwards and progress since then could perhaps be described as not insignificant. Research in this area has resulted in the following six notable advances: (a) the definition of two new length-scales characterizing grid-generated turbulence; (b) enhanced and energy-efficient stirring and scalar transfer by fractal grid and fractal openings/flanges with applications, in particular, to improved turbulence generation for combustion; (c) the non-equilibrium turbulent dissipation law; (d) non-equilibrium axisymmetric wake laws; (e) insights into the dependence of drag forces and vortex shedding on the fractal geometry of fractal objects and simulation methods for the calculation of drag of fractal trees; and (f) the invention and successful proof of concept of fractal spoilers and fractal fences. The present special issue contains papers directly related to these advances and can be seen as a reflection of the current research in the field of fractal-generated turbulent flows and their differences and commonalities with other turbulent flows. The financial support from the Japan Society for the Promotion of Science has been decisive for the organization and success of this workshop. We are also grateful to ERCOFTAC who put in place the EU-wide Special Interest Group on multiscale-generated turbulence and for supporting the workshop both financially and by way of advertisement. Last but by no means least, we express our deep gratitude to the editors of FDR who handled this issue: M Funakoshi, A D Gilbert, L B Mydlarski and K Suga.
Generic features of the primary relaxation in glass-forming materials (Review Article)

NASA Astrophysics Data System (ADS)

Kokshenev, Valery B.

2017-08-01

We discuss structural relaxation in molecular and polymeric supercooled liquids, metallic alloys and orientational glass crystals. The study stresses especially the relationships between observables raised from underlying constraints imposed on degrees of freedom of vitrification systems. A self-consistent parametrization of the α-timescale on macroscopic level results in the material-and-model independent universal equation, relating three fundamental temperatures, characteristic of the primary relaxation, that is numerically proven in all studied glass formers. During the primary relaxation, the corresponding small and large mesoscopic clusters modify their size and structure in a self-similar way, regardless of underlying microscopic realizations. We show that cluster-shape similarity, instead of cluster-size fictive divergence, gives rise to universal features observed in primary relaxation. In all glass formers with structural disorder, including orientational-glass materials (with the exception of plastic crystals), structural relaxation is shown to be driven by local random fields. Within the dynamic stochastic approach, the universal subdiffusive dynamics corresponds to random walks on small and large fractals.
Spectral statistics and scattering resonances of complex primes arrays

NASA Astrophysics Data System (ADS)

Wang, Ren; Pinheiro, Felipe A.; Dal Negro, Luca

2018-01-01

We introduce a class of aperiodic arrays of electric dipoles generated from the distribution of prime numbers in complex quadratic fields (Eisenstein and Gaussian primes) as well as quaternion primes (Hurwitz and Lifschitz primes), and study the nature of their scattering resonances using the vectorial Green's matrix method. In these systems we demonstrate several distinctive spectral properties, such as the absence of level repulsion in the strongly scattering regime, critical statistics of level spacings, and the existence of critical modes, which are extended fractal modes with long lifetimes not supported by either random or periodic systems. Moreover, we show that one can predict important physical properties, such as the existence spectral gaps, by analyzing the eigenvalue distribution of the Green's matrix of the arrays in the complex plane. Our results unveil the importance of aperiodic correlations in prime number arrays for the engineering of gapped photonic media that support far richer mode localization and spectral properties compared to usual periodic and random media.
What is the alternative to the Alexander-Orbach relation?

NASA Astrophysics Data System (ADS)

Sokolov, Igor M.

2016-03-01

The Alexander-Orbach (AO) relation d w = 2d f /d s connecting the fractal dimension of a random walk’s (RW) trajectory d w or the exponent of anomalous diffusion α = 2/d w on a fractal structure with the fractal and spectral dimension of the structure itself plays a key role in discussion of dynamical properties of complex systems including living cells and single biomolecules. This relation however does not hold universally and breaks down for some structures like diffusion limited aggregates and Eden trees. We show that the alternative to the AO relation is the explicit dependence of the coefficient of the anomalous diffusion on the system’s size, i.e. the absence of its thermodynamical limit. The prerequisite for its breakdown is the dependence of the local structure of possible steps of the RW on the system’s size. The discussion is illustrated by the examples of diffusion on a Koch curve (AO-conform) and on a Cantor dust (violating AO relation).
Metasurface base on uneven layered fractal elements for ultra-wideband RCS reduction

NASA Astrophysics Data System (ADS)

Su, Jianxun; Cui, Yueyang; Li, Zengrui; Yang, Yaoqing Lamar; Che, Yongxing; Yin, Hongcheng

2018-03-01

A novel metasurface based on uneven layered fractal elements is designed and fabricated for ultra-wideband radar cross section (RCS) reduction in this paper. The proposed metasurface consists of two fractal subwavelength elements with different layer thickness. The reflection phase difference of 180° (±37°) between two unit cells covers an ultra-wide frequency range. Ultra-wideband RCS reduction results from the phase cancellation between two local waves produced by these two unit cells. The diffuse scattering of electromagnetic (EM) waves is caused by the randomized phase distribution, leading to a low monostatic and bistatic RCS simultaneously. This metasurface can achieve -10dB RCS reduction in an ultra-wide frequency range from 6.6 to 23.9 GHz with a ratio bandwidth (fH/fL) of 3.62:1 under normal incidences for both x- and y-polarized waves. Both the simulation and the measurement results are consistent to verify this excellent RCS reduction performance of the proposed metasurface.

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.
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.
Fractional kinetics of glioma treatment by a radio-frequency electric field

NASA Astrophysics Data System (ADS)

Iomin, A.

2013-09-01

A realistic model for estimation of the medical effect of brain cancer (glioma) treatment by a radio-frequency (RF) electric field is suggested. This low intensity, intermediate-frequency alternating electric field is known as the tumor-treating field (TTF). The model is based on a construction of 3D comb model for a description of the cancer cells dynamics, where the migration-proliferation dichotomy becomes naturally apparent, and the outer-invasive region of glioma cancer is considered as a fractal composite embedded in the 3D space. In the framework of this model, the interplay between the TTF and the migration-proliferation dichotomy of cancer cells is considered, and the efficiency of this TTF is estimated. It is shown that the efficiency of the medical treatment by the TTF depends essentially on the mass fractal dimension of the cancer in the outer-invasive region.
Strong light absorption capability directed by structured profile of vertical Si nanowires

NASA Astrophysics Data System (ADS)

Chaliyawala, Harsh A.; Ray, Abhijit; Pati, Ranjan K.; Mukhopadhyay, Indrajit

2017-11-01

Si nanowire arrays (SiNWAs) with random fractal geometry was fabricated using fast, mask-less, non-lithographic and facile approach by incorporating metal assisted electroless etching of n-type Si (111) substrates. The FESEM images demonstrate the formation of nano-porous surfaces that provide effective path for the incoming light to get trapped into the cavity of nanowires. The length of NWs increases from ∼1 to 10 μm with increase in the etching time having a diameter in the range of ∼25-82 nm. A transformation from zero to first order kinetics after a prolonged etching has been determined. The synthesized SiNWAs show high light trapping properties, including a maximum photon absorption across the entire visible and near IR range below the band gap of Si. The SiNWAs etched for 15 min exhibit extremely low specular and total reflectance of ∼0.2% and 4.5%, respectively over a broadband of wavelength. The reduction in the reflection loss is accompanied with the gradient of refractive index from air to Si substrate as well as due to the sub-wavelength structures, which manifests the light scattering effect. The COMSOL multiphysics simulation has been performed to study the high broadband light absorption capability in terms of the strong localized light field confinement by varying the length of the nanowire. Moreover, the SiNWs induces the dewetting ability at the solid/liquid interface and enhances the superhydrophobicity. Furthermore, a maximum length scale of 100-200 nm manifests a strong heterogeneity along the planar section of the surface of SiNWs. The study thus provides an insight on the light propagation into the random fractal geometries of Si nanowires. These outstanding properties should contribute to the structural optimization of various optoelectronic and photonic devices.
Nonlinear growth dynamics and the origin of fluctuating asymmetry

USGS Publications Warehouse

Emlen, J.M.; Freeman, D.C.; Graham, J.H.

1993-01-01

The nonlinear, complex nature of biosynthesis magnifies the impacts of small, random perturbations on organism growth, leading to distortions in adaptive allometries and, in particular, to fluctuating asymmetry. These distortions can be partly checked by cell-cell and inter-body part feedback during growth and development, though the latter mechanism also may lead to complex patterns in right-left asymmetry. Stress can be expected to increase the degree to which random growth perturbations are magnified and may also result in disruption of the check mechanisms, thus exaggerating fluctuating asymmetry.The processes described not only provide one explanation for the existence of fluctuating asymmetry and its augmentation under stress, but suggest additional effects of stress as well. Specifically, stress is predicted to lead to decreased fractal dimension of bone sutures and branching structures in animals, and in increased dimension of growth trace patterns such as those found in mollusc shells and fish otoliths and scales.A basic yet broad primer on fractals and chaos is provided as background for the theoretical development in this manuscript.
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.
Fractal analysis of multiscale spatial autocorrelation among point data

USGS Publications Warehouse

De Cola, L.

1991-01-01

The analysis of spatial autocorrelation among point-data quadrats is a well-developed technique that has made limited but intriguing use of the multiscale aspects of pattern. In this paper are presented theoretical and algorithmic approaches to the analysis of aggregations of quadrats at or above a given density, in which these sets are treated as multifractal regions whose fractal dimension, D, may vary with phenomenon intensity, scale, and location. The technique is illustrated with Matui's quadrat house-count data, which yield measurements consistent with a nonautocorrelated simulated Poisson process but not with an orthogonal unit-step random walk. The paper concludes with a discussion of the implications of such analysis for multiscale geographic analysis systems. -Author
Seeing shapes in seemingly random spatial patterns: Fractal analysis of Rorschach inkblots

PubMed Central

Taylor, R. P.; Martin, T. P.; Montgomery, R. D.; Smith, J. H.; Micolich, A. P.; Boydston, C.; Scannell, B. C.; Fairbanks, M. S.; Spehar, B.

2017-01-01

Rorschach inkblots have had a striking impact on the worlds of art and science because of the remarkable variety of associations with recognizable and namable objects they induce. Originally adopted as a projective psychological tool to probe mental health, psychologists and artists have more recently interpreted the variety of induced images simply as a signature of the observers’ creativity. Here we analyze the relationship between the spatial scaling parameters of the inkblot patterns and the number of induced associations, and suggest that the perceived images are induced by the fractal characteristics of the blot edges. We discuss how this relationship explains the frequent observation of images in natural scenery. PMID:28196082
Fractal interrelationships in field and seismic data. Quarterly report, September 21 - December 31, 1995

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

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

1995-12-31

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

NASA Astrophysics Data System (ADS)

Liu, Xingrun; Xu, Qingshan; Li, Xia; Wu, Kaifeng; Dong, Yanbing

2018-02-01

Cloud is an important natural phenomenon, and its radiation causes serious interference to infrared detector. Based on fractal and statistical data, a method is proposed to realize cloud background simulation, and cloud infrared radiation data field is assigned using satellite radiation data of cloud. A cloud infrared radiation simulation model is established using matlab, and it can generate cloud background infrared images for different cloud types (low cloud, middle cloud, and high cloud) in different months, bands and sensor zenith angles.
Generating a fractal butterfly Floquet spectrum in a class of driven SU(2) systems

NASA Astrophysics Data System (ADS)

Wang, Jiao; Gong, Jiangbin

2010-02-01

A scheme for generating a fractal butterfly Floquet spectrum, first proposed by Wang and Gong [Phys. Rev. A 77, 031405(R) (2008)], is extended to driven SU(2) systems such as a driven two-mode Bose-Einstein condensate. A class of driven systems without a link with the Harper-model context is shown to have an intriguing butterfly Floquet spectrum. The found butterfly spectrum shows remarkable deviations from the known Hofstadter’s butterfly. In addition, the level crossings between Floquet states of the same parity and between Floquet states of different parities are studied and highlighted. The results are relevant to studies of fractal statistics, quantum chaos, and coherent destruction of tunneling, as well as the validity of mean-field descriptions of Bose-Einstein condensates.
Generating a fractal butterfly Floquet spectrum in a class of driven SU(2) systems

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

Wang Jiao; Temasek Laboratories, National University of Singapore, Singapore 117542; Gong Jiangbin

2010-02-15

A scheme for generating a fractal butterfly Floquet spectrum, first proposed by Wang and Gong [Phys. Rev. A 77, 031405(R) (2008)], is extended to driven SU(2) systems such as a driven two-mode Bose-Einstein condensate. A class of driven systems without a link with the Harper-model context is shown to have an intriguing butterfly Floquet spectrum. The found butterfly spectrum shows remarkable deviations from the known Hofstadter's butterfly. In addition, the level crossings between Floquet states of the same parity and between Floquet states of different parities are studied and highlighted. The results are relevant to studies of fractal statistics, quantummore » chaos, and coherent destruction of tunneling, as well as the validity of mean-field descriptions of Bose-Einstein condensates.« less
An Explanation for the Arctic Sea Ice Melt Pond Fractal Transition

NASA Astrophysics Data System (ADS)

Popovic, P.; Abbot, D. S.

2016-12-01

As Arctic sea ice melts during the summer, pools of melt water form on its surface. This decreases the ice's albedo, which signifcantly impacts its subsequent evolution. Understanding this process is essential for buiding accurate sea ice models in GCMs and using them to forecast future changes in sea ice. A feature of melt ponds that helps determine their impact on ice albedo is that they often form complex geometric shapes. One characteristic of their shape, the fractal dimension of the pond boundaries, D, has been shown to transition between the two fundamental limits of D = 1 and D = 2 at some critical pond size. Here, we provide an explanation for this behavior. First, using aerial photographs taken during the SHEBA mission, we show how this fractal transition curve changes with time, and show that there is a qualitative difference in the pond shape as ice transitions from impermeable to permeable. While ice is impermeable, the maximum fractal dimension is less than 2, whereas after it becomes permeable, the maximum fractal dimension becomes very close to 2. We then show how the fractal dimension of the boundary of a collection of overlapping circles placed randomly on a plane also transitions from D = 1 to D = 2 at a size equal to the average size of a single circle. We, therefore, conclude that this transition is a simple geometric consequence of regular shapes connecting. The one physical parameter that can be extracted from the fractal transition curve is the length scale at which transition occurs. Previously, this length scale has been associated with the typical size of snow dunes created on the ice surface during winter. We provide an alternative explanation by noting that the flexural wavelength of the ice poses a fundamental limit on the size of melt ponds on permeable ice. If this is true, melt ponds could be used as a proxy for ice thickness. Finally, we provide some remarks on how to observationally distinguish between the two ideas for what determines the fundamental length scale.
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…
Detrended Fluctuation Analysis and Adaptive Fractal Analysis of Stride Time Data in Parkinson's Disease: Stitching Together Short Gait Trials

PubMed Central

Liebherr, Magnus; Haas, Christian T.

2014-01-01

Variability indicates motor control disturbances and is suitable to identify gait pathologies. It can be quantified by linear parameters (amplitude estimators) and more sophisticated nonlinear methods (structural information). Detrended Fluctuation Analysis (DFA) is one method to measure structural information, e.g., from stride time series. Recently, an improved method, Adaptive Fractal Analysis (AFA), has been proposed. This method has not been applied to gait data before. Fractal scaling methods (FS) require long stride-to-stride data to obtain valid results. However, in clinical studies, it is not usual to measure a large number of strides (e.g., strides). Amongst others, clinical gait analysis is limited due to short walkways, thus, FS seem to be inapplicable. The purpose of the present study was to evaluate FS under clinical conditions. Stride time data of five self-paced walking trials ( strides each) of subjects with PD and a healthy control group (CG) was measured. To generate longer time series, stride time sequences were stitched together. The coefficient of variation (CV), fractal scaling exponents (DFA) and (AFA) were calculated. Two surrogate tests were performed: A) the whole time series was randomly shuffled; B) the single trials were randomly shuffled separately and afterwards stitched together. CV did not discriminate between PD and CG. However, significant differences between PD and CG were found concerning and . Surrogate version B yielded a higher mean squared error and empirical quantiles than version A. Hence, we conclude that the stitching procedure creates an artificial structure resulting in an overestimation of true . The method of stitching together sections of gait seems to be appropriate in order to distinguish between PD and CG with FS. It provides an approach to integrate FS as standard in clinical gait analysis and to overcome limitations such as short walkways. PMID:24465708
Fractal and Chaos Analysis for Dynamics of Radon Exhalation from Uranium Mill Tailings

NASA Astrophysics Data System (ADS)

Li, Yongmei; Tan, Wanyu; Tan, Kaixuan; Liu, Zehua; Xie, Yanshi

2016-08-01

Tailings from mining and milling of uranium ores potentially are large volumes of low-level radioactive materials. A typical environmental problem associated with uranium tailings is radon exhalation, which can significantly pose risks to environment and human health. In order to reduce these risks, it is essential to study the dynamical nature and underlying mechanism of radon exhalation from uranium mill tailings. This motivates the conduction of this study, which is based on the fractal and chaotic methods (e.g. calculating the Hurst exponent, Lyapunov exponent and correlation dimension) and laboratory experiments of the radon exhalation rates. The experimental results show that the radon exhalation rate from uranium mill tailings is highly oscillated. In addition, the nonlinear analyses of the time series of radon exhalation rate demonstrate the following points: (1) the value of Hurst exponent much larger than 0.5 indicates non-random behavior of the radon time series; (2) the positive Lyapunov exponent and non-integer correlation dimension of the time series imply that the radon exhalation from uranium tailings is a chaotic dynamical process; (3) the required minimum number of variables should be five to describe the time evolution of radon exhalation. Therefore, it can be concluded that the internal factors, including heterogeneous distribution of radium, and randomness of radium decay, as well as the fractal characteristics of the tailings, can result in the chaotic evolution of radon exhalation from the tailings.
Influence of material ductility and crack surface roughness on fracture instability

NASA Astrophysics Data System (ADS)

Khezrzadeh, Hamed; Wnuk, Michael P.; Yavari, Arash

2011-10-01

This paper presents a stability analysis for fractal cracks. First, the Westergaard stress functions are proposed for semi-infinite and finite smooth cracks embedded in the stress fields associated with the corresponding self-affine fractal cracks. These new stress functions satisfy all the required boundary conditions and according to Wnuk and Yavari's (2003 Eng. Fract. Mech. 70 1659-74) embedded crack model they are used to derive the stress and displacement fields generated around a fractal crack. These results are then used in conjunction with the final stretch criterion to study the quasi-static stable crack extension, which in ductile materials precedes the global failure. The material resistance curves are determined by solving certain nonlinear differential equations and then employed in predicting the stress levels at the onset of stable crack growth and at the critical point, where a transition to the catastrophic failure occurs. It is shown that the incorporation of the fractal geometry into the crack model, i.e. accounting for the roughness of the crack surfaces, results in (1) higher threshold levels of the material resistance to crack propagation and (2) higher levels of the critical stresses associated with the onset of catastrophic fracture. While the process of quasi-static stable crack growth (SCG) is viewed as a sequence of local instability states, the terminal instability attained at the end of this process is identified with the global instability. The phenomenon of SCG can be used as an early warning sign in fracture detection and prevention.
Signal-Noise Identification of Magnetotelluric Signals Using Fractal-Entropy and Clustering Algorithm for Targeted De-Noising

NASA Astrophysics Data System (ADS)

Li, Jin; Zhang, Xian; Gong, Jinzhe; Tang, Jingtian; Ren, Zhengyong; Li, Guang; Deng, Yanli; Cai, Jin

A new technique is proposed for signal-noise identification and targeted de-noising of Magnetotelluric (MT) signals. This method is based on fractal-entropy and clustering algorithm, which automatically identifies signal sections corrupted by common interference (square, triangle and pulse waves), enabling targeted de-noising and preventing the loss of useful information in filtering. To implement the technique, four characteristic parameters — fractal box dimension (FBD), higuchi fractal dimension (HFD), fuzzy entropy (FuEn) and approximate entropy (ApEn) — are extracted from MT time-series. The fuzzy c-means (FCM) clustering technique is used to analyze the characteristic parameters and automatically distinguish signals with strong interference from the rest. The wavelet threshold (WT) de-noising method is used only to suppress the identified strong interference in selected signal sections. The technique is validated through signal samples with known interference, before being applied to a set of field measured MT/Audio Magnetotelluric (AMT) data. Compared with the conventional de-noising strategy that blindly applies the filter to the overall dataset, the proposed method can automatically identify and purposefully suppress the intermittent interference in the MT/AMT signal. The resulted apparent resistivity-phase curve is more continuous and smooth, and the slow-change trend in the low-frequency range is more precisely reserved. Moreover, the characteristic of the target-filtered MT/AMT signal is close to the essential characteristic of the natural field, and the result more accurately reflects the inherent electrical structure information of the measured site.
Modeling fractal cities using the correlated percolation model.

NASA Astrophysics Data System (ADS)

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

1996-03-01

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

PubMed Central

Hsieh, Wan-Hsin; Escobar, Carolina; Yugay, Tatiana; Lo, Men-Tzung; Pittman-Polletta, Benjamin; Salgado-Delgado, Roberto; Scheer, Frank A. J. L.; Shea, Steven A.; Buijs, Ruud M.; Hu, Kun

2014-01-01

Motor activity possesses a multiscale regulation that is characterized by fractal activity fluctuations with similar structure across a wide range of timescales spanning minutes to hours. Fractal activity patterns are disturbed in animals after ablating the master circadian pacemaker (suprachiasmatic nucleus, SCN) and in humans with SCN dysfunction as occurs with aging and in dementia, suggesting the crucial role of the circadian system in the multiscale activity regulation. We hypothesized that the normal synchronization between behavioural cycles and the SCN-generated circadian rhythms is required for multiscale activity regulation. To test the hypothesis, we studied activity fluctuations of rats in a simulated shift work protocol that was designed to force animals to be active during the habitual resting phase of the circadian/daily cycle. We found that these animals had gradually decreased mean activity level and reduced 24-h activity rhythm amplitude, indicating disturbed circadian and behavioural cycles. Moreover, these animals had disrupted fractal activity patterns as characterized by more random activity fluctuations at multiple timescales from 4 to 12 h. Intriguingly, these activity disturbances exacerbated when the shift work schedule lasted longer and persisted even in the normal days (without forced activity) following the shift work. The disrupted circadian and fractal patterns resemble those of SCN-lesioned animals and of human patients with dementia, suggesting a detrimental impact of shift work on multiscale activity regulation. PMID:24829282

Bridging Three Orders of Magnitude: Multiple Scattered Waves Sense Fractal Microscopic Structures via Dispersion

NASA Astrophysics Data System (ADS)

Lambert, Simon A.; Näsholm, Sven Peter; Nordsletten, David; Michler, Christian; Juge, Lauriane; Serfaty, Jean-Michel; Bilston, Lynne; Guzina, Bojan; Holm, Sverre; Sinkus, Ralph

2015-08-01

Wave scattering provides profound insight into the structure of matter. Typically, the ability to sense microstructure is determined by the ratio of scatterer size to probing wavelength. Here, we address the question of whether macroscopic waves can report back the presence and distribution of microscopic scatterers despite several orders of magnitude difference in scale between wavelength and scatterer size. In our analysis, monosized hard scatterers 5 μ m in radius are immersed in lossless gelatin phantoms to investigate the effect of multiple reflections on the propagation of shear waves with millimeter wavelength. Steady-state monochromatic waves are imaged in situ via magnetic resonance imaging, enabling quantification of the phase velocity at a voxel size big enough to contain thousands of individual scatterers, but small enough to resolve the wavelength. We show in theory, experiments, and simulations that the resulting coherent superposition of multiple reflections gives rise to power-law dispersion at the macroscopic scale if the scatterer distribution exhibits apparent fractality over an effective length scale that is comparable to the probing wavelength. Since apparent fractality is naturally present in any random medium, microstructure can thereby leave its fingerprint on the macroscopically quantifiable power-law exponent. Our results are generic to wave phenomena and carry great potential for sensing microstructure that exhibits intrinsic fractality, such as, for instance, vasculature.
Paretian Poisson Processes

NASA Astrophysics Data System (ADS)

Eliazar, Iddo; Klafter, Joseph

2008-05-01

Many random populations can be modeled as a countable set of points scattered randomly on the positive half-line. The points may represent magnitudes of earthquakes and tornados, masses of stars, market values of public companies, etc. In this article we explore a specific class of random such populations we coin ` Paretian Poisson processes'. This class is elemental in statistical physics—connecting together, in a deep and fundamental way, diverse issues including: the Poisson distribution of the Law of Small Numbers; Paretian tail statistics; the Fréchet distribution of Extreme Value Theory; the one-sided Lévy distribution of the Central Limit Theorem; scale-invariance, renormalization and fractality; resilience to random perturbations.
Image encryption based on fractal-structured phase mask in fractional Fourier transform domain

NASA Astrophysics Data System (ADS)

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

2018-04-01

We present an optical encryption approach based on the combination of fractal Fresnel lens (FFL) and fractional Fourier transform (FrFT). Our encryption approach is in fact a four-fold encryption scheme, including the random phase encoding produced by the Gerchberg–Saxton algorithm, a FFL, and two FrFTs. A FFL is composed of a Sierpinski carpet fractal plate and a Fresnel zone plate. In our encryption approach, the security is enhanced due to the more expandable key spaces and the use of FFL overcomes the alignment problem of the optical axis in optical system. Only using the perfectly matched parameters of the FFL and the FrFT, the plaintext can be recovered well. We present an image encryption algorithm that from the ciphertext we can get two original images by the FrFT with two different phase distribution keys, obtained by performing 100 iterations between the two plaintext and ciphertext, respectively. We test the sensitivity of our approach to various parameters such as the wavelength of light, the focal length of FFL, and the fractional orders of FrFT. Our approach can resist various attacks.
Eigenvalues of normalized Laplacian matrices of fractal trees and dendrimers: Analytical results and applications

NASA Astrophysics Data System (ADS)

Julaiti, Alafate; Wu, Bin; Zhang, Zhongzhi

2013-05-01

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

NASA Astrophysics Data System (ADS)

Reza, Syed M. S.; Mays, Randall; Iftekharuddin, Khan M.

2015-03-01

We propose a novel non-invasive brain tumor type classification using Multi-fractal Detrended Fluctuation Analysis (MFDFA) [1] in structural magnetic resonance (MR) images. This preliminary work investigates the efficacy of the MFDFA features along with our novel texture feature known as multifractional Brownian motion (mBm) [2] in classifying (grading) brain tumors as High Grade (HG) and Low Grade (LG). Based on prior performance, Random Forest (RF) [3] is employed for tumor grading using two different datasets such as BRATS-2013 [4] and BRATS-2014 [5]. Quantitative scores such as precision, recall, accuracy are obtained using the confusion matrix. On an average 90% precision and 85% recall from the inter-dataset cross-validation confirm the efficacy of the proposed method.
Reduced Tolerance to Night Shift in Chronic Shift Workers: Insight From Fractal Regulation.

PubMed

Li, Peng; Morris, Christopher J; Patxot, Melissa; Yugay, Tatiana; Mistretta, Joseph; Purvis, Taylor E; Scheer, Frank A J L; Hu, Kun

2017-07-01

Healthy physiology is characterized by fractal regulation (FR) that generates similar structures in the fluctuations of physiological outputs at different time scales. Perturbed FR is associated with aging and age-related pathological conditions. Shift work, involving repeated and chronic exposure to misaligned environmental and behavioral cycles, disrupts circadian coordination. We tested whether night shifts perturb FR in motor activity and whether night shifts affect FR in chronic shift workers and non-shift workers differently. We studied 13 chronic shift workers and 14 non-shift workers as controls using both field and in-laboratory experiments. In the in-laboratory study, simulated night shifts were used to induce a misalignment between the endogenous circadian pacemaker and the sleep-wake cycles (ie, circadian misalignment) while environmental conditions and food intake were controlled. In the field study, we found that FR was robust in controls but broke down in shift workers during night shifts, leading to more random activity fluctuations as observed in patients with dementia. The night shift effect was present even 2 days after ending night shifts. The in-laboratory study confirmed that night shifts perturbed FR in chronic shift workers and showed that FR in controls was more resilience to the circadian misalignment. Moreover, FR during real and simulated night shifts was more perturbed in those who started shift work at older ages. Chronic shift work causes night shift intolerance, which is probably linked to the degraded plasticity of the circadian control system. © Sleep Research Society 2017. Published by Oxford University Press on behalf of the Sleep Research Society. All rights reserved. For permissions, please e-mail journals.permissions@oup.com.
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.
Dynamics of Fractal Cluster Gels with Embedded Active Colloids

NASA Astrophysics Data System (ADS)

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

2017-08-01

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

NASA Astrophysics Data System (ADS)

Heydari, Samaneh; Rastan, Iman; Parvin, Amin; Pirooj, Azadeh; Zarrabi, Ferdows B.

2017-01-01

Recently, nano-aperture is noticed due to its good transmission in the optical regime. Also, the nano-apertures are developed at the metasurface design for circular polarization; for this aim, various shapes of the nano-aperture are suggested. To reach this objective, we have developed a novel Jerusalem cross fractal shape for a mid-infrared application. We have simulated various formations of the nano-fractal Jerusalem cross based on a simple cross to show the effect of nano-aperture shape on electrical field enhancement in the near-field which is important in spectroscopy and optical imaging. In addition, we have used a single layer graphene over the aperture as a coat for making reconfigurable characteristic also creating a membrane for placement of nano-particle over the aperture. Implementation of the graphene is an amendment to the transfer of the nano-apertures. The biological materials with a thickness of 80 nm have been placed over the graphene layer and the Figures of Merits (FOM) have been obtained. Additionally, the prototype of nano-antenna is independent from incident wave polarization. The Finite Difference Time Domain (FDTD) calculations have been implemented in the simulation and modeling the nano-apertures.
Intermediate quantum maps for quantum computation

NASA Astrophysics Data System (ADS)

Giraud, O.; Georgeot, B.

2005-10-01

We study quantum maps displaying spectral statistics intermediate between Poisson and Wigner-Dyson. It is shown that they can be simulated on a quantum computer with a small number of gates, and efficiently yield information about fidelity decay or spectral statistics. We study their matrix elements and entanglement production and show that they converge with time to distributions which differ from random matrix predictions. A randomized version of these maps can be implemented even more economically and yields pseudorandom operators with original properties, enabling, for example, one to produce fractal random vectors. These algorithms are within reach of present-day quantum computers.
Self-organization of local magnetoplasma structures in the upper layers of the solar convection zone

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

Chumak, O. V., E-mail: chuo@yandex.ru

Self-organization and evolution of magnetoplasma structures in the upper layers of the solar convection zone are discussed as a process of diffuse aggregation of magnetic flux tubes. Equations describing the tube motion under the action of magnetic interaction forces, hydrodynamic forces, and random forces are written explicitly. The process of aggregation of magnetic flux tubes into magnetic flux clusters of different shapes and dimensions is simulated numerically. The obtained structures are compared with the observed morphological types of sunspot groups. The quantitative comparison with the observational data was performed by comparing the fractal dimensions of the photospheric magnetic structures observedmore » in solar active regions with those of structures obtained in the numerical experiment. The model has the following free parameters: the numbers of magnetic flux tubes with opposite polarities on the considered area element (Nn and Ns), the average radius of the cross section of the magnetic flux tube (a), its effective length (l), the twist factor of the tube field (k), and the absolute value of the average velocity of chaotic tube displacements (d). Variations in these parameters in physically reasonable limits leads to the formation of structures (tube clusters of different morphological types) having different fractal dimensions. Using the NOAA 10488 active region, which appeared and developed into a complicated configuration near the central meridian, as an example, it is shown that good quantitative agreement between the fractal dimensions is achieved at the following parameters of the model: Nn = Ns = 250 ± 50; a = 150 ± 50 km; l ∼ 5000 km, and d = 80 ± 10 m/s. These results do not contradict the observational data and theoretical estimates obtained in the framework of the Parker “spaghetti” model and provide new information on the physical processes resulting in the origin and evolution of local magnetic plasma structures in the near-photospheric layers of the solar convection zone.« less
Ultrametric properties of the attractor spaces for random iterated linear function systems

NASA Astrophysics Data System (ADS)

Buchovets, A. G.; Moskalev, P. V.

2018-03-01

We investigate attractors of random iterated linear function systems as independent spaces embedded in the ordinary Euclidean space. The introduction on the set of attractor points of a metric that satisfies the strengthened triangle inequality makes this space ultrametric. Then inherent in ultrametric spaces the properties of disconnectedness and hierarchical self-similarity make it possible to define an attractor as a fractal. We note that a rigorous proof of these properties in the case of an ordinary Euclidean space is very difficult.
Schramm-Loewner evolution and Liouville quantum gravity.

PubMed

Duplantier, Bertrand; Sheffield, Scott

2011-09-23

We show that when two boundary arcs of a Liouville quantum gravity random surface are conformally welded to each other (in a boundary length-preserving way) the resulting interface is a random curve called the Schramm-Loewner evolution. We also develop a theory of quantum fractal measures (consistent with the Knizhnik-Polyakov-Zamolochikov relation) and analyze their evolution under conformal welding maps related to Schramm-Loewner evolution. As an application, we construct quantum length and boundary intersection measures on the Schramm-Loewner evolution curve itself.
Application of Fractal theory for crash rate prediction: Insights from random parameters and latent class tobit models.

PubMed

Chand, Sai; Dixit, Vinayak V

2018-03-01

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

PubMed Central

Xu, Min

2017-01-01

Biological tissue has a complex structure and exhibits rich spectroscopic behavior. There has been no tissue model until now that has been able to account for the observed spectroscopy of tissue light scattering and its anisotropy. Here we present, for the first time, a plum pudding random medium (PPRM) model for biological tissue which succinctly describes tissue as a superposition of distinctive scattering structures (plum) embedded inside a fractal continuous medium of background refractive index fluctuation (pudding). PPRM faithfully reproduces the wavelength dependence of tissue light scattering and attributes the “anomalous” trend in the anisotropy to the plum and the powerlaw dependence of the reduced scattering coefficient to the fractal scattering pudding. Most importantly, PPRM opens up a novel venue of quantifying the tissue architecture and microscopic structures on average from macroscopic probing of the bulk with scattered light alone without tissue excision. We demonstrate this potential by visualizing the fine microscopic structural alterations in breast tissue (adipose, glandular, fibrocystic, fibroadenoma, and ductal carcinoma) deduced from noncontact spectroscopic measurement. PMID:28663913
Beyond multi-fractals: surrogate time series and fields

NASA Astrophysics Data System (ADS)

Venema, V.; Simmer, C.

2007-12-01

Most natural complex are characterised by variability on a large range of temporal and spatial scales. The two main methodologies to generate such structures are Fourier/FARIMA based algorithms and multifractal methods. The former is restricted to Gaussian data, whereas the latter requires the structure to be self-similar. This work will present so-called surrogate data as an alternative that works with any (empirical) distribution and power spectrum. The best-known surrogate algorithm is the iterative amplitude adjusted Fourier transform (IAAFT) algorithm. We have studied six different geophysical time series (two clouds, runoff of a small and a large river, temperature and rain) and their surrogates. The power spectra and consequently the 2nd order structure functions were replicated accurately. Even the fourth order structure function was more accurately reproduced by the surrogates as would be possible by a fractal method, because the measured structure deviated too strong from fractal scaling. Only in case of the daily rain sums a fractal method could have been more accurate. Just as Fourier and multifractal methods, the current surrogates are not able to model the asymmetric increment distributions observed for runoff, i.e., they cannot reproduce nonlinear dynamical processes that are asymmetric in time. Furthermore, we have found differences for the structure functions on small scales. Surrogate methods are especially valuable for empirical studies, because the time series and fields that are generated are able to mimic measured variables accurately. Our main application is radiative transfer through structured clouds. Like many geophysical fields, clouds can only be sampled sparsely, e.g. with in-situ airborne instruments. However, for radiative transfer calculations we need full 3-dimensional cloud fields. A first study relating the measured properties of the cloud droplets and the radiative properties of the cloud field by generating surrogate cloud fields yielded good results within the measurement error. A further test of the suitability of the surrogate clouds for radiative transfer is evaluated by comparing the radiative properties of model cloud fields of sparse cumulus and stratocumulus with their surrogate fields. The bias and root mean square error in various radiative properties is small and the deviations in the radiances and irradiances are not statistically significant, i.e. these deviations can be attributed to the Monte Carlo noise of the radiative transfer calculations. We compared these results with optical properties of synthetic clouds that have either the correct distribution (but no spatial correlations) or the correct power spectrum (but a Gaussian distribution). These clouds did show statistical significant deviations. For more information see: http://www.meteo.uni-bonn.de/venema/themes/surrogates/
Dynamical implications of sample shape for avalanches in 2-dimensional random-field Ising model with saw-tooth domain wall

NASA Astrophysics Data System (ADS)

Tadić, Bosiljka

2018-03-01

We study dynamics of a built-in domain wall (DW) in 2-dimensional disordered ferromagnets with different sample shapes using random-field Ising model on a square lattice rotated by 45 degrees. The saw-tooth DW of the length Lx is created along one side and swept through the sample by slow ramping of the external field until the complete magnetisation reversal and the wall annihilation at the open top boundary at a distance Ly. By fixing the number of spins N =Lx ×Ly = 106 and the random-field distribution at a value above the critical disorder, we vary the ratio of the DW length to the annihilation distance in the range Lx /Ly ∈ [ 1 / 16 , 16 ] . The periodic boundary conditions are applied in the y-direction so that these ratios comprise different samples, i.e., surfaces of cylinders with the changing perimeter Lx and height Ly. We analyse the avalanches of the DW slips between following field updates, and the multifractal structure of the magnetisation fluctuation time series. Our main findings are that the domain-wall lengths materialised in different sample shapes have an impact on the dynamics at all scales. Moreover, the domain-wall motion at the beginning of the hysteresis loop (HLB) probes the disorder effects resulting in the fluctuations that are significantly different from the large avalanches in the central part of the loop (HLC), where the strong fields dominate. Specifically, the fluctuations in HLB exhibit a wide multi-fractal spectrum, which shifts towards higher values of the exponents when the DW length is reduced. The distributions of the avalanches in this segments of the loops obey power-law decay and the exponential cutoffs with the exponents firmly in the mean-field universality class for long DW. In contrast, the avalanches in the HLC obey Tsallis density distribution with the power-law tails which indicate the new categories of the scale invariant behaviour for different ratios Lx /Ly. The large fluctuations in the HLC, on the other hand, have a rather narrow spectrum which is less sensitive to the length of the wall. These findings shed light to the dynamical criticality of the random-field Ising model at its lower critical dimension; they can be relevant to applications of the dynamics of injected domain walls in two-dimensional nanowires and ferromagnetic films.
Multi-level structure in the large scale distribution of optically luminous galaxies

NASA Astrophysics Data System (ADS)

Deng, Xin-fa; Deng, Zu-gan; Liu, Yong-zhen

1992-04-01

Fractal dimensions in the large scale distribution of galaxies have been calculated with the method given by Wen et al. [1] Samples are taken from CfA redshift survey in northern and southern galactic [2] hemisphere in our analysis respectively. Results from these two regions are compared with each other. There are significant differences between the distributions in these two regions. However, our analyses do show some common features of the distributions in these two regions. All subsamples show multi-level fractal character distinctly. Combining it with the results from analyses of samples given by IRAS galaxies and results from samples given by redshift survey in pencil-beam fields, [3,4] we suggest that multi-level fractal structure is most likely to be a general and important character in the large scale distribution of galaxies. The possible implications of this character are discussed.
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.

Advanced analysis of forest fire clustering

NASA Astrophysics Data System (ADS)

Kanevski, Mikhail; Pereira, Mario; Golay, Jean

2017-04-01

Analysis of point pattern clustering is an important topic in spatial statistics and for many applications: biodiversity, epidemiology, natural hazards, geomarketing, etc. There are several fundamental approaches used to quantify spatial data clustering using topological, statistical and fractal measures. In the present research, the recently introduced multi-point Morisita index (mMI) is applied to study the spatial clustering of forest fires in Portugal. The data set consists of more than 30000 fire events covering the time period from 1975 to 2013. The distribution of forest fires is very complex and highly variable in space. mMI is a multi-point extension of the classical two-point Morisita index. In essence, mMI is estimated by covering the region under study by a grid and by computing how many times more likely it is that m points selected at random will be from the same grid cell than it would be in the case of a complete random Poisson process. By changing the number of grid cells (size of the grid cells), mMI characterizes the scaling properties of spatial clustering. From mMI, the data intrinsic dimension (fractal dimension) of the point distribution can be estimated as well. In this study, the mMI of forest fires is compared with the mMI of random patterns (RPs) generated within the validity domain defined as the forest area of Portugal. It turns out that the forest fires are highly clustered inside the validity domain in comparison with the RPs. Moreover, they demonstrate different scaling properties at different spatial scales. The results obtained from the mMI analysis are also compared with those of fractal measures of clustering - box counting and sand box counting approaches. REFERENCES Golay J., Kanevski M., Vega Orozco C., Leuenberger M., 2014: The multipoint Morisita index for the analysis of spatial patterns. Physica A, 406, 191-202. Golay J., Kanevski M. 2015: A new estimator of intrinsic dimension based on the multipoint Morisita index. Pattern Recognition, 48, 4070-4081.
Mapping of the Bak, Tang, and Wiesenfeld sandpile model on a two-dimensional Ising-correlated percolation lattice to the two-dimensional self-avoiding random walk

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

NASA Astrophysics Data System (ADS)

Raupov, Dmitry S.; Myakinin, Oleg O.; Bratchenko, Ivan A.; Kornilin, Dmitry V.; Zakharov, Valery P.; Khramov, Alexander G.

2016-04-01

Optical coherence tomography (OCT) is usually employed for the measurement of tumor topology, which reflects structural changes of a tissue. We investigated the possibility of OCT in detecting changes using a computer texture analysis method based on Haralick texture features, fractal dimension and the complex directional field method from different tissues. These features were used to identify special spatial characteristics, which differ healthy tissue from various skin cancers in cross-section OCT images (B-scans). Speckle reduction is an important pre-processing stage for OCT image processing. In this paper, an interval type-II fuzzy anisotropic diffusion algorithm for speckle noise reduction in OCT images was used. The Haralick texture feature set includes contrast, correlation, energy, and homogeneity evaluated in different directions. A box-counting method is applied to compute fractal dimension of investigated tissues. Additionally, we used the complex directional field calculated by the local gradient methodology to increase of the assessment quality of the diagnosis method. The complex directional field (as well as the "classical" directional field) can help describe an image as set of directions. Considering to a fact that malignant tissue grows anisotropically, some principal grooves may be observed on dermoscopic images, which mean possible existence of principal directions on OCT images. Our results suggest that described texture features may provide useful information to differentiate pathological from healthy patients. The problem of recognition melanoma from nevi is decided in this work due to the big quantity of experimental data (143 OCT-images include tumors as Basal Cell Carcinoma (BCC), Malignant Melanoma (MM) and Nevi). We have sensitivity about 90% and specificity about 85%. Further research is warranted to determine how this approach may be used to select the regions of interest automatically.
Complexity methods applied to turbulence in plasma astrophysics

NASA Astrophysics Data System (ADS)

Vlahos, L.; Isliker, H.

2016-09-01

In this review many of the well known tools for the analysis of Complex systems are used in order to study the global coupling of the turbulent convection zone with the solar atmosphere where the magnetic energy is dissipated explosively. Several well documented observations are not easy to interpret with the use of Magnetohydrodynamic (MHD) and/or Kinetic numerical codes. Such observations are: (1) The size distribution of the Active Regions (AR) on the solar surface, (2) The fractal and multi fractal characteristics of the observed magnetograms, (3) The Self-Organised characteristics of the explosive magnetic energy release and (4) the very efficient acceleration of particles during the flaring periods in the solar corona. We review briefly the work published the last twenty five years on the above issues and propose solutions by using methods borrowed from the analysis of complex systems. The scenario which emerged is as follows: (a) The fully developed turbulence in the convection zone generates and transports magnetic flux tubes to the solar surface. Using probabilistic percolation models we were able to reproduce the size distribution and the fractal properties of the emerged and randomly moving magnetic flux tubes. (b) Using a Non Linear Force Free (NLFF) magnetic extrapolation numerical code we can explore how the emerged magnetic flux tubes interact nonlinearly and form thin and Unstable Current Sheets (UCS) inside the coronal part of the AR. (c) The fragmentation of the UCS and the redistribution of the magnetic field locally, when the local current exceeds a Critical threshold, is a key process which drives avalanches and forms coherent structures. This local reorganization of the magnetic field enhances the energy dissipation and influences the global evolution of the complex magnetic topology. Using a Cellular Automaton and following the simple rules of Self Organized Criticality (SOC), we were able to reproduce the statistical characteristics of the observed time series of the explosive events, (d) finally, when the AR reaches the turbulently reconnecting state (in the language of the SOC theory this is called SOC state) it is densely populated by UCS which can act as local scatterers (replacing the magnetic clouds in the Fermi scenario) and enhance dramatically the heating and acceleration of charged particles.
Internal structure of the upwelling events at Punta Gallinas (Colombian Caribbean) from modis-sst imagery

NASA Astrophysics Data System (ADS)

Alonso, J.; Blázquez, E.; Isaza-Toro, E.; Vidal, J.

2015-10-01

The upwelling at Punta Gallinas in the Guajira Peninsula (Colombian Caribbean) was studied from the point of view of the Mathematical Morphology using 10 years of monthly composite MODIS-SST imagery. Among all the morphological operators, the skeleton is widely used to compute the axis of the of the SST fields for the observed upwelling events. The skeleton is characterized by means of the Geometrical Theory of Measurement using the fractal dimension. The upwelling in the area is driven by the dynamic of the ITCZ (InterTropical Convergence Zone) and the relationship between the area and the East-West component of the trade winds has a lag of about 4 months. It has been found that the fractal dimension of the skeleton and the area of the upwelling are related. Some relationship was found between the fractal dimension of the skeleton (its complexity) and the Southern Oscillation Index by means of linear regression and cross-spectral analysis finding coherent energy at 1 year, 6 months and in the low frequency band. Finally, a sensitivity analysis between fractal dimension and threshold SST points out to take an extreme care at the time of fixing the last one.
Toward a fractal spectrum approach for neutron and gamma pulse shape discrimination

NASA Astrophysics Data System (ADS)

Liu, Ming-Zhe; Liu, Bing-Qi; Zuo, Zhuo; Wang, Lei; Zan, Gui-Bin; Tuo, Xian-Guo

2016-06-01

Accurately selecting neutron signals and discriminating γ signals from a mixed radiation field is a key research issue in neutron detection. This paper proposes a fractal spectrum discrimination approach by means of different spectral characteristics of neutrons and γ rays. Figure of merit and average discriminant error ratio are used together to evaluate the discrimination effects. Different neutron and γ signals with various noise and pulse pile-up are simulated according to real data in the literature. The proposed approach is compared with the digital charge integration and pulse gradient methods. It is found that the fractal approach exhibits the best discrimination performance, followed by the digital charge integration method and the pulse gradient method, respectively. The fractal spectrum approach is not sensitive to high frequency noise and pulse pile-up. This means that the proposed approach has superior performance for effective and efficient anti-noise and high discrimination in neutron detection. Supported by the National Natural Science Foundation of China (41274109), Sichuan Youth Science and Technology Innovation Research Team (2015TD0020), Scientific and Technological Support Program of Sichuan Province (2013FZ0022), and the Creative Team Program of Chengdu University of Technology.
Eifel maars: Quantitative shape characterization of juvenile ash particles (Eifel Volcanic Field, Germany)

NASA Astrophysics Data System (ADS)

Rausch, Juanita; Grobéty, Bernard; Vonlanthen, Pierre

2015-01-01

The Eifel region in western central Germany is the type locality for maar volcanism, which is classically interpreted to be the result of explosive eruptions due to shallow interaction between magma and external water (i.e. phreatomagmatic eruptions). Sedimentary structures, deposit features and particle morphology found in many maar deposits of the West Eifel Volcanic Field (WEVF), in contrast to deposits in the East Eifel Volcanic Field (EEVF), lack the diagnostic criteria of typical phreatomagmatic deposits. The aim of this study was to determine quantitatively the shape of WEVF and EEVF maar ash particles in order to infer the governing eruption style in Eifel maar volcanoes. The quantitative shape characterization was done by analyzing fractal dimensions of particle contours (125-250 μm sieve fraction) obtained from Scanning electron microscopy (SEM) and SEM micro-computed tomography (SEM micro-CT) images. The fractal analysis (dilation method) and the fractal spectrum technique confirmed that the WEVF and EEVF maar particles have contrasting multifractal shapes. Whereas the low small-scale dimensions of EEVF particles (Eppelsberg Green Unit) coincide with previously published values for phreatomagmatic particles, the WEVF particles (Meerfelder Maar, Pulvermaar and Ulmener Maar) have larger values indicating more complex small-scale features, which are characteristic for magmatic particles. These quantitative results are strengthening the qualitative microscopic observations, that the studied WEVF maar eruptions are rather dominated by magmatic processes. The different eruption styles in the two volcanic fields can be explained by the different geological and hydrological settings found in both regions and the different chemical compositions of the magmas.
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)
Atomized scan strategy for high definition for VR application

NASA Astrophysics Data System (ADS)

Huang, Shuping; Ran, Feng; Ji, Yuan; Chen, Wendong

2017-10-01

Silicon-based OLED (Organic Light Emitting Display) microdisplay technology begins to attract people's attention in the emerging VR and AR devices. The high display frame refresh rate is an important solution to alleviate the dizziness in VR applications. Traditional display circuit drivers use the analog method or the digital PWM method that follow the serial scan order from the first pixel to the last pixel by using the shift registers. This paper proposes a novel atomized scan strategy based on the digital fractal scan strategy using the pseudo-random scan order. It can be used to realize the high frame refresh rate with the moderate pixel clock frequency in the high definition OLED microdisplay. The linearity of the gray level is also improved compared with the Z fractal scan strategy.
Optical devices and methods employing nanoparticles, microcavities, and semicontinuous metal films

NASA Technical Reports Server (NTRS)

Shalaev, Vladimir M. (Inventor); Sarychev, Andrey K. (Inventor); Armstrong, Robert L. (Inventor); Smith, Harold V. (Inventor); Ying, Z. Charles (Inventor)

2006-01-01

An optical sensing enhancing material (and corresponding method of making) comprising: a medium, the medium comprising a plurality of aggregated nanoparticles comprising fractals; and a microcavity, wherein the medium is located in a vicinity of the microcavity. Also an optical sensor and sensing method comprising: providing a doped medium, the medium comprising a plurality of aggregated nanoparticles comprising fractals, with the material; locating the doped medium in the vicinity of a microcavity; exciting the doped medium with a light source; and detecting light reflected from the doped medium. Also an optical sensing enhancing material comprising a medium, the medium comprising a semicontinuous metal film of randomly distributed metal particles and their clusters at approximately their percolation threshold. The medium preferably additionally comprises a microcavity/microresonator. Also devices and methods employing such material.
Simulated shift work in rats perturbs multiscale regulation of locomotor activity.

PubMed

Hsieh, Wan-Hsin; Escobar, Carolina; Yugay, Tatiana; Lo, Men-Tzung; Pittman-Polletta, Benjamin; Salgado-Delgado, Roberto; Scheer, Frank A J L; Shea, Steven A; Buijs, Ruud M; Hu, Kun

2014-07-06

Motor activity possesses a multiscale regulation that is characterized by fractal activity fluctuations with similar structure across a wide range of timescales spanning minutes to hours. Fractal activity patterns are disturbed in animals after ablating the master circadian pacemaker (suprachiasmatic nucleus, SCN) and in humans with SCN dysfunction as occurs with aging and in dementia, suggesting the crucial role of the circadian system in the multiscale activity regulation. We hypothesized that the normal synchronization between behavioural cycles and the SCN-generated circadian rhythms is required for multiscale activity regulation. To test the hypothesis, we studied activity fluctuations of rats in a simulated shift work protocol that was designed to force animals to be active during the habitual resting phase of the circadian/daily cycle. We found that these animals had gradually decreased mean activity level and reduced 24-h activity rhythm amplitude, indicating disturbed circadian and behavioural cycles. Moreover, these animals had disrupted fractal activity patterns as characterized by more random activity fluctuations at multiple timescales from 4 to 12 h. Intriguingly, these activity disturbances exacerbated when the shift work schedule lasted longer and persisted even in the normal days (without forced activity) following the shift work. The disrupted circadian and fractal patterns resemble those of SCN-lesioned animals and of human patients with dementia, suggesting a detrimental impact of shift work on multiscale activity regulation. © 2014 The Author(s) Published by the Royal Society. All rights reserved.
Applications of ICA and fractal dimension in sEMG signal processing for subtle movement analysis: a review.

PubMed

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

2011-06-01

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

PubMed

Bernaola-Galván, P; Oliver, J L; Hackenberg, M; Coronado, A V; Ivanov, P Ch; Carpena, P

2012-06-01

Segmentation is a standard method of data analysis to identify change-points dividing a nonstationary time series into homogeneous segments. However, for long-range fractal correlated series, most of the segmentation techniques detect spurious change-points which are simply due to the heterogeneities induced by the correlations and not to real nonstationarities. To avoid this oversegmentation, we present a segmentation algorithm which takes as a reference for homogeneity, instead of a random i.i.d. series, a correlated series modeled by a fractional noise with the same degree of correlations as the series to be segmented. We apply our algorithm to artificial series with long-range correlations and show that it systematically detects only the change-points produced by real nonstationarities and not those created by the correlations of the signal. Further, we apply the method to the sequence of the long arm of human chromosome 21, which is known to have long-range fractal correlations. We obtain only three segments that clearly correspond to the three regions of different G + C composition revealed by means of a multi-scale wavelet plot. Similar results have been obtained when segmenting all human chromosome sequences, showing the existence of previously unknown huge compositional superstructures in the human genome.
High-frequency spectral falloff of earthquakes, fractal dimension of complex rupture, b value, and the scaling of strength on faults

USGS Publications Warehouse

Frankel, A.

1991-01-01

The high-frequency falloff ??-y of earthquake displacement spectra and the b value of aftershock sequences are attributed to the character of spatially varying strength along fault zones. I assume that the high frequency energy of a main shock is produced by a self-similar distribution of subevents, where the number of subevents with radii greater than R is proportional to R-D, D being the fractal dimension. In the model, an earthquake is composed of a hierarchical set of smaller earthquakes. The static stress drop is parameterized to be proportional to R??, and strength is assumed to be proportional to static stress drop. I find that a distribution of subevents with D = 2 and stress drop independent of seismic moment (?? = 0) produces a main shock with an ??-2 falloff, if the subevent areas fill the rupture area of the main shock. By equating subevents to "islands' of high stress of a random, self-similar stress field on a fault, I relate D to the scaling of strength on a fault, such that D = 2 - ??. Thus D = 2 corresponds to constant stress drop scaling (?? = 0) and scale-invariant fault strength. A self-similar model of aftershock rupture zones on a fault is used to determine the relationship between the b value, the size distribution of aftershock rupture zones, and the scaling of strength on a fault. -from Author
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.
Preparation methodologies and nano/microstructural evaluation of metal/semiconductor thin films.

PubMed

Chen, Zhiwen; Jiao, Zheng; Wu, Minghong; Shek, Chan-Hung; Wu, C M Lawrence; Lai, Joseph K L

2012-01-01

Metal/semiconductor thin films are a class of unique materials that are widespread technological applications, particularly in the field of microelectronic devices. Assessment strategies of fractal and tures are of fundamental importance in the development of nano/microdevices. This review presents the preparation methodologies and nano/microstructural evaluation of metal/semiconductor thin films including Au/Ge bilayer films and Pd-Ge alloy thin films, which show in the form of fractals and nanocrystals. Firstly, the extended version of Au/Ge thin films for the fractal crystallization of amorphous Ge and the formation of nanocrystals developed with improved micro- and nanostructured features are described in Section 2. Secondly, the nano/microstructural characteristics of Pd/Ge alloy thin films during annealing have been investigated in detail and described in Section 3. Finally, we will draw the conclusions from the present work as shown in Section 4. It is expected that the preparation methodologies developed and the knowledge of nano/microstructural evolution gained in metal/semiconductor thin films, including Au/Ge bilayer films and Pd-Ge alloy thin films, will provide an important fundamental basis underpinning further interdisciplinary research in these fields such as physics, chemistry, materials science, and nanoscience and nanotechnology, leading to promising exciting opportunities for future technological applications involving these thin films.
Low field scaling properties of high Tc superconductor glasses

NASA Astrophysics Data System (ADS)

Giovannella, C.; Fruchter, L.; Chappert, C.

We show that the zero field cooling (ZFC) M/H curves of both the YBaCuO and the LaSrCuO granular superconductor glasses (SuG) are subjected to scaling when plotted against the reduced variable t/H1/ψ . The breaking of the scaling for too weak or too strong magnetic fields is discussed and justified by the introduction of a phenomenological fractal picture, describing the behaviour of the disordered intergranular junction network. Nous montrons que les courbes M/H caractéristiques des verres de supraconducteurs granulaires sont sujettes à une loi d'échelle lorsqu'elles sont tracées en fonction de la variable réduite t/H1/ψ. La brisure de la loi d'échelle pour des champs trop forts ou trop faibles est justifiée par l'introduction d'un modèle phénoménologique fractal capable de décrire le comportement d'un réseau désordonné des jonctions.
Tailoring plasmonic nanoparticles and fractal patterns

NASA Astrophysics Data System (ADS)

Rosa, Lorenzo; Juodkazis, Saulius

2011-12-01

We studied new three-dimensional tailoring of nano-particles by ion-beam and electron-beam lithographies, aiming for features and nano-gaps down to 10 nm size. Electron-beam patterning is demonstrated for 2D fabrication in combination with plasmonic metal deposition and lift-off, with full control of spectral features of plasmonic nano-particles and patterns on dielectric substrates. We present wide-angle bow-tie rounded nano-antennas whose plasmonic resonances achieve strong field enhancement at engineered wavelength range, and show how the addition of fractal patterns defined by standard electron beam lithography achieve light field enhancement from visible to far-IR spectral range and scalable up towards THz band. Field enhancement is evaluated by FDTD modeling on full-3D simulation domains using complex material models, showing the modeling method capabilities and the effect of staircase approximations on field enhancement and resonance conditions, especially at metal corners, where a minimum rounding radius of 2 nm is resolved and a five-fold reduction of spurious ringing at sharp corners is obtained by the use of conformal meshing.

Music and fractals

NASA Astrophysics Data System (ADS)

Wuorinen, Charles

2015-03-01

Any of the arts may produce exemplars that have fractal characteristics. There may be fractal painting, fractal poetry, and the like. But these will always be specific instances, not necessarily displaying intrinsic properties of the art-medium itself. Only music, I believe, of all the arts possesses an intrinsically fractal character, so that its very nature is fractally determined. Thus, it is reasonable to assert that any instance of music is fractal...
Fractal Characteristics of Pores in Taiyuan Formation Shale from Hedong Coal Field, China

NASA Astrophysics Data System (ADS)

Li, Kunjie; Zeng, Fangui; Cai, Jianchao; Sheng, Guanglong; Xia, Peng; Zhang, Kun

For the purpose of investigating the fractal characteristics of pores in Taiyuan formation shale, a series of qualitative and quantitative experiments were conducted on 17 shale samples from well HD-1 in Hedong coal field of North China. The results of geochemical experiments show that Total organic carbon (TOC) varies from 0.67% to 5.32% and the organic matters are in the high mature or over mature stage. The shale samples consist mainly of clay minerals and quartz with minor pyrite and carbonates. The FE-SEM images indicate that three types of pores, organic-related pores, inorganic-related pores and micro-fractures related pores, are developed well, and a certain number of intragranular pores are found inside quartz and carbonates formed by acid liquid corrosion. The pore size distributions (PSDs) broadly range from several to hundreds nanometers, but most pores are smaller than 10nm. As the result of different adsorption features at relative pressure (0-0.5) and (0.5-1) on the N2 adsorption isotherm, two fractal dimensions D1 and D2 were obtained with the Frenkel-Halsey-Hill (FHH) model. D1 and D2 vary from 2.4227 to 2.6219 and from 2.6049 to 2.7877, respectively. Both TOC and brittle minerals have positive effect on D1 and D2, whereas clay minerals, have a negative influence on them. The fractal dimensions are also influenced by the pore structure parameters, such as the specific surface area, BJH pore volume, etc. Shale samples with higher D1 could provide more adsorption sites leading to a greater methane adsorption capacity, whereas shale samples with higher D2 have little influence on methane adsorption capacity.
Characterizing the structure of diffuse emission in Hi-GAL maps

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

Elia, D.; Molinari, S.; Rygl, K. L. J.

We present a study of the structure of the Galactic interstellar medium (ISM) through the Δ-variance technique, related to the power spectrum and the fractal properties of infrared/submillimeter maps. Through this method, it is possible to provide quantitative parameters, which are useful for characterizing different morphological and physical conditions, and better constraining the theoretical models. In this respect, the Herschel Infrared Galactic Plane Survey, carried out at five photometric bands from 70 to 500 μm, constitutes a unique database for applying statistical tools to a variety of regions across the Milky Way. In this paper, we derive a robust estimatemore » of the power-law portion of the power spectrum of four contiguous 2° × 2° Hi-GAL tiles located in the third Galactic quadrant (217° ≲ ℓ ≲ 225°, –2° ≲ b ≲ 0°). The low level of confusion along the line of sight, testified by CO observations, makes this region an ideal case. We find very different values for the power spectrum slope from tile to tile but also from wavelength to wavelength (2 ≲ β ≲ 3), with similarities between fields attributable to components located at the same distance. Thanks to comparisons with models of turbulence, an explanation of the determined slopes in terms of the fractal geometry is also provided, and possible relations with the underlying physics are investigated. In particular, an anti-correlation between ISM fractal dimension and star formation efficiency is found for the two main distance components observed in these fields. A possible link between the fractal properties of the diffuse emission and the resulting clump mass function is discussed.« less
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.
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.
Scattering Properties of Heterogeneous Mineral Particles with Absorbing Inclusions

NASA Technical Reports Server (NTRS)

Dlugach, Janna M.; Mishchenko, Michael I.

2015-01-01

We analyze the results of numerically exact computer modeling of scattering and absorption properties of randomly oriented poly-disperse heterogeneous particles obtained by placing microscopic absorbing grains randomly on the surfaces of much larger spherical mineral hosts or by imbedding them randomly inside the hosts. These computations are paralleled by those for heterogeneous particles obtained by fully encapsulating fractal-like absorbing clusters in the mineral hosts. All computations are performed using the superposition T-matrix method. In the case of randomly distributed inclusions, the results are compared with the outcome of Lorenz-Mie computations for an external mixture of the mineral hosts and absorbing grains. We conclude that internal aggregation can affect strongly both the integral radiometric and differential scattering characteristics of the heterogeneous particle mixtures.
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.
Crystallization Dynamics of Organolead Halide Perovskite by Real-Time X-ray Diffraction.

PubMed

Miyadera, Tetsuhiko; Shibata, Yosei; Koganezawa, Tomoyuki; Murakami, Takurou N; Sugita, Takeshi; Tanigaki, Nobutaka; Chikamatsu, Masayuki

2015-08-12

We analyzed the crystallization process of the CH3NH3PbI3 perovskite by observing real-time X-ray diffraction immediately after combining a PbI2 thin film with a CH3NH3I solution. A detailed analysis of the transformation kinetics demonstrated the fractal diffusion of the CH3NH3I solution into the PbI2 film. Moreover, the perovskite crystal was found to be initially oriented based on the PbI2 crystal orientation but to gradually transition to a random orientation. The fluctuating characteristics of the crystallization process of perovskites, such as fractal penetration and orientational transformation, should be controlled to allow the fabrication of high-quality perovskite crystals. The characteristic reaction dynamics observed in this study should assist in establishing reproducible fabrication processes for perovskite solar cells.
FORMATION AND ALIGNMENT OF ELONGATED, FRACTAL-LIKE WATER-ICE GRAINS IN EXTREMELY COLD, WEAKLY IONIZED PLASMA

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

Chai, Kil-Byoung; Bellan, Paul M., E-mail: kbchai@caltech.edu, E-mail: pbellan@caltech.edu

2015-04-01

Elongated, fractal-like water-ice grains are observed to form spontaneously when water vapor is injected into a weakly ionized laboratory plasma formed in a background gas cooled to an astrophysically relevant temperature. The water-ice grains form in 1–2 minutes, levitate with regular spacing, and are aligned parallel to the sheath electric field. Water-ice grains formed in plasma where the neutrals and ions have low mass, such as hydrogen and helium, are larger, more elongated, and more fractal-like than water-ice grains formed in plasmas where the neutrals and ions have high mass such as argon and krypton. Typical aspect ratios (length tomore » width ratio) are as great as 5 while typical fractal dimensions are ∼1.7. Water-ice grain lengths in plasmas with low neutral and ion masses can be several hundred microns long. Infrared absorption spectroscopy reveals that the water-ice grains are crystalline and so are similar in constitution to the water-ice grains in protoplanetary disks, Saturn’s rings, and mesospheric clouds. The properties and behavior of these laboratory water-ice grains may provide insights into morphology and alignment behavior of water-ice grains in astrophysical dusty plasmas.« less
Thin-film fractal nanostructures formed by electrical breakdown

NASA Astrophysics Data System (ADS)

Tadtaev, P. O.; Bobkov, A. A.; Borodzyulya, V. F.; Lamkin, I. A.; Mihailov, I. I.; Moshnikov, V. A.; Permyakov, N. V.; Solomonov, A. V.; Sudar, N. T.; Tarasov, S. A.

2017-11-01

This is a study of the fractal micro- and nanostructures formation caused by the electrical breakdown of the indium-tin oxide (ITO) covered with various organic coatings. The samples were created by covering a glass substrate with a 1 to 10um-thick layer of indium-tin oxide. Some of the samples were then coated with organic layers of polycarbonate, poly(methyl methacrylate) and others. In order to create high local electrical field densities a special setup based on a eutectic GaIn liquid needle was created: it allowed for the contact area of 60um in diameter and application of the step voltage swept from 20 to 300 volts. The setup also contained a spectrometer for measuring the spectra of the breakdown optical effects. The results showed that the destruction of ITO led to the formation of the spiral fractal nanostructures, parameters of which depended on the thickness of the layer and the presence of the organic cover. In case of the latter, polymer coating was shown to visualize and zoom the topography of the nanostructures which might be used as a method of “polymer photography” for such fractal formations. The analysis of the spectra showed their dependence on the parameters of the structures which proves the possibility of conducting optical diagnostics of the created structures.
Advances in the Quantitative Characterization of the Shape of Ash-Sized Pyroclast Populations: Fractal Analyses Coupled to Micro- and Nano-Computed Tomography Techniques

NASA Astrophysics Data System (ADS)

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

2014-12-01

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

NASA Astrophysics Data System (ADS)

China, S.; Mazzoleni, C.; Dubey, M. K.; Chakrabarty, R. K.; Moosmuller, H.; Onasch, T. B.; Herndon, S. C.

2010-12-01

We present an analysis of morphological characteristics of atmospheric aerosol collected during the MILAGRO (Megacity Initiative: Local and Global Research Observations) field campaign that took place in Mexico City in March 2006. The sampler was installed on the Aerodyne mobile laboratory. The aerosol samples were collected on nuclepore clear polycarbonate filters mounted in Costar pop-top membrane holders. More than one hundred filters were collected at different ground sites with different atmospheric and geographical characteristics (urban, sub-urban, mountain-top, industrial, etc.) over a month period. Selected subsets of these filters were analyzed for aerosol morphology using a scanning electron microscope and image analysis techniques. In this study we investigate spatial and temporal variations of aerosol shape descriptors, morphological parameters, and fractal dimension. We also compare the morphological results with other aerosol measurements such as aerosol optical properties(scattering and absorption) and size distribution data. Atmospheric aerosols have different morphological characteristics depending on many parameters such as emission sources, atmospheric formation pathways, aging processes, and aerosol mixing state. The aerosol morphology influences aerosol chemical and mechanical interactions with the environment, physical properties, and radiative effects. In this study, ambient aerosol particles have been classified in different shape groups as spherical, irregularly shaped, and fractal-like aggregates. Different morphological parameters such as aspect ratio, roundness, feret diameter, etc. have been estimated for irregular shaped and spherical particles and for different kinds of soot particles including fresh soot, collapsed and coated soot. Fractal geometry and image processing have been used to obtain morphological characteristics of different soot particles. The number of monomers constituting each aggregate and their diameters were measured and used to estimate an ensemble three-dimensional (3-d) fractal dimension. One-dimensional (1-d) and two-dimensional (2-d) fractal geometries have been measured using a power-law scaling relationship between 1-d and 2-d properties of projected images. Temporal variations in fractal dimension of soot-like aggregates have been observed at the mountaintop site and spatial variation of fractal dimension and other morphological descriptors of different shaped particles have been investigated for the different ground sites.
Connotations of pixel-based scale effect in remote sensing and the modified fractal-based analysis method

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

NASA Technical Reports Server (NTRS)

Makikallio, T. H.; Hoiber, S.; Kober, L.; Torp-Pedersen, C.; Peng, C. K.; Goldberger, A. L.; Huikuri, H. V.

1999-01-01

A number of new methods have been recently developed to quantify complex heart rate (HR) dynamics based on nonlinear and fractal analysis, but their value in risk stratification has not been evaluated. This study was designed to determine whether selected new dynamic analysis methods of HR variability predict mortality in patients with depressed left ventricular (LV) function after acute myocardial infarction (AMI). Traditional time- and frequency-domain HR variability indexes along with short-term fractal-like correlation properties of RR intervals (exponent alpha) and power-law scaling (exponent beta) were studied in 159 patients with depressed LV function (ejection fraction <35%) after an AMI. By the end of 4-year follow-up, 72 patients (45%) had died and 87 (55%) were still alive. Short-term scaling exponent alpha (1.07 +/- 0.26 vs 0.90 +/- 0.26, p <0.001) and power-law slope beta (-1.35 +/- 0.23 vs -1.44 +/- 0.25, p <0.05) differed between survivors and those who died, but none of the traditional HR variability measures differed between these groups. Among all analyzed variables, reduced scaling exponent alpha (<0.85) was the best univariable predictor of mortality (relative risk 3.17, 95% confidence interval 1.96 to 5.15, p <0.0001), with positive and negative predictive accuracies of 65% and 86%, respectively. In the multivariable Cox proportional hazards analysis, mortality was independently predicted by the reduced exponent alpha (p <0.001) after adjustment for several clinical variables and LV function. A short-term fractal-like scaling exponent was the most powerful HR variability index in predicting mortality in patients with depressed LV function. Reduction in fractal correlation properties implies more random short-term HR dynamics in patients with increased risk of death after AMI.
Sub- and super-diffusion on Cantor sets: Beyond the paradox

NASA Astrophysics Data System (ADS)

K. Golmankhaneh, Alireza; Balankin, Alexander S.

2018-04-01

There is no way to build a nontrivial Markov process having continuous trajectories on a totally disconnected fractal embedded in the Euclidean space. Accordingly, in order to delineate the diffusion process on the totally disconnected fractal, one needs to relax the continuum requirement. Consequently, a diffusion process depends on how the continuum requirement is handled. This explains the emergence of different types of anomalous diffusion on the same totally disconnected set. In this regard, we argue that the number of effective spatial degrees of freedom of a random walker on the totally disconnected Cantor set is equal to nsp = [ D ] + 1, where [ D ] is the integer part of the Hausdorff dimension of the Cantor set. Conversely, the number of effective dynamical degrees of freedom (ds) depends on the definition of a Markov process on the totally disconnected Cantor set embedded in the Euclidean space En (n ≥nsp). This allows us to deduce the equation of diffusion by employing the local differential operators on the Fα-support. The exact solutions of this equation are obtained on the middle-ɛ Cantor sets for different kinds of the Markovian random processes. The relation of our findings to physical phenomena observed in complex systems is highlighted.
The Fibonacci Life-Chart Method (FLCM) as a foundation for Carl Jung's theory of synchronicity.

PubMed

Sacco, Robert G

2016-04-01

Since the scientific method requires events to be subject to controlled examination it would seem that synchronicities are not scientifically investigable. Jung speculated that because these incredible events are like the random sparks of a firefly they cannot be pinned down. However, doubting Jung's doubts, the author provides a possible method of elucidating these seemingly random and elusive events. The author draws on a new method, designated the Fibonacci Life-Chart Method (FLCM), which categorizes phase transitions and Phi fractal scaling in human development based on the occurrence of Fibonacci numbers in biological cell division and self-organizing systems. The FLCM offers an orientation towards psychological experience that may have relevance to Jung's theory of synchronicity in which connections are deemed to be intrinsically meaningful rather than demonstrable consequences of cause and effect. In such a model synchronistic events can be seen to be, as the self-organizing system enlarges, manifestations of self-organized critical moments and Phi fractal scaling. Recommendations for future studies include testing the results of the FLCM using case reports of synchronistic and spiritual experiences. © 2016, The Society of Analytical Psychology.
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.
DOE Office of Scientific and Technical Information (OSTI.GOV)

Nottale, Laurent; Célérier, Marie-Noëlle

One of the main results of scale relativity as regards the foundation of quantum mechanics is its explanation of the origin of the complex nature of the wave function. The scale relativity theory introduces an explicit dependence of physical quantities on scale variables, founding itself on the theorem according to which a continuous and non-differentiable space-time is fractal (i.e., scale-divergent). In the present paper, the nature of the scale variables and their relations to resolutions and differential elements are specified in the non-relativistic case (fractal space). We show that, owing to the scale-dependence which it induces, non-differentiability involves a fundamentalmore » two-valuedness of the mean derivatives. Since, in the scale relativity framework, the wave function is a manifestation of the velocity field of fractal space-time geodesics, the two-valuedness of velocities leads to write them in terms of complex numbers, and yields therefore the complex nature of the wave function, from which the usual expression of the Schrödinger equation can be derived.« less
An ultrathin wide-band planar metamaterial absorber based on a fractal frequency selective surface and resistive film

NASA Astrophysics Data System (ADS)

Fan, Yue-Nong; Cheng, Yong-Zhi; Nie, Yan; Wang, Xian; Gong, Rong-Zhou

2013-06-01

We propose an ultrathin wide-band metamaterial absorber (MA) based on a Minkowski (MIK) fractal frequency selective surface and resistive film. This absorber consists of a periodic arrangement of dielectric substrates sandwiched with an MIK fractal loop structure electric resonator and a resistive film. The finite element method is used to simulate and analyze the absorption of the MA. Compared with the MA-backed copper film, the designed MA-backed resistive film exhibits an absorption of 90% at a frequency region of 2 GHz-20 GHz. The power loss density distribution of the MA is further illustrated to explain the mechanism of the proposed MA. Simulated absorptions at different incidence cases indicate that this absorber is polarization-insensitive and wide-angled. Finally, further simulated results indicate that the surface resistance of the resistive film and the dielectric constant of the substrate can affect the absorbing property of the MA. This absorber may be used in many military fields.

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

PubMed

Wu, Shuai; Ma, Ming

2017-11-01

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

NASA Astrophysics Data System (ADS)

Kim, Kyungsik; Jung, Jae Won; Kim, Soo Yong

2010-03-01

The pattern of stone distribution in the game of Go (Baduk, Weiqi, or Igo) can be treated in the mathematical and physical languages of multifractals. The concepts of fractals and multifractals have relevance to many fields of science and even arts. A significant and fascinating feature of this approach is that it provides a proper interpretation for the pattern of the two-colored (black and white) stones in terms of the numerical values of the generalized dimension and the scaling exponent. For our case, these statistical quantities can be estimated numerically from the black, white, and mixed stones, assuming the excluded edge effect that the cell form of the Go game has the self-similar structure. The result from the multifractal structure allows us to find a definite and reliable fractal dimension, and it precisely verifies that the fractal dimension becomes larger, as the cell of grids increases. We also find the strength of multifractal structures from the difference in the scaling exponents in the black, white, and mixed stones.
Morphology and Fractal Characterization of Multiscale Pore Structures for Organic-Rich Lacustrine Shale Reservoirs

NASA Astrophysics Data System (ADS)

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

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

NASA Technical Reports Server (NTRS)

Wiscombe, W.

1999-01-01

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

PubMed

Verma, Rupesh; Audhkhasi, Romil; Thyagarajan, Krishna; Banerjee, Varsha

2018-03-01

Many of the present-day optical devices use photonic crystals. These are multilayers of dielectric media that control the reflection and transmission of light falling on them. In this paper, we study the optical properties of periodic, fractal, and aperiodic photonic crystals and compare them based on their attributes. Our calculations of the band reflectivity and degree of robustness reveal novel features, e.g., fractal photonic crystals are found to reflect the maximum amount of incident light. On the other hand, aperiodic photonic crystals have the largest immunity to disorder. We believe that such properties will be useful in a variety of applications in the field of optical communication.
Age-related alterations in the fractal scaling of cardiac interbeat interval dynamics

NASA Technical Reports Server (NTRS)

Iyengar, N.; Peng, C. K.; Morin, R.; Goldberger, A. L.; Lipsitz, L. A.

1996-01-01

We postulated that aging is associated with disruption in the fractallike long-range correlations that characterize healthy sinus rhythm cardiac interval dynamics. Ten young (21-34 yr) and 10 elderly (68-81 yr) rigorously screened healthy subjects underwent 120 min of continuous supine resting electrocardiographic recording. We analyzed the interbeat interval time series using standard time and frequency domain statistics and using a fractal measure, detrended fluctuation analysis, to quantify long-range correlation properties. In healthy young subjects, interbeat intervals demonstrated fractal scaling, with scaling exponents (alpha) from the fluctuation analysis close to a value of 1.0. In the group of healthy elderly subjects, the interbeat interval time series had two scaling regions. Over the short range, interbeat interval fluctuations resembled a random walk process (Brownian noise, alpha = 1.5), whereas over the longer range they resembled white noise (alpha = 0.5). Short (alpha s)- and long-range (alpha 1) scaling exponents were significantly different in the elderly subjects compared with young (alpha s = 1.12 +/- 0.19 vs. 0.90 +/- 0.14, respectively, P = 0.009; alpha 1 = 0.75 +/- 0.17 vs. 0.99 +/- 0.10, respectively, P = 0.002). The crossover behavior from one scaling region to another could be modeled as a first-order autoregressive process, which closely fit the data from four elderly subjects. This implies that a single characteristic time scale may be dominating heartbeat control in these subjects. The age-related loss of fractal organization in heartbeat dynamics may reflect the degradation of integrated physiological regulatory systems and may impair an individual's ability to adapt to stress.
Multifractal analysis of 2001 Mw 7 . 7 Bhuj earthquake sequence in Gujarat, Western India

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

NASA Astrophysics Data System (ADS)

Park, So-Myoung; Goodwin, Simon P.; Kim, Sungsoo S.

2018-07-01

We examine the dynamical evolution of both Plummer sphere and substructured (fractal) star-forming regions in Galactic Centre (GC) strong tidal fields to see what initial conditions could give rise to an Arches-like massive star cluster by ˜2 Myr. We find that any initial distribution has to be contained within its initial tidal radius to survive, which sets a lower limit of the initial density of the Arches of ˜600 M⊙ pc-3 if the Arches is at 30 pc from the GC, or ˜200 M⊙ pc-3 if the Arches is at 100 pc from the GC. Plummer spheres that survive change little other than to dynamically mass segregate, but initially fractal distributions rapidly erase substructure, dynamically mass segregate and by 2 Myr look extremely similar to initial Plummer spheres, therefore it is almost impossible to determine the initial conditions of clusters in strong tidal fields.
The early dynamical evolution of star clusters near the Galactic Centre

NASA Astrophysics Data System (ADS)

Park, So-Myoung; Goodwin, Simon P.; Kim, Sungsoo S.

2018-04-01

We examine the dynamical evolution of both Plummer sphere and substructured (fractal) star forming regions in Galactic Centre (GC) strong tidal fields to see what initial conditions could give rise to an Arches-like massive star cluster by ˜2 Myr. We find that any initial distribution has to be contained within its initial tidal radius to survive, which sets a lower limit of the initial density of the Arches of ˜ 600 M⊙ pc-3 if the Arches is at 30 pc from the GC, or ˜ 200 M⊙ pc-3 if the Arches is at 100 pc from the GC. Plummer spheres that survive change little other than to dynamically mass segregate, but initially fractal distributions rapidly erase substructure, dynamically mass segregate and by 2 Myr look extremely similar to initial Plummer spheres, therefore it is almost impossible to determine the initial conditions of clusters in strong tidal fields.
Teaching (an introduction to!) fractals and rainfall features in kinder garden

NASA Astrophysics Data System (ADS)

Gires, Auguste; Villepoux, Mélanie; Rouellé, Valérie

2014-05-01

Why trying to teach fractals or rainfall drop size distribution to 3 to 5 year old children? Because it can easily be done in a (rather!) fun way, enabling children to grasp some complex notions and more generally get familiarized with science. This paper presents the outputs of a collaboration between a researcher and two kinder garden teachers which resulted in activities dealing with fractals and rainfall that were implemented in their class. Fractals are geometrical objects that exhibit a similar structure at all scales. A classical natural example is a fern leaf around which an activity was developed and implemented with children aged 3-4. The first step consisted in trying to make them feel the fractal nature of the fern leaf, i.e. a whole leaf is made of smaller leafs which are also made of even smaller leafs exhibiting similar shapes. Four activities were specifically designed for this. In the second step the fractal nature of the fern leaf was used to enable the class to draw a large leaf in a collaborative way. More precisely, each child draw a leaf and they were all assembled to draw a greater one. A similar activity but this time with geometrical shapes based on triangles was implemented with kids aged 4-5. The output was a great Sierpinski triangle. Rain drops typically exhibit sizes ranging from 0.2 to 5 mm (in terms of equivolumic diameter), and scientists uses disdrometers to analyse this distribution. An activity that consisted in developing and testing two disdrometers was implemented in a class with children aged 5-6. The disdrometers consisted of a plate with a thin layer of either flour or oil. The features of the two devices were initially compared with the help of artificial drops generated by the children with a pipette. Then the disdrometers were briefly (few seconds) put under the rain. In order to help children notice the wide variety of drop sizes they were asked to draw what they saw. Finally an activity based on times series of rainy and non-rainy days (recorded by the class) whose aim is to the show the fractal nature of rainfall and to introduce the notion of random models will briefly be discussed. Authors acknowledged the North-West Europe Interreg IV RainGain project (raingain.eu) and the Climate KIC Blue Green Dream project (bgd.org.uk) for funding the underlying research associated with these activities.
Models for the hotspot distribution

NASA Technical Reports Server (NTRS)

Jurdy, Donna M.; Stefanick, Michael

1990-01-01

Published hotspot catalogs all show a hemispheric concentration beyond what can be expected by chance. Cumulative distributions about the center of concentration are described by a power law with a fractal dimension closer to 1 than 2. Random sets of the corresponding sizes do not show this effect. A simple shift of the random sets away from a point would produce distributions similar to those of hotspot sets. The possible relation of the hotspots to the locations of ridges and subduction zones is tested using large sets of randomly-generated points to estimate areas within given distances of the plate boundaries. The probability of finding the observed number of hotspots within 10 deg of the ridges is about what is expected.
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.
Exploring the role of turbulent acceleration and heating in fractal current sheet of solar flares from hybrid particle in cell and lattice Boltzmann virtual test

NASA Astrophysics Data System (ADS)

Zhu, B.; Lin, J.; Yuan, X.; Li, Y.; Shen, C.

2016-12-01

The role of turbulent acceleration and heating in the fractal magnetic reconnection of solar flares is still not clear, especially at the X-point in the diffusion region. At virtual test aspect, it is hardly to quantitatively analyze the vortex generation, turbulence evolution, particle acceleration and heating in the magnetic islands coalesce in fractal manner, formatting into largest plasmid and ejection process in diffusion region through classical magnetohydrodynamics numerical method. With the development of physical particle numerical method (particle in cell method [PIC], Lattice Boltzmann method [LBM]) and high performance computing technology in recently two decades. Kinetic simulation has developed into an effectively manner to exploring the role of magnetic field and electric field turbulence in charged particles acceleration and heating process, since all the physical aspects relating to turbulent reconnection are taken into account. In this paper, the LBM based lattice DxQy grid and extended distribution are added into charged-particles-to-grid-interpolation of PIC based finite difference time domain scheme and Yee Grid, the hybrid PIC-LBM simulation tool is developed to investigating turbulence acceleration on TIANHE-2. The actual solar coronal condition (L≈105Km,B≈50-500G,T≈5×106K, n≈108-109, mi/me≈500-1836) is applied to study the turbulent acceleration and heating in solar flare fractal current sheet. At stage I, magnetic islands shrink due to magnetic tension forces, the process of island shrinking halts when the kinetic energy of the accelerated particles is sufficient to halt the further collapse due to magnetic tension forces, the particle energy gain is naturally a large fraction of the released magnetic energy. At stage II and III, the particles from the energized group come in to the center of the diffusion region and stay longer in the area. In contract, the particles from non energized group only skim the outer part of the diffusion regions. At stage IV, the magnetic reconnection type nanoplasmid (200km) stop expanding and carrying enough energy to eject particles as constant velocity. Last, the role of magnetic field turbulence and electric field turbulence in electron and ion acceleration at the diffusion regions in solar flare fractural current sheet is given.
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.
Nanostructured Dielectric Fractals on Resonant Plasmonic Metasurfaces for Selective and Sensitive Optical Sensing of Volatile Compounds.

PubMed

Fusco, Zelio; Rahmani, Mohsen; Bo, Renheng; Verre, Ruggero; Motta, Nunzio; Käll, Mikael; Neshev, Dragomir; Tricoli, Antonio

2018-06-04

Advances in the understanding and fabrication of plasmonic nanostructures have led to a plethora of unprecedented optoelectronic and optochemical applications. Plasmon resonance has found widespread use in efficient optical transducers of refractive index changes in liquids. However, it has proven challenging to translate these achievements to the selective detection of gases, which typically adsorb non-specifically and induce refractive index changes below the detection limit. Here, it's shown that integration of tailored fractals of dielectric TiO 2 nanoparticles on a plasmonic metasurface strongly enhances the interaction between the plasmonic field and volatile organic molecules and provides a means for their selective detection. Notably, this superior optical response is due to the enhancement of the interaction between the dielectric fractals and the plasmonic metasurface for thickness of up to 1.8 μm, much higher than the evanescent plasmonic near-field (≈30 nm) . Optimal dielectric-plasmonic structures allow measurements of changes in the refractive index of the gas mixture down to <8 × 10 -6 at room temperature and selective identification of three exemplary volatile organic compounds. These findings provide a basis for the development of a novel family of dielectric-plasmonic materials with application extending from light harvesting and photocatalysts to contactless sensors for noninvasive medical diagnostics. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
COMPARISON OF CHAOTIC AND FRACTAL PROPERTIES OF POLAR FACULAE WITH SUNSPOT ACTIVITY

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

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

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

NASA Astrophysics Data System (ADS)

Sears, Suzanne M.

From the stripes of a zebra, to the spirals of cream in a hot cup of coffee, we are surrounded by patterns in the natural world. But why are there patterns? Why drives their formation? In this thesis we study some of the diverse ways patterns can arise due to the interactions between solitary waves in nonlinear systems, sometimes starting from nothing more than random noise. What follows is a set of three studies. In the first, we show how a nonlinear system that supports solitons can be driven to generate exact (regular) Cantor set fractals. As an example, we use numerical simulations to demonstrate the formation of Cantor set fractals by temporal optical solitons. This fractal formation occurs in a cascade of nonlinear optical fibers through the dynamical evolution of a single input soliton. In the second study, we investigate pattern formation initiated by modulation instability in nonlinear partially coherent wave fronts and show that anisotropic noise and/or anisotropic correlation statistics can lead to ordered patterns such as grids and stripes. For the final study, we demonstrate the spontaneous clustering of solitons in partially coherent wavefronts during the final stages of pattern formation initiated by modulation instability and noise. Experimental observations are in agreement with theoretical predictions and are confirmed using numerical simulations.

Segmentation of time series with long-range fractal correlations

PubMed Central

Bernaola-Galván, P.; Oliver, J.L.; Hackenberg, M.; Coronado, A.V.; Ivanov, P.Ch.; Carpena, P.

2012-01-01

Segmentation is a standard method of data analysis to identify change-points dividing a nonstationary time series into homogeneous segments. However, for long-range fractal correlated series, most of the segmentation techniques detect spurious change-points which are simply due to the heterogeneities induced by the correlations and not to real nonstationarities. To avoid this oversegmentation, we present a segmentation algorithm which takes as a reference for homogeneity, instead of a random i.i.d. series, a correlated series modeled by a fractional noise with the same degree of correlations as the series to be segmented. We apply our algorithm to artificial series with long-range correlations and show that it systematically detects only the change-points produced by real nonstationarities and not those created by the correlations of the signal. Further, we apply the method to the sequence of the long arm of human chromosome 21, which is known to have long-range fractal correlations. We obtain only three segments that clearly correspond to the three regions of different G + C composition revealed by means of a multi-scale wavelet plot. Similar results have been obtained when segmenting all human chromosome sequences, showing the existence of previously unknown huge compositional superstructures in the human genome. PMID:23645997
Spatial Distributions of Young Stars

NASA Astrophysics Data System (ADS)

Kraus, Adam L.; Hillenbrand, Lynne A.

2008-10-01

We analyze the spatial distribution of young stars in Taurus-Auriga and Upper Sco, as determined from the two-point correlation function (i.e., the mean surface density of neighbors). The corresponding power-law fits allow us to determine the fractal dimensions of each association's spatial distribution, measure the stellar velocity dispersions, and distinguish between the bound binary population and chance alignments of members. We find that the fractal dimension of Taurus is D ~ 1.05, consistent with its filamentary structure. The fractal dimension of Upper Sco may be even shallower (D ~ 0.7), but this fit is uncertain due to the limited area and possible spatially variable incompleteness. We also find that random stellar motions have erased all primordial structure on scales of lsim0.07° in Taurus and lsim1.7° in Upper Sco; given ages of ~1 and ~5 Myr, the corresponding internal velocity dispersions are ~0.2 and ~1.0 km s-1, respectively. Finally, we find that binaries can be distinguished from chance alignments at separations of lsim120'' (17,000 AU) in Taurus and lsim75'' (11,000 AU) in Upper Sco. The binary populations in these associations that we previously studied, spanning separations of 3''-30'', is dominated by binary systems. However, the few lowest mass pairs (Mprim <~ 0.3 M⊙) might be chance alignments.
Study of the grazing-incidence X-ray scattering of strongly disturbed fractal surfaces

NASA Astrophysics Data System (ADS)

Roshchin, B. S.; Chukhovsky, F. N.; Pavlyuk, M. D.; Opolchentsev, A. M.; Asadchikov, V. E.

2017-03-01

The applicability of different approaches to the description of hard X-ray scattering from rough surfaces is generally limited by a maximum surface roughness height of no more than 1 nm. Meanwhile, this value is several times larger for the surfaces of different materials subjected to treatment, especially in the initial treatment stages. To control the roughness parameters in all stages of surface treatment, a new approach has been developed, which is based on a series expansion of wavefield over the plane eigenstate-function waves describing the small-angle scattering of incident X-rays in terms of plane q-waves propagating through the interface between two media with a random function of relief heights. To determine the amplitudes of reflected and transmitted plane q-waves, a system of two linked integral equations was derived. The solutions to these equations correspond (in zero order) to the well-known Fresnel expressions for a smooth plane interface. Based on these solutions, a statistical fractal model of an isotropic rough interface is built in terms of root-mean-square roughness σ, two-point correlation length l, and fractal surface index h. The model is used to interpret X-ray scattering data for polished surfaces of single-crystal cadmium telluride samples.
Study of the grazing-incidence X-ray scattering of strongly disturbed fractal surfaces

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

Roshchin, B. S., E-mail: ross@crys.ras.ru; Chukhovsky, F. N.; Pavlyuk, M. D.

2017-03-15

The applicability of different approaches to the description of hard X-ray scattering from rough surfaces is generally limited by a maximum surface roughness height of no more than 1 nm. Meanwhile, this value is several times larger for the surfaces of different materials subjected to treatment, especially in the initial treatment stages. To control the roughness parameters in all stages of surface treatment, a new approach has been developed, which is based on a series expansion of wavefield over the plane eigenstate-function waves describing the small-angle scattering of incident X-rays in terms of plane q-waves propagating through the interface betweenmore » two media with a random function of relief heights. To determine the amplitudes of reflected and transmitted plane q-waves, a system of two linked integral equations was derived. The solutions to these equations correspond (in zero order) to the well-known Fresnel expressions for a smooth plane interface. Based on these solutions, a statistical fractal model of an isotropic rough interface is built in terms of root-mean-square roughness σ, two-point correlation length l, and fractal surface index h. The model is used to interpret X-ray scattering data for polished surfaces of single-crystal cadmium telluride samples.« less
Scaling and intermittency of brain events as a manifestation of consciousness

NASA Astrophysics Data System (ADS)

Paradisi, P.; Allegrini, P.; Gemignani, A.; Laurino, M.; Menicucci, D.; Piarulli, A.

2013-01-01

We discuss the critical brain hypothesis and its relationship with intermittent renewal processes displaying power-law decay in the distribution of waiting times between two consecutive renewal events. In particular, studies on complex systems in a "critical" condition show that macroscopic variables, integrating the activities of many individual functional units, undergo fluctuations with an intermittent serial structure characterized by avalanches with inverse-power-law (scale-free) distribution densities of sizes and inter-event times. This condition, which is denoted as "fractal intermittency", was found in the electroencephalograms of subjects observed during a resting state wake condition. It remained unsolved whether fractal intermittency correlates with the stream of consciousness or with a non-task-driven default mode activity, also present in non-conscious states, like deep sleep. After reviewing a method of scaling analysis of intermittent systems based of eventdriven random walks, we show that during deep sleep fractal intermittency breaks down, and reestablishes during REM (Rapid Eye Movement) sleep, with essentially the same anomalous scaling of the pre-sleep wake condition. From the comparison of the pre-sleep wake, deep sleep and REM conditions we argue that the scaling features of intermittent brain events are related to the level of consciousness and, consequently, could be exploited as a possible indicator of consciousness in clinical applications.
Seismic random noise attenuation method based on empirical mode decomposition of Hausdorff dimension

NASA Astrophysics Data System (ADS)

Yan, Z.; Luan, X.

2017-12-01

Introduction Empirical mode decomposition (EMD) is a noise suppression algorithm by using wave field separation, which is based on the scale differences between effective signal and noise. However, since the complexity of the real seismic wave field results in serious aliasing modes, it is not ideal and effective to denoise with this method alone. Based on the multi-scale decomposition characteristics of the signal EMD algorithm, combining with Hausdorff dimension constraints, we propose a new method for seismic random noise attenuation. First of all, We apply EMD algorithm adaptive decomposition of seismic data and obtain a series of intrinsic mode function (IMF)with different scales. Based on the difference of Hausdorff dimension between effectively signals and random noise, we identify IMF component mixed with random noise. Then we use threshold correlation filtering process to separate the valid signal and random noise effectively. Compared with traditional EMD method, the results show that the new method of seismic random noise attenuation has a better suppression effect. The implementation process The EMD algorithm is used to decompose seismic signals into IMF sets and analyze its spectrum. Since most of the random noise is high frequency noise, the IMF sets can be divided into three categories: the first category is the effective wave composition of the larger scale; the second category is the noise part of the smaller scale; the third category is the IMF component containing random noise. Then, the third kind of IMF component is processed by the Hausdorff dimension algorithm, and the appropriate time window size, initial step and increment amount are selected to calculate the Hausdorff instantaneous dimension of each component. The dimension of the random noise is between 1.0 and 1.05, while the dimension of the effective wave is between 1.05 and 2.0. On the basis of the previous steps, according to the dimension difference between the random noise and effective signal, we extracted the sample points, whose fractal dimension value is less than or equal to 1.05 for the each IMF components, to separate the residual noise. Using the IMF components after dimension filtering processing and the effective wave IMF components after the first selection for reconstruction, we can obtained the results of de-noising.
Mapping of the Bak, Tang, and Wiesenfeld sandpile model on a two-dimensional Ising-correlated percolation lattice to the two-dimensional self-avoiding random walk.

PubMed

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

2017-11-01

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

We analyze a discrete time two-sector economic growth model where the production technologies in the final and human capital sectors are affected by random shocks both directly (via productivity and factor shares) and indirectly (via a pollution externality). We determine the optimal dynamics in the decentralized economy and show how these dynamics can be described in terms of a two-dimensional affine iterated function system with probability. This allows us to identify a suitable parameter configuration capable of generating exactly the classical Barnsley's fern as the attractor of the log-linearized optimal dynamical system.
Time irreversibility and intrinsics revealing of series with complex network approach

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

USGS Publications Warehouse

Ahlbrandt, T.S.; Klett, T.R.

2005-01-01

Various methods for assessing undiscovered oil, natural gas, and natural gas liquid resources were compared in support of the USGS World Petroleum Assessment 2000. Discovery process, linear fractal, parabolic fractal, engineering estimates, PETRIMES, Delphi, and the USGS 2000 methods were compared. Three comparisons of these methods were made in: (1) the Neuquen Basin province, Argentina (different assessors, same input data); (2) provinces in North Africa, Oman, and Yemen (same assessors, different methods); and (3) the Arabian Peninsula, Arabian (Persian) Gulf, and North Sea (different assessors, different methods). A fourth comparison (same assessors, same assessment methods but different geologic models), between results from structural and stratigraphic assessment units in the North Sea used only the USGS 2000 method, and hence compared the type of assessment unit rather than the method. In comparing methods, differences arise from inherent differences in assumptions regarding: (1) the underlying distribution of the parent field population (all fields, discovered and undiscovered), (2) the population of fields being estimated; that is, the entire parent distribution or the undiscovered resource distribution, (3) inclusion or exclusion of large outlier fields; (4) inclusion or exclusion of field (reserve) growth, (5) deterministic or probabilistic models, (6) data requirements, and (7) scale and time frame of the assessment. Discovery process, Delphi subjective consensus, and the USGS 2000 method yield comparable results because similar procedures are employed. In mature areas such as the Neuquen Basin province in Argentina, the linear and parabolic fractal and engineering methods were conservative compared to the other five methods and relative to new reserve additions there since 1995. The PETRIMES method gave the most optimistic estimates in the Neuquen Basin. In less mature areas, the linear fractal method yielded larger estimates relative to other methods. A geologically based model, such as one using the total petroleum system approach, is preferred in that it combines the elements of petroleum source, reservoir, trap and seal with the tectono-stratigraphic history of basin evolution with petroleum resource potential. Care must be taken to demonstrate that homogeneous populations in terms of geology, geologic risk, exploration, and discovery processes are used in the assessment process. The USGS 2000 method (7th Approximation Model, EMC computational program) is robust; that is, it can be used in both mature and immature areas, and provides comparable results when using different geologic models (e.g. stratigraphic or structural) with differing amounts of subdivisions, assessment units, within the total petroleum system. ?? 2005 International Association for Mathematical Geology.
Adaptive Schools in a Quantum Universe.

ERIC Educational Resources Information Center

Garmston, Robert; Wellman, Bruce

1995-01-01

Information from quantum mechanics, chaos theory, fractal geometry, and the new biology can help educators rethink school-improvement approaches. Chaos and order exist simultaneously. Adaptability, the central operating principle of successful organizations, stems from five human energy fields: efficacy, flexibility, craftsmanship, consciousness,…
Fractal analysis of the susceptibility weighted imaging patterns in malignant brain tumors during antiangiogenic treatment: technical report on four cases serially imaged by 7 T magnetic resonance during a period of four weeks.

PubMed

Di Ieva, Antonio; Matula, Christian; Grizzi, Fabio; Grabner, Günther; Trattnig, Siegfried; Tschabitscher, Manfred

2012-01-01

The need for new and objective indexes for the neuroradiologic follow-up of brain tumors and for monitoring the effects of antiangiogenic strategies in vivo led us to perform a technical study on four patients who received computerized analysis of tumor-associated vasculature with ultra-high-field (7 T) magnetic resonance imaging (MRI). The image analysis involved the application of susceptibility weighted imaging (SWI) to evaluate vascular structures. Four patients affected by recurrent malignant brain tumors were enrolled in the present study. After the first 7-T SWI MRI procedure, the patients underwent antiangiogenic treatment with bevacizumab. The imaging was repeated every 2 weeks for a period of 4 weeks. The SWI patterns visualized in the three MRI temporal sequences were analyzed by means of a computer-aided fractal-based method to objectively quantify their geometric complexity. In two clinically deteriorating patients we found an increase of the geometric complexity of the space-filling properties of the SWI patterns over time despite the antiangiogenic treatment. In one patient, who showed improvement with the therapy, the fractal dimension of the intratumoral structure decreased, whereas in the fourth patient, no differences were found. The qualitative changes of the intratumoral SWI patterns during a period of 4 weeks were quantified with the fractal dimension. Because SWI patterns are also related to the presence of vascular structures, the quantification of their space-filling properties with fractal dimension seemed to be a valid tool for the in vivo neuroradiologic follow-up of brain tumors. Copyright © 2012 Elsevier Inc. All rights reserved.
Microelectronics and nanotechnology, and the fractal-like structure of information, knowledge, and science

NASA Astrophysics Data System (ADS)

Nutu, Catalin Silviu; Axinte, Tiberiu

2016-12-01

The article is centralizing and is concentrating the information from a considerable amount of papers related to the field of microelectronics and nanotechnology and also provides an approach to science and to the future evolution of science, based on the theory of the fractals. The new science of microelectronics and nanotechnology is one of the best examples of how the science of future will look like, namely at the confluence of increasingly more other sciences, where increasingly more sciences are to be added in the structure of the new science and the role of the multidisciplinary and interdisciplinary is becoming more and more important. Although not giving explicit details (e.g. specific formulas) the theory of fractals is used in the paper to explain the way of generation of new science for the specific case of microelectronics and nanotechnology, but is also used in the paper to outline a different way to approach new science and eventually to approach new sciences to come. There are mainly two motivations for the present article, namely: on the one hand, the position of the microelectronics and nanotechnologies in the fractal-like structure of science, and, on the other hand, that much of the communication, information, knowledge and science transfer, dissemination and advancement in sciences are taking place using the new technologies related to microelectronics and nanotechnologies.
Scaling relationships of channel networks at large scales: Examples from two large-magnitude watersheds in Brittany, France

NASA Astrophysics Data System (ADS)

Crave, A.; Davy, P.

1997-01-01

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

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
Reply to "Comment on 'Hydrodynamics of fractal continuum flow' and 'Map of fluid flow in fractal porous medium into fractal continuum flow'".

PubMed

Balankin, Alexander S; Elizarraraz, Benjamin Espinoza

2013-11-01

The aim of this Reply is to elucidate the difference between the fractal continuum models used in the preceding Comment and the models of fractal continuum flow which were put forward in our previous articles [Phys. Rev. E 85, 025302(R) (2012); 85, 056314 (2012)]. In this way, some drawbacks of the former models are highlighted. Specifically, inconsistencies in the definitions of the fractal derivative, the Jacobian of transformation, the displacement vector, and angular momentum are revealed. The proper forms of the Reynolds' transport theorem and angular momentum principle for the fractal continuum are reaffirmed in a more illustrative manner. Consequently, we emphasize that in the absence of any internal angular momentum, body couples, and couple stresses, the Cauchy stress tensor in the fractal continuum should be symmetric. Furthermore, we stress that the approach based on the Cartesian product measured and used in the preceding Comment cannot be employed to study the path-connected fractals, such as a flow in a fractally permeable medium. Thus, all statements of our previous works remain unchallenged.
Quasi Eighth-Mode Substrate Integrated Waveguide (SIW) Fractal Resonator Filter Utilizing Gap Coupling Compensation

NASA Astrophysics Data System (ADS)

Zhang, Sheng; Rao, Jia-Yu; Tai, Wen-Si; Wang, Ting; Liu, Fa-Lin

2016-09-01

In this paper, a kind of quasi eighth substrate integrated waveguide resonator (QESIWR) with defected fractal structure (DFS) is proposed firstly. Compared with the eighth substrate integrated waveguide resonator (ESIWR), this kind of resonator has lower resonant frequency (f0), acceptable unloaded quality (Qu) value and almost unchanged electric field distribution. In order to validate the properties of QESIWR, a cascaded quadruplet QESIWRs filter is designed and optimized. By using cross coupling and gap coupling compensation, this filter has two transmission zeros (TZs) at each side of the passband. Meanwhile, in comparison with the conventional ones, its size is cut down over 90 %. The measured results agree well with the simulated ones.
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.
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)
Gaussian free field in the background of correlated random clusters, formed by metallic nanoparticles

NASA Astrophysics Data System (ADS)

Cheraghalizadeh, Jafar; Najafi, Morteza N.; Mohammadzadeh, Hossein

2018-05-01

The effect of metallic nano-particles (MNPs) on the electrostatic potential of a disordered 2D dielectric media is considered. The disorder in the media is assumed to be white-noise Coulomb impurities with normal distribution. To realize the correlations between the MNPs we have used the Ising model with an artificial temperature T that controls the number of MNPs as well as their correlations. In the T → 0 limit, one retrieves the Gaussian free field (GFF), and in the finite temperature the problem is equivalent to a GFF in iso-potential islands. The problem is argued to be equivalent to a scale-invariant random surface with some critical exponents which vary with T and correspondingly are correlation-dependent. Two type of observables have been considered: local and global quantities. We have observed that the MNPs soften the random potential and reduce its statistical fluctuations. This softening is observed in the local as well as the geometrical quantities. The correlation function of the electrostatic and its total variance are observed to be logarithmic just like the GFF, i.e. the roughness exponent remains zero for all temperatures, whereas the proportionality constants scale with T - T c . The fractal dimension of iso-potential lines ( D f ), the exponent of the distribution function of the gyration radius ( τ r ), and the loop lengths ( τ l ), and also the exponent of the loop Green function x l change in terms of T - T c in a power-law fashion, with some critical exponents reported in the text. Importantly we have observed that D f ( T) - D f ( T c ) 1/√ ξ( T), in which ξ( T) is the spin correlation length in the Ising model.
Kinematic variability, fractal dynamics and local dynamic stability of treadmill walking

PubMed Central

2011-01-01

Background Motorized treadmills are widely used in research or in clinical therapy. Small kinematics, kinetics and energetics changes induced by Treadmill Walking (TW) as compared to Overground Walking (OW) have been reported in literature. The purpose of the present study was to characterize the differences between OW and TW in terms of stride-to-stride variability. Classical (Standard Deviation, SD) and non-linear (fractal dynamics, local dynamic stability) methods were used. In addition, the correlations between the different variability indexes were analyzed. Methods Twenty healthy subjects performed 10 min TW and OW in a random sequence. A triaxial accelerometer recorded trunk accelerations. Kinematic variability was computed as the average SD (MeanSD) of acceleration patterns among standardized strides. Fractal dynamics (scaling exponent α) was assessed by Detrended Fluctuation Analysis (DFA) of stride intervals. Short-term and long-term dynamic stability were estimated by computing the maximal Lyapunov exponents of acceleration signals. Results TW did not modify kinematic gait variability as compared to OW (multivariate T2, p = 0.87). Conversely, TW significantly modified fractal dynamics (t-test, p = 0.01), and both short and long term local dynamic stability (T2 p = 0.0002). No relationship was observed between variability indexes with the exception of significant negative correlation between MeanSD and dynamic stability in TW (3 × 6 canonical correlation, r = 0.94). Conclusions Treadmill induced a less correlated pattern in the stride intervals and increased gait stability, but did not modify kinematic variability in healthy subjects. This could be due to changes in perceptual information induced by treadmill walking that would affect locomotor control of the gait and hence specifically alter non-linear dependencies among consecutive strides. Consequently, the type of walking (i.e. treadmill or overground) is important to consider in each protocol design. PMID:21345241
Segmentation of anatomical branching structures based on texture features and conditional random field

NASA Astrophysics Data System (ADS)

Nuzhnaya, Tatyana; Bakic, Predrag; Kontos, Despina; Megalooikonomou, Vasileios; Ling, Haibin

2012-02-01

This work is a part of our ongoing study aimed at understanding a relation between the topology of anatomical branching structures with the underlying image texture. Morphological variability of the breast ductal network is associated with subsequent development of abnormalities in patients with nipple discharge such as papilloma, breast cancer and atypia. In this work, we investigate complex dependence among ductal components to perform segmentation, the first step for analyzing topology of ductal lobes. Our automated framework is based on incorporating a conditional random field with texture descriptors of skewness, coarseness, contrast, energy and fractal dimension. These features are selected to capture the architectural variability of the enhanced ducts by encoding spatial variations between pixel patches in galactographic image. The segmentation algorithm was applied to a dataset of 20 x-ray galactograms obtained at the Hospital of the University of Pennsylvania. We compared the performance of the proposed approach with fully and semi automated segmentation algorithms based on neural network classification, fuzzy-connectedness, vesselness filter and graph cuts. Global consistency error and confusion matrix analysis were used as accuracy measurements. For the proposed approach, the true positive rate was higher and the false negative rate was significantly lower compared to other fully automated methods. This indicates that segmentation based on CRF incorporated with texture descriptors has potential to efficiently support the analysis of complex topology of the ducts and aid in development of realistic breast anatomy phantoms.
Emergence of fractal scaling in complex networks

NASA Astrophysics Data System (ADS)

Wei, Zong-Wen; Wang, Bing-Hong

2016-09-01

Some real-world networks are shown to be fractal or self-similar. It is widespread that such a phenomenon originates from the repulsion between hubs or disassortativity. Here we show that this common belief fails to capture the causality. Our key insight to address it is to pinpoint links critical to fractality. Those links with small edge betweenness centrality (BC) constitute a special architecture called fractal reference system, which gives birth to the fractal structure of those reported networks. In contrast, a small amount of links with high BC enable small-world effects, hiding the intrinsic fractality. With enough of such links removed, fractal scaling spontaneously arises from nonfractal networks. Our results provide a multiple-scale view on the structure and dynamics and place fractality as a generic organizing principle of complex networks on a firmer ground.
Complex behaviour and predictability of the European dry spell regimes

NASA Astrophysics Data System (ADS)

Lana, X.; Martínez, M. D.; Serra, C.; Burgueño, A.

2010-09-01

The complex spatial and temporal characteristics of European dry spell lengths, DSL, (sequences of consecutive days with rainfall amount below a certain threshold) and their randomness and predictive instability are analysed from daily pluviometric series recorded at 267 rain gauges along the second half of the 20th century. DSL are obtained by considering four thresholds, R0, of 0.1, 1.0, 5.0 and 10.0 mm/day. A proper quantification of the complexity, randomness and predictive instability of the different DSL regimes in Europe is achieved on the basis of fractal analyses and dynamic system theory, including the reconstruction theorem. First, the concept of lacunarity is applied to the series of daily rainfall, and the lacunarity curves are well fitted to Cantor and random Cantor sets. Second, the rescaled analysis reveals that randomness, persistence and anti-persistence are present on the European DSL series. Third, the complexity of the physical process governing the DSL series is quantified by the minimum number of nonlinear equations determined by the correlation dimension. And fourth, the loss of memory of the physical process, which is one of the reasons for the complex predictability, is characterized by the values of the Kolmogorov entropy, and the predictive instability is directly associated with positive Lyapunov exponents. In this way, new bases for a better prediction of DSLs in Europe, sometimes leading to drought episodes, are established. Concretely, three predictive strategies are proposed in Sect. 5. It is worth mentioning that the spatial distribution of all fractal parameters does not solely depend on latitude and longitude but also reflects the effects of orography, continental climate or vicinity to the Atlantic and Arctic Oceans and Mediterranean Sea.
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.
Spherical cluster ensembles with fractal structure in LaSrMnO: New form of self-organization in solids

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

Okunev, V. D.; Samoilenko, Z. A.; Burkhovetski, V. V.

The growth of La{sub 0.7}Sr{sub 0.3}MnO{sub 3} films in magnetron plasma, in special conditions, leads to the appearance of ensembles of micron-sized spherical crystalline clusters with fractal structure, which we consider to be a new form of self-organization in solids. Each ensemble contains 10{sup 5}-10{sup 6} elementary clusters, 100-250 A in diameter. Interaction of the clusters in the ensemble is realized through the interatomic chemical bonds, intrinsic to the manganites. Integration of peripheral areas of interacting clusters results in the formation of common intercluster medium in the ensemble. We argue that the ensembles with fractal structure built into paramagnetic disorderedmore » matrix have ferromagnetic properties. Absence of sharp borders between elementary clusters and the presence of common intercluster medium inside each ensemble permits to rearrange magnetic order and to change the volume of the ferromagnetic phase, providing automatically a high sensitivity of the material to the external field.« less
Fractal Complexity-Based Feature Extraction Algorithm of Communication Signals

NASA Astrophysics Data System (ADS)

Wang, Hui; Li, Jingchao; Guo, Lili; Dou, Zheng; Lin, Yun; Zhou, Ruolin

How to analyze and identify the characteristics of radiation sources and estimate the threat level by means of detecting, intercepting and locating has been the central issue of electronic support in the electronic warfare, and communication signal recognition is one of the key points to solve this issue. Aiming at accurately extracting the individual characteristics of the radiation source for the increasingly complex communication electromagnetic environment, a novel feature extraction algorithm for individual characteristics of the communication radiation source based on the fractal complexity of the signal is proposed. According to the complexity of the received signal and the situation of environmental noise, use the fractal dimension characteristics of different complexity to depict the subtle characteristics of the signal to establish the characteristic database, and then identify different broadcasting station by gray relation theory system. The simulation results demonstrate that the algorithm can achieve recognition rate of 94% even in the environment with SNR of -10dB, and this provides an important theoretical basis for the accurate identification of the subtle features of the signal at low SNR in the field of information confrontation.
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.
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.
Nature of size effects in compact models of field effect transistors

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

Torkhov, N. A., E-mail: trkf@mail.ru; Scientific-Research Institute of Semiconductor Devices, Tomsk 634050; Tomsk State University of Control Systems and Radioelectronics, Tomsk 634050

Investigations have shown that in the local approximation (for sizes L < 100 μm), AlGaN/GaN high electron mobility transistor (HEMT) structures satisfy to all properties of chaotic systems and can be described in the language of fractal geometry of fractional dimensions. For such objects, values of their electrophysical characteristics depend on the linear sizes of the examined regions, which explain the presence of the so-called size effects—dependences of the electrophysical and instrumental characteristics on the linear sizes of the active elements of semiconductor devices. In the present work, a relationship has been established for the linear model parameters of themore » equivalent circuit elements of internal transistors with fractal geometry of the heteroepitaxial structure manifested through a dependence of its relative electrophysical characteristics on the linear sizes of the examined surface areas. For the HEMTs, this implies dependences of their relative static (A/mm, mA/V/mm, Ω/mm, etc.) and microwave characteristics (W/mm) on the width d of the sink-source channel and on the number of sections n that leads to a nonlinear dependence of the retrieved parameter values of equivalent circuit elements of linear internal transistor models on n and d. Thus, it has been demonstrated that the size effects in semiconductors determined by the fractal geometry must be taken into account when investigating the properties of semiconductor objects on the levels less than the local approximation limit and designing and manufacturing field effect transistors. In general, the suggested approach allows a complex of problems to be solved on designing, optimizing, and retrieving the parameters of equivalent circuits of linear and nonlinear models of not only field effect transistors but also any arbitrary semiconductor devices with nonlinear instrumental characteristics.« less
Magnetorheological response of highly filled magnetoactive elastomers from perspective of mechanical energy density: Fractal aggregates above the nanometer scale?

PubMed

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

2017-06-01

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

From Fractals to Fractional Vector Calculus: Measurement in the Correct Metric

NASA Astrophysics Data System (ADS)

Wheatcraft, S. W.; Meerschaert, M. M.; Mortensen, J.

2005-12-01

Traditional (stationary) stochastic theories have been fairly successful in reproducing transport behavior at relatively homogeneous field sites such as the Borden and Cape Code sites. However, the highly heterogeneous MADE site has produced tracer data that can not be adequately explained with traditional stochastic theories. In recent years, considerable attention has been focused on developing more sophisticated theories that can predict or reproduce the behavior of complex sites such as the MADE site. People began to realize that the model for geologic complexity may in many cases be very different than the model required for stochastic theory. Fractal approaches were useful in conceptualizing scale-invariant heterogeneity by demonstrating that scale dependant transport was just an artifact of our measurement system. Fractal media have dimensions larger than the dimension that measurement is taking place in, thus assuring the scale-dependence of parameters such as dispersivity. What was needed was a rigorous way to develop a theory that was consistent with the fractal dimension of the heterogeneity. The fractional advection-dispersion equation (FADE) was developed with this idea in mind. The second derivative in the dispersion term of the advection-dispersion equation is replaced with a fractional derivative. The order of differentiation, α, is fractional. Values of α in the range: 1 < α < 2 produce super-Fickian dispersion; in essence, the dispersion scaling is controlled by the value of α. When α = 2, the traditional advection-dispersion equation is recovered. The 1-D version of the FADE has been used successfully to back-predict tracer test behavior at several heterogeneous field sites, including the MADE site. It has been hypothesized that the order of differentiation in the FADE is equivalent to (or at least related to) the fractal dimension of the particle tracks (or geologic heterogeneity). With this way of thinking, one can think of the FADE as a governing equation written for the correct dimension, thus eliminating scale-dependent behavior. Before a generalized multi-dimensional form of the FADE can be developed, it has been necessary to develop a generalized fractional vector calculus. The authors have recently developed generalized canonical fractional forms of the gradient, divergence and curl. This fractional vector calculus will be useful in developing fractional forms of many governing equations in physics.
Fractal kinetics of radiation-induced point-defect formation and decay in amorphous insulators: Application to color centers in silica-based optical fibers

NASA Astrophysics Data System (ADS)

Griscom, David L.

2001-11-01

Formalisms have been developed to express the time evolution of bimolecular processes taking place in fractal spaces. These ``stretched-second-order'' solutions are specifically applicable to radiation-induced electron-hole pairs and/or vacancy-interstitial pairs in insulating glasses. Like the analogous Kohlrausch-type (stretched-first-order) expressions, the present solutions are functions of (kt)β, where 0<β<1, k is an effective rate coefficient, and t is time. Both the new second-order formalism and the familiar Kohlrausch approach have been used to fit experimental data (induced optical absorptions in silica-based glasses monitored at selected wavelengths) that serve as proxies for the numbers of color centers created by γ irradiation and/or destroyed by processes involving thermal, optical, or γ-ray activation. Two material systems were investigated: (1) optical fibers with Ge-doped-silica cores and (2) fibers with low-OH/low-chloride pure-silica cores. Successful fits of the growth curves for the Ge-doped-silica-core fibers at four widely separated dose rates were accomplished using solutions for color-center concentrations, N[(kt)β], which approach steady-state values, Nsat, as t-->∞. The parametrization of these fits reveals some unexpected, and potentially useful, empirical rules regarding the dose-rate dependences of β, k, and Nsat in the fractal regime (0<β<1). Similar, though possibly not identical, rules evidently apply to color centers in the pure-silica-core fibers as well. In both material systems, there appear to be fractal<==> classical phase transitions at certain threshold values of dose rate, below which the dose-rate dependencies of k and Nsat revert to those specified by classical (β=1) first- or second-order kinetics. For kt<<1, both the first- and second-order fractal kinetic growth curves become identical, i.e., N((kt)β)~Atβ, where the coefficient A depends on dose rate but not kinetic order. It is found empirically that A depends on the 3β/2 power of dose rate in both first- and second-order kinetics, thus ``accidentally'' becoming linearly proportional to dose rate in cases where β~2/3 (characteristic of random fractals and many disordered materials). If interfering dose-rate-independent components are absent, it is possible to distinguish the order of the kinetics from the shapes of the growth and decay curves in both fractal and classical regimes. However, for reasons that are discussed, the parameters that successfully fit the experimental growth curves could not be used as bases for closed-form predictions of the shapes of the decay curves recorded when the irradiation is interrupted.
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.
Passenger flow analysis of Beijing urban rail transit network using fractal approach

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2016-07-01

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

NASA Astrophysics Data System (ADS)

Fan, Rong

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

PubMed

Smirnov, Igor

2008-01-01

This article is related to the proposed hypothesis and experimental data regarding the ability of defined polar polymer compound (MRET polymer) applied to RF phones to increase the dielectric permittivity of water based solutions and to reduce the SAR (Specific Absorption Rate) values inside the "phantom head" filled with the jelly simulating muscle and brain tissues. Due to the high organizational state of fractal structures of MRET polymer compounds and the phenomenon of piezoelectricity, this polymer generates specific subtle, low frequency, non-coherent electromagnetic oscillations (optimal random field) that can affect the hydrogen lattice of the molecular structure of water and subsequently modify the electrodynamic properties of water. The increase of dielectric permittivity of water finally leads to the reduction of the absorption rate of the electromagnetic field by living tissue. The reduction of SAR values is confirmed by the research conducted in June - July of 2006 at RF Exposure Laboratory in Escondido, California. This test also confirmed that the application of MRET polymer to RF phones does not significantly affect the air measurements of RF phone signals, and subsequently does not lead to any significant distortion of transmitted RF signals.
Simple Process-Based Simulators for Generating Spatial Patterns of Habitat Loss and Fragmentation: A Review and Introduction to the G-RaFFe Model

PubMed Central

Pe'er, Guy; Zurita, Gustavo A.; Schober, Lucia; Bellocq, Maria I.; Strer, Maximilian; Müller, Michael; Pütz, Sandro

2013-01-01

Landscape simulators are widely applied in landscape ecology for generating landscape patterns. These models can be divided into two categories: pattern-based models that generate spatial patterns irrespective of the processes that shape them, and process-based models that attempt to generate patterns based on the processes that shape them. The latter often tend toward complexity in an attempt to obtain high predictive precision, but are rarely used for generic or theoretical purposes. Here we show that a simple process-based simulator can generate a variety of spatial patterns including realistic ones, typifying landscapes fragmented by anthropogenic activities. The model “G-RaFFe” generates roads and fields to reproduce the processes in which forests are converted into arable lands. For a selected level of habitat cover, three factors dominate its outcomes: the number of roads (accessibility), maximum field size (accounting for land ownership patterns), and maximum field disconnection (which enables field to be detached from roads). We compared the performance of G-RaFFe to three other models: Simmap (neutral model), Qrule (fractal-based) and Dinamica EGO (with 4 model versions differing in complexity). A PCA-based analysis indicated G-RaFFe and Dinamica version 4 (most complex) to perform best in matching realistic spatial patterns, but an alternative analysis which considers model variability identified G-RaFFe and Qrule as performing best. We also found model performance to be affected by habitat cover and the actual land-uses, the latter reflecting on land ownership patterns. We suggest that simple process-based generators such as G-RaFFe can be used to generate spatial patterns as templates for theoretical analyses, as well as for gaining better understanding of the relation between spatial processes and patterns. We suggest caution in applying neutral or fractal-based approaches, since spatial patterns that typify anthropogenic landscapes are often non-fractal in nature. PMID:23724108
Simple process-based simulators for generating spatial patterns of habitat loss and fragmentation: a review and introduction to the G-RaFFe model.

PubMed

Pe'er, Guy; Zurita, Gustavo A; Schober, Lucia; Bellocq, Maria I; Strer, Maximilian; Müller, Michael; Pütz, Sandro

2013-01-01

Landscape simulators are widely applied in landscape ecology for generating landscape patterns. These models can be divided into two categories: pattern-based models that generate spatial patterns irrespective of the processes that shape them, and process-based models that attempt to generate patterns based on the processes that shape them. The latter often tend toward complexity in an attempt to obtain high predictive precision, but are rarely used for generic or theoretical purposes. Here we show that a simple process-based simulator can generate a variety of spatial patterns including realistic ones, typifying landscapes fragmented by anthropogenic activities. The model "G-RaFFe" generates roads and fields to reproduce the processes in which forests are converted into arable lands. For a selected level of habitat cover, three factors dominate its outcomes: the number of roads (accessibility), maximum field size (accounting for land ownership patterns), and maximum field disconnection (which enables field to be detached from roads). We compared the performance of G-RaFFe to three other models: Simmap (neutral model), Qrule (fractal-based) and Dinamica EGO (with 4 model versions differing in complexity). A PCA-based analysis indicated G-RaFFe and Dinamica version 4 (most complex) to perform best in matching realistic spatial patterns, but an alternative analysis which considers model variability identified G-RaFFe and Qrule as performing best. We also found model performance to be affected by habitat cover and the actual land-uses, the latter reflecting on land ownership patterns. We suggest that simple process-based generators such as G-RaFFe can be used to generate spatial patterns as templates for theoretical analyses, as well as for gaining better understanding of the relation between spatial processes and patterns. We suggest caution in applying neutral or fractal-based approaches, since spatial patterns that typify anthropogenic landscapes are often non-fractal in nature.
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.
Advances in fractal germanium micro/nanoclusters induced by gold: microstructures and properties.

PubMed

Chen, Zhiwen; Shek, Chan-Hung; Wu, C M Lawrence; Lai, Joseph K L

2014-02-01

Germanium materials are a class of unique semiconductor materials with widespread technological applications because of their valuable semiconducting, electrical, optical, and thermoelectric power properties in the fields of macro/mesoscopic materials and micro/nanodevices. In this review, we describe the efforts toward understanding the microstructures and various properties of the fractal germanium micro/nanoclusters induced by gold prepared by high vacuum thermal evaporation techniques, highlighting contributions from our laboratory. First, we present the integer and non-integer dimensional germanium micro/nanoclusters such as nanoparticles, nanorings, and nanofractals induced by gold and annealing. In particular, the nonlinear electrical behavior of a gold/germanium bilayer film with the interesting nanofractal is discussed in detail. In addition, the third-order optical nonlinearities of the fractal germanium nanocrystals embedded in gold matrix will be summarized by using the sensitive and reliable Z-scan techniques aimed to determine the nonlinear absorption coefficient and nonlinear refractive index. Finally, we emphasize the thermoelectric power properties of the gold/germanium bilayer films. The thermoelectric power measurement is considered to be a more effective method than the conductivity for investigating superlocalization in a percolating system. This research may provide a novel insight to modulate their competent performance and promote rational design of micro/nanodevices. Once mastered, germanium thin films with a variety of fascinating micro/nanoclusters will offer vast and unforeseen opportunities in the semiconductor industry as well as in other fields of science and technology.
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
Initial Dynamical Evolution of Star Clusters with Tidal Field

NASA Astrophysics Data System (ADS)

Park, So-Myoung; Goodwin, Simon P.; Kim, Sungsoo S.

2017-03-01

Observations have been suggested that star clusters could form from the rapid collapse and violent relaxation of substructured distributions. We investigate the collapse of fractal stellar distributions in no, weak, and very strong tidal fields. We find that the rapid collapse of substructure into spherical clusters happens quickly with no or a weak tidal field, but very strong tidal fields prevent a cluster forming. However, we also find that dense Plummer spheres are also rapidly destroyed in strong tidal fields. We suggest that this is why the low-mass star clusters cannot survive near the galactic centre which has strong tidal field.
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.

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.
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.
Surface Modeling to Support Small-Body Spacecraft Exploration and Proximity Operations

NASA Technical Reports Server (NTRS)

Riedel, Joseph E.; Mastrodemos, Nickolaos; Gaskell, Robert W.

2011-01-01

In order to simulate physically plausible surfaces that represent geologically evolved surfaces, demonstrating demanding surface-relative guidance navigation and control (GN&C) actions, such surfaces must be made to mimic the geological processes themselves. A report describes how, using software and algorithms to model body surfaces as a series of digital terrain maps, a series of processes was put in place that evolve the surface from some assumed nominal starting condition. The physical processes modeled in this algorithmic technique include fractal regolith substrate texturing, fractally textured rocks (of empirically derived size and distribution power laws), cratering, and regolith migration under potential energy gradient. Starting with a global model that may be determined observationally or created ad hoc, the surface evolution is begun. First, material of some assumed strength is layered on the global model in a fractally random pattern. Then, rocks are distributed according to power laws measured on the Moon. Cratering then takes place in a temporal fashion, including modeling of ejecta blankets and taking into account the gravity of the object (which determines how much of the ejecta blanket falls back to the surface), and causing the observed phenomena of older craters being progressively buried by the ejecta of earlier impacts. Finally, regolith migration occurs which stratifies finer materials from coarser, as the fine material progressively migrates to regions of lower potential energy.
Altered fractal dynamics of gait: reduced stride-interval correlations with aging and Huntington's disease

NASA Technical Reports Server (NTRS)

Hausdorff, J. M.; Mitchell, S. L.; Firtion, R.; Peng, C. K.; Cudkowicz, M. E.; Wei, J. Y.; Goldberger, A. L.

1997-01-01

Fluctuations in the duration of the gait cycle (the stride interval) display fractal dynamics and long-range correlations in healthy young adults. We hypothesized that these stride-interval correlations would be altered by changes in neurological function associated with aging and certain disease states. To test this hypothesis, we compared the stride-interval time series of 1) healthy elderly subjects and young controls and of 2) subjects with Huntington's disease and healthy controls. Using detrended fluctuation analysis we computed alpha, a measure of the degree to which one stride interval is correlated with previous and subsequent intervals over different time scales. The scaling exponent alpha was significantly lower in elderly subjects compared with young subjects (elderly: 0.68 +/- 0.14; young: 0.87 +/- 0.15; P < 0.003). The scaling exponent alpha was also smaller in the subjects with Huntington's disease compared with disease-free controls (Huntington's disease: 0.60 +/- 0.24; controls: 0.88 +/-0.17; P < 0.005). Moreover, alpha was linearly related to degree of functional impairment in subjects with Huntington's disease (r = 0.78, P < 0.0005). These findings demonstrate that strike-interval fluctuations are more random (i.e., less correlated) in elderly subjects and in subjects with Huntington's disease. Abnormal alterations in the fractal properties of gait dynamics are apparently associated with changes in central nervous system control.
Stress resistance strategy in an arid land shrub: interactions between developmental instability and fractal dimention

USGS Publications Warehouse

Escos, J.; Alados, C.L.; Pugnaire, F. I.; Puigdefábregas, J.; Emlen, J.

2000-01-01

This paper investigates allocation of energy to mechanisms that generate and preserve architectural forms (i.e. developmental stability, complexity of branching patterns) and productivity (growth and reproduction) in response to environmental disturbances (i.e. grazing and resource availability). The statistical error in translational symmetry was used to detect random intra-individual variability during development. This can be thought of as a measure of developmental instability caused by stress. Additionally, we use changes in fractal complexity and shoot distribution of branch structures as an alternate indicator of stress. These methods were applied to Anthyllis cytisoides L., a semi-arid environment shrub, to ascertain the effect of grazing and slope exposure on developmental traits in a 2×2 factorial design. The results show that A. cytisoidesmaintains developmental stability at the expense of productivity. Anthyllis cytisoides was developmentally more stable when grazed and when on south-facing, as opposed to north-facing slopes. On the contrary, shoot length, leaf area, fractal dimension and reproductive-to-vegetative allocation ratio were larger in north- than in south-facing slopes. As a consequence, under extreme xeric conditions, shrub mortality increased in north-facing slopes, especially when not grazed. The removal of transpiring area and the reduction of plant competition favoured developmental stability and survival in grazed plants. Differences between grazed and ungrazed plants were most evident in more mesic (north-facing) areas.
Memory matters: influence from a cognitive map on animal space use.

PubMed

Gautestad, Arild O

2011-10-21

A vertebrate individual's cognitive map provides a capacity for site fidelity and long-distance returns to favorable patches. Fractal-geometrical analysis of individual space use based on collection of telemetry fixes makes it possible to verify the influence of a cognitive map on the spatial scatter of habitat use and also to what extent space use has been of a scale-specific versus a scale-free kind. This approach rests on a statistical mechanical level of system abstraction, where micro-scale details of behavioral interactions are coarse-grained to macro-scale observables like the fractal dimension of space use. In this manner, the magnitude of the fractal dimension becomes a proxy variable for distinguishing between main classes of habitat exploration and site fidelity, like memory-less (Markovian) Brownian motion and Levy walk and memory-enhanced space use like Multi-scaled Random Walk (MRW). In this paper previous analyses are extended by exploring MRW simulations under three scenarios: (1) central place foraging, (2) behavioral adaptation to resource depletion (avoidance of latest visited locations) and (3) transition from MRW towards Levy walk by narrowing memory capacity to a trailing time window. A generalized statistical-mechanical theory with the power to model cognitive map influence on individual space use will be important for statistical analyses of animal habitat preferences and the mechanics behind site fidelity and home ranges. Copyright © 2011 Elsevier Ltd. All rights reserved.
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.
Analysis of Fractional Flow for Transient Two-Phase Flow in Fractal Porous Medium

NASA Astrophysics Data System (ADS)

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

2016-03-01

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

PubMed

Zhonggang, Liang; Hong, Yan

2006-10-01

A new method of calculating fractal dimension of short-term heart rate variability signals is presented. The method is based on wavelet transform and filter banks. The implementation of the method is: First of all we pick-up the fractal component from HRV signals using wavelet transform. Next, we estimate the power spectrum distribution of fractal component using auto-regressive model, and we estimate parameter 7 using the least square method. Finally according to formula D = 2- (gamma-1)/2 estimate fractal dimension of HRV signal. To validate the stability and reliability of the proposed method, using fractional brown movement simulate 24 fractal signals that fractal value is 1.6 to validate, the result shows that the method has stability and reliability.
Making rainfall features fun: scientific activities for teaching children aged 5-12 years

NASA Astrophysics Data System (ADS)

Gires, Auguste; Muller, Catherine L.; le Gueut, Marie-Agathe; Schertzer, Daniel

2016-05-01

Research projects now rely on an array of different channels to increase impact, including high-level scientific output, tools, and equipment, but also communication, outreach, and educational activities. This paper focuses on education for children aged 5-12 years and presents activities that aim to help them (and their teachers) grasp some of the complex underlying issues in environmental science. More generally, it helps children to become familiarized with science and scientists, with the aim to enhance scientific culture and promote careers in this field. The activities developed are focused on rainfall: (a) designing and using a disdrometer to observe the variety of drop sizes; (b) careful recording of successive dry and rainy days and reproducing patterns using a simple model based on fractal random multiplicative cascades; and (c) collaboratively writing a children's book about rainfall. These activities are discussed in the context of current state-of-the-art pedagogical practices and goals set by project funders, especially in a European Union framework.
Fractional Langevin Equation Model for Characterization of Anomalous Brownian Motion from NMR Signals

NASA Astrophysics Data System (ADS)

Lisý, Vladimír; Tóthová, Jana

2018-02-01

Nuclear magnetic resonance is often used to study random motion of spins in different systems. In the long-time limit the current mathematical description of the experiments allows proper interpretation of measurements of normal and anomalous diffusion. The shorter-time dynamics is however correctly considered only in a few works that do not go beyond the standard Langevin theory of the Brownian motion (BM). In the present work, the attenuation function S (t) for an ensemble of spins in a magnetic-field gradient, expressed in a form applicable for any kind of stationary stochastic dynamics of spins with or without a memory, is calculated in the frame of the model of fractional BM. The solution of the model for particles trapped in a harmonic potential is obtained in a simple way and used for the calculation of S (t). In the limit of free particles coupled to a fractal heat bath, the results compare favorably with experiments acquired in human neuronal tissues.
New Metrics from a Fractional Gravitational Field

NASA Astrophysics Data System (ADS)

El-Nabulsi, Rami Ahmad

2017-09-01

Agop et al. proved in Commun. Theor. Phys. (2008) that, a Reissner-Nordstrom type metric is obtained, if gauge gravitational field in a fractal spacetime is constructed by means of concepts of scale relativity. We prove in this short communication that similar result is obtained if gravity in D-spacetime dimensions is fractionalized by means of the Glaeske-Kilbas-Saigo fractional. Besides, non-singular gravitational fields are obtained without using extra-dimensions. We present few examples to show that these gravitational fields hold a number of motivating features in spacetime physics.
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.
Improvements in RF Shimming in High Field MRI Using High Permittivity Materials With Low Order Pre-Fractal Geometries.

PubMed

Schmidt, Rita; Webb, Andrew

2016-08-01

Ultra-high field MRI is an area of great interest for clinical research and basic science due to the increased signal-to-noise, spatial resolution and magnetic-susceptibility-based contrast. However, the fact that the electromagnetic wavelength in tissue is comparable to the relevant body dimensions means that the uniformity of the excitation field is much poorer than at lower field strengths. In addition to techniques such as transmit arrays, one simple but effective method to counteract this effect is to use high permittivity "pads". Very high permittivities enable thinner, flexible pads to be used, but the limiting factor is wavelength effects within the pads themselves, which can lead to image artifacts. So far, all studies have used simple continuous rectangular/circular pad geometries. In this work we investigate how the wavelength effects can be partially mitigated utilizing shaped pad with holes. Several arrangements have been simulated, including low order pre-fractal geometries, which maintain the overall coverage of the pad, but can provide better image homogeneity in the region of interest or higher sensitivity depending on the setup. Experimental data in the form of in vivo human images at 7T were acquired to validate the simulation results.
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.
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.…
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.
Fractal boundary basins in spherically symmetric ϕ4 theory

NASA Astrophysics Data System (ADS)

Honda, Ethan

2010-07-01

Results are presented from numerical simulations of the flat-space nonlinear Klein-Gordon equation with an asymmetric double-well potential in spherical symmetry. Exit criteria are defined for the simulations that are used to help understand the boundaries of the basins of attraction for Gaussian “bubble” initial data. The first exit criterion, based on the immediate collapse or expansion of bubble radius, is used to observe the departure of the scalar field from a static intermediate attractor solution. The boundary separating these two behaviors in parameter space is smooth and demonstrates a time-scaling law with an exponent that depends on the asymmetry of the potential. The second exit criterion differentiates between the creation of an expanding true-vacuum bubble and dispersion of the field leaving the false vacuum; the boundary separating these basins of attraction is shown to demonstrate fractal behavior. The basins are defined by the number of bounces that the field undergoes before inducing a phase transition. A third, hybrid exit criterion is used to determine the location of the boundary to arbitrary precision and to characterize the threshold behavior. The possible effects this behavior might have on cosmological phase transitions are briefly discussed.
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.
Interplay of Determinism and Randomness: From Irreversibility to Chaos, Fractals, and Stochasticity

NASA Astrophysics Data System (ADS)

Tsonis, A.

2017-12-01

We will start our discussion into randomness by looking exclusively at our formal mathematical system to show that even in this pure and strictly logical system one cannot do away with randomness. By employing simple mathematical models, we will identify the three possible sources of randomness: randomness due to inability to find the rules (irreversibility), randomness due to inability to have infinite power (chaos), and randomness due to stochastic processes. Subsequently we will move from the mathematical system to our physical world to show that randomness, through the quantum mechanical character of small scales, through chaos, and because of the second law of thermodynamics, is an intrinsic property of nature as well. We will subsequently argue that the randomness in the physical world is consistent with the three sources of randomness suggested from the study of simple mathematical systems. Many examples ranging from purely mathematical to natural processes will be presented, which clearly demonstrate how the combination of rules and randomness produces the world we live in. Finally, the principle of least effort or the principle of minimum energy consumption will be suggested as the underlying principle behind this symbiosis between determinism and randomness.
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.
Global mean first-passage times of random walks on complex networks.

PubMed

Tejedor, V; Bénichou, O; Voituriez, R

2009-12-01

We present a general framework, applicable to a broad class of random walks on complex networks, which provides a rigorous lower bound for the mean first-passage time of a random walker to a target site averaged over its starting position, the so-called global mean first-passage time (GMFPT). This bound is simply expressed in terms of the equilibrium distribution at the target and implies a minimal scaling of the GMFPT with the network size. We show that this minimal scaling, which can be arbitrarily slow, is realized under the simple condition that the random walk is transient at the target site and independently of the small-world, scale-free, or fractal properties of the network. Last, we put forward that the GMFPT to a specific target is not a representative property of the network since the target averaged GMFPT satisfies much more restrictive bounds.
A new way of describing meiosis that uses fractal dimension to predict metaphase I

PubMed Central

2005-01-01

Meiosis, the reductive nuclear division, is a continuum, but for purposes of communication, is described in stages. In sexually-reproducing organisms, including the dwarf mistletoe Arceuthobium americanum, prophase I of meiosis is prolonged (8 months for female A. americanum). Conversely, metaphase I, where chromosome pairs line up along a dividing cell's "equator", is relatively brief, difficult to predict, but critical regarding the random distribution of the paternal and maternal chromosomes in sexual organisms. However, descriptions of meiosis as either a continuum or stages are limited to qualitative observations. A quantification of meiosis can provide mathematical descriptors and allow for the prediction of when chromosomes reach the equator; this will not only be useful to researchers of cell division, but also to those requiring a large sample of metaphase I materials. Here, the probability-density function was used to calculate the fractal dimension of A. americanum nuclei undergoing early meiosis, and it predicted the onset of metaphase I by 2 days. PMID:16094465
Bohman-Frieze-Wormald model on the lattice, yielding a discontinuous percolation transition

NASA Astrophysics Data System (ADS)

Schrenk, K. J.; Felder, A.; Deflorin, S.; Araújo, N. A. M.; D'Souza, R. M.; Herrmann, H. J.

2012-03-01

The BFW model introduced by Bohman, Frieze, and Wormald [Random Struct. Algorithms1042-983210.1002/rsa.20038, 25, 432 (2004)], and recently investigated in the framework of discontinuous percolation by Chen and D'Souza [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.106.115701 106, 115701 (2011)], is studied on the square and simple-cubic lattices. In two and three dimensions, we find numerical evidence for a strongly discontinuous transition. In two dimensions, the clusters at the threshold are compact with a fractal surface of fractal dimension df=1.49±0.02. On the simple-cubic lattice, distinct jumps in the size of the largest cluster are observed. We proceed to analyze the tree-like version of the model, where only merging bonds are sampled, for dimension two to seven. The transition is again discontinuous in any considered dimension. Finally, the dependence of the cluster-size distribution at the threshold on the spatial dimension is also investigated.
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
Template-Directed Copolymerization, Random Walks along Disordered Tracks, and Fractals

NASA Astrophysics Data System (ADS)

Gaspard, Pierre

2016-12-01

In biology, template-directed copolymerization is the fundamental mechanism responsible for the synthesis of DNA, RNA, and proteins. More than 50 years have passed since the discovery of DNA structure and its role in coding genetic information. Yet, the kinetics and thermodynamics of information processing in DNA replication, transcription, and translation remain poorly understood. Challenging issues are the facts that DNA or RNA sequences constitute disordered media for the motion of polymerases or ribosomes while errors occur in copying the template. Here, it is shown that these issues can be addressed and sequence heterogeneity effects can be quantitatively understood within a framework revealing universal aspects of information processing at the molecular scale. In steady growth regimes, the local velocities of polymerases or ribosomes along the template are distributed as the continuous or fractal invariant set of a so-called iterated function system, which determines the copying error probabilities. The growth may become sublinear in time with a scaling exponent that can also be deduced from the iterated function system.
Culturomics meets random fractal theory: insights into long-range correlations of social and natural phenomena over the past two centuries

PubMed Central

Gao, Jianbo; Hu, Jing; Mao, Xiang; Perc, Matjaž

2012-01-01

Culturomics was recently introduced as the application of high-throughput data collection and analysis to the study of human culture. Here, we make use of these data by investigating fluctuations in yearly usage frequencies of specific words that describe social and natural phenomena, as derived from books that were published over the course of the past two centuries. We show that the determination of the Hurst parameter by means of fractal analysis provides fundamental insights into the nature of long-range correlations contained in the culturomic trajectories, and by doing so offers new interpretations as to what might be the main driving forces behind the examined phenomena. Quite remarkably, we find that social and natural phenomena are governed by fundamentally different processes. While natural phenomena have properties that are typical for processes with persistent long-range correlations, social phenomena are better described as non-stationary, on–off intermittent or Lévy walk processes. PMID:22337632
[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.

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.
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.
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.
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.
Active Region Photospheric Magnetic Properties Derived from Line-of-Sight and Radial Fields

NASA Astrophysics Data System (ADS)

Guerra, J. A.; Park, S.-H.; Gallagher, P. T.; Kontogiannis, I.; Georgoulis, M. K.; Bloomfield, D. S.

2018-01-01

The effect of using two representations of the normal-to-surface magnetic field to calculate photospheric measures that are related to the active region (AR) potential for flaring is presented. Several AR properties were computed using line-of-sight (B_{los}) and spherical-radial (Br) magnetograms from the Space-weather HMI Active Region Patch (SHARP) products of the Solar Dynamics Observatory, characterizing the presence and features of magnetic polarity inversion lines, fractality, and magnetic connectivity of the AR photospheric field. The data analyzed correspond to {≈ }4{,}000 AR observations, achieved by randomly selecting 25% of days between September 2012 and May 2016 for analysis at 6-hr cadence. Results from this statistical study include: i) the Br component results in a slight upwards shift of property values in a manner consistent with a field-strength underestimation by the B_{los} component; ii) using the Br component results in significantly lower inter-property correlation in one-third of the cases, implying more independent information as regards the state of the AR photospheric magnetic field; iii) flaring rates for each property vary between the field components in a manner consistent with the differences in property-value ranges resulting from the components; iv) flaring rates generally increase for higher values of properties, except the Fourier spectral power index that has flare rates peaking around a value of 5/3. These findings indicate that there may be advantages in using Br rather than B_{los} in calculating flare-related AR magnetic properties, especially for regions located far from central meridian.
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 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".
The Sun-Earth connect 2: Modelling patterns of a fractal Sun in time and space using the fine structure constant

NASA Astrophysics Data System (ADS)

Baker, Robert G. V.

2017-02-01

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

PubMed

Churchill, Nathan W; Spring, Robyn; Grady, Cheryl; Cimprich, Bernadine; Askren, Mary K; Reuter-Lorenz, Patricia A; Jung, Mi Sook; Peltier, Scott; Strother, Stephen C; Berman, Marc G

2016-08-08

There is growing evidence that fluctuations in brain activity may exhibit scale-free ("fractal") dynamics. Scale-free signals follow a spectral-power curve of the form P(f ) ∝ f(-β), where spectral power decreases in a power-law fashion with increasing frequency. In this study, we demonstrated that fractal scaling of BOLD fMRI signal is consistently suppressed for different sources of cognitive effort. Decreases in the Hurst exponent (H), which quantifies scale-free signal, was related to three different sources of cognitive effort/task engagement: 1) task difficulty, 2) task novelty, and 3) aging effects. These results were consistently observed across multiple datasets and task paradigms. We also demonstrated that estimates of H are robust across a range of time-window sizes. H was also compared to alternative metrics of BOLD variability (SDBOLD) and global connectivity (Gconn), with effort-related decreases in H producing similar decreases in SDBOLD and Gconn. These results indicate a potential global brain phenomenon that unites research from different fields and indicates that fractal scaling may be a highly sensitive metric for indexing cognitive effort/task engagement.
Renormalization Analysis of a Composite Ultrasonic Transducer with a Fractal Architecture

NASA Astrophysics Data System (ADS)

Algehyne, Ebrahem A.; Mulholland, Anthony J.

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

PubMed

Ming, Hai; Tang, Lin; Sun, Xiaohong; Zhang, Jiangying; Wang, Pei; Lu, Yonghua; Bai, Ming; Guo, Yang; Xie, Aifang; Zhang, Zebo

2004-01-01

This article summarizes the near-field optical technique applied for investigating the characteristics of polymer fiber and waveguide structures. The near-field optical technique is used to analyze multimode interference structures of fiber. The localized fluctuation of the transmission caused by fractal cluster is carried out in Nd3+- and Eu3+-doped polymer fiber and film by means of a scanning near-field optical microscopy. The near-field optical spectrum of Nd3+-doped polymer fiber is investigated. The topography and near-field intensity images of Azo-polymer liquid crystal film for waveguide are obtained simultaneously.
Novel Test Fixture for Characterizing Microcontacts: Performance and Reliability

DTIC Science & Technology

2013-03-01

limited to the resolution of the measuring instrument [30]. A fractal method, on the other hand, random surface texture is characterized by scale...areas and allows the exposed 1805 to be developed away (f). After the 1805 is developed, the exposed SF-11 is subjected to deep ultra violet light (DUV...separated by a combination of fracture and plasticity [78]. Gold exhibited ductile behavior at both T=150K and T=300K [78, 80]. The difference in
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.
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.

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

NASA Astrophysics Data System (ADS)

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

2013-12-01

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

PubMed

Cai, Xiang; Shen, Liguo; Zhang, Meijia; Chen, Jianrong; Hong, Huachang; Lin, Hongjun

2017-11-01

Quantitatively evaluating interaction energy between two randomly rough surfaces is the prerequisite to quantitatively understand and control membrane fouling in membrane bioreactors (MBRs). In this study, a new unified approach to construct rough topographies and to quantify interaction energy between a randomly rough particle and a randomly rough membrane was proposed. It was found that, natural rough topographies of both foulants and membrane could be well constructed by a modified two-variable Weierstrass-Mandelbrot (WM) function included in fractal theory. Spatial differential relationships between two constructed surfaces were accordingly established. Thereafter, a new approach combining these relationships, surface element integration (SEI) approach and composite Simpson's rule was deduced to calculate the interaction energy between two randomly rough surfaces in a submerged MBR. The obtained results indicate the profound effects of surface morphology on interaction energy and membrane fouling. This study provided a basic approach to investigate membrane fouling and interface behaviors. Copyright © 2017 Elsevier Ltd. All rights reserved.
Schramm-Loewner evolution of the accessible perimeter of isoheight lines of correlated landscapes

NASA Astrophysics Data System (ADS)

Posé, N.; Schrenk, K. J.; Araújo, N. A. M.; Herrmann, H. J.

Real landscapes exhibit long-range height-height correlations, which are quantified by the Hurst exponent H. We give evidence that for negative H, in spite of the long-range nature of correlations, the statistics of the accessible perimeter of isoheight lines is compatible with Schramm-Loewner evolution curves and therefore can be mapped to random walks, their fractal dimension determining the diffusion constant. Analytic results are recovered for H=-1 and H=0 and a conjecture is proposed for the values in between. By contrast, for positive H, we find that the random walk is not Markovian but strongly correlated in time. Theoretical and practical implications are discussed.
Discrete angle radiative transfer. 3. Numerical results and meteorological applications

NASA Astrophysics Data System (ADS)

Davis, Anthony; Gabriel, Philip; Lovejoy, Shuan; Schertzer, Daniel; Austin, Geoffrey L.

1990-07-01

In the first two installments of this series, various cloud models were studied with angularly discretized versions of radiative transfer. This simplification allows the effects of cloud inhomogeneity to be studied in some detail. The families of scattering media investigated were those whose members are related to each other by scale changing operations that involve only ratios of their sizes (``scaling'' geometries). In part 1 it was argued that, in the case of conservative scattering, the reflection and transmission coefficients of these families should vary algebraically with cloud size in the asymptotically thick regime, thus allowing us to define scaling exponents and corresponding ``universality'' classes. In part 2 this was further justified (by using analytical renormalization methods) for homogeneous clouds in one, two, and three spatial dimensions (i.e., slabs, squares, or triangles and cubes, respectively) as well as for a simple deterministic fractal cloud. Here the same systems are studied numerically. The results confirm (1) that renormalization is qualitatively correct (while quantitatively poor), and (2) more importantly, they support the conjecture that the universality classes of discrete and continuous angle radiative transfer are generally identical. Additional numerical results are obtained for a simple class of scale invariant (fractal) clouds that arises when modeling the concentration of cloud liquid water into ever smaller regions by advection in turbulent cascades. These so-called random ``β models'' are (also) characterized by a single fractal dimension. Both open and cyclical horizontal boundary conditions are considered. These and previous results are constrasted with plane-parallel predictions, and measures of systematic error are defined as ``packing factors'' which are found to diverge algebraically with average optical thickness and are significant even when the scaling behavior is very limited in range. Several meteorological consequences, especially concerning the ``albedo paradox'' and global climate models, are discussed, and future directions of investigation are outlined. Throughout this series it is shown that spatial variability of the optical density field (i.e., cloud geometry) determines the exponent of optical thickness (hence universality class), whereas changes in phase function can only affect the multiplicative prefactors. It is therefore argued that much more emphasis should be placed on modeling spatial inhomogeneity and investigating its radiative signature, even if this implies crude treatment of the angular aspect of the radiative transfer problem.
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.
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 continuum model for tracer transport in a porous medium.

PubMed

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

2013-12-01

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

NASA Astrophysics Data System (ADS)

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

2016-05-01

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

NASA Astrophysics Data System (ADS)

Atangana, Abdon; Jain, Sonal

2018-02-01

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

PubMed Central

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

2013-01-01

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

PubMed Central

Taylor, Richard P.; Spehar, Branka; Van Donkelaar, Paul; Hagerhall, Caroline M.

2011-01-01

Fractals have been very successful in quantifying the visual complexity exhibited by many natural patterns, and have captured the imagination of scientists and artists alike. Our research has shown that the poured patterns of the American abstract painter Jackson Pollock are also fractal. This discovery raises an intriguing possibility – are the visual characteristics of fractals responsible for the long-term appeal of Pollock's work? To address this question, we have conducted 10 years of scientific investigation of human response to fractals and here we present, for the first time, a review of this research that examines the inter-relationship between the various results. The investigations include eye tracking, visual preference, skin conductance, and EEG measurement techniques. We discuss the artistic implications of the positive perceptual and physiological responses to fractal patterns. PMID:21734876
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.
Scaling the Fractal Plain: Towards a General View of Knowledge Management

ERIC Educational Resources Information Center

Griffiths, David; Evans, Peter

2011-01-01

Purpose: The purpose of the paper is to explore coherence across key disciplines of knowledge management (KM) for a general model as a way to address performance dissatisfaction in the field. Design/methodology/approach: Research employed an evidence-based meta-analysis (287 aspects of literature), triangulated through an exploratory survey (91…
Polarization-phase tomography of biological fluids polycrystalline structure

NASA Astrophysics Data System (ADS)

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

2013-12-01

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

NASA Astrophysics Data System (ADS)

Rocha, Rodrigo P.; Figueiredo, Wagner; Suweis, Samir; Maritan, Amos

2016-10-01

In this work we study the likelihood of survival of single-species in the context of hostile and disordered environments. Population dynamics in this environment, as modeled by the Fisher equation, is characterized by negative average growth rate, except in some random spatially distributed patches that may support life. In particular, we are interested in the phase diagram of the survival probability and in the critical size problem, i.e., the minimum patch size required for surviving in the long-time dynamics. We propose a measure for the critical patch size as being proportional to the participation ratio of the eigenvector corresponding to the largest eigenvalue of the linearized Fisher dynamics. We obtain the (extinction-survival) phase diagram and the probability distribution function (PDF) of the critical patch sizes for two topologies, namely, the one-dimensional system and the fractal Peano basin. We show that both topologies share the same qualitative features, but the fractal topology requires higher spatial fluctuations to guarantee species survival. We perform a finite-size scaling and we obtain the associated scaling exponents. In addition, we show that the PDF of the critical patch sizes has an universal shape for the 1D case in terms of the model parameters (diffusion, growth rate, etc.). In contrast, the diffusion coefficient has a drastic effect on the PDF of the critical patch sizes of the fractal Peano basin, and it does not obey the same scaling law of the 1D case.
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.
Fractal lacunarity of trabecular bone and magnetic resonance imaging: New perspectives for osteoporotic fracture risk assessment

PubMed Central

Zaia, Annamaria

2015-01-01

Osteoporosis represents one major health condition for our growing elderly population. It accounts for severe morbidity and increased mortality in postmenopausal women and it is becoming an emerging health concern even in aging men. Screening of the population at risk for bone degeneration and treatment assessment of osteoporotic patients to prevent bone fragility fractures represent useful tools to improve quality of life in the elderly and to lighten the related socio-economic impact. Bone mineral density (BMD) estimate by means of dual-energy X-ray absorptiometry is normally used in clinical practice for osteoporosis diagnosis. Nevertheless, BMD alone does not represent a good predictor of fracture risk. From a clinical point of view, bone microarchitecture seems to be an intriguing aspect to characterize bone alteration patterns in aging and pathology. The widening into clinical practice of medical imaging techniques and the impressive advances in information technologies together with enhanced capacity of power calculation have promoted proliferation of new methods to assess changes of trabecular bone architecture (TBA) during aging and osteoporosis. Magnetic resonance imaging (MRI) has recently arisen as a useful tool to measure bone structure in vivo. In particular, high-resolution MRI techniques have introduced new perspectives for TBA characterization by non-invasive non-ionizing methods. However, texture analysis methods have not found favor with clinicians as they produce quite a few parameters whose interpretation is difficult. The introduction in biomedical field of paradigms, such as theory of complexity, chaos, and fractals, suggests new approaches and provides innovative tools to develop computerized methods that, by producing a limited number of parameters sensitive to pathology onset and progression, would speed up their application into clinical practice. Complexity of living beings and fractality of several physio-anatomic structures suggest fractal analysis as a promising approach to quantify morpho-functional changes in both aging and pathology. In this particular context, fractal lacunarity seems to be the proper tool to characterize TBA texture as it is able to describe both discontinuity of bone network and sizes of bone marrow spaces, whose changes are an index of bone fracture risk. In this paper, an original method of MRI texture analysis, based on TBA fractal lacunarity is described and discussed in the light of new perspectives for early diagnosis of osteoporotic fractures. PMID:25793162
Diffusion, subdiffusion, and localization of active colloids in random post lattices

NASA Astrophysics Data System (ADS)

Morin, Alexandre; Lopes Cardozo, David; Chikkadi, Vijayakumar; Bartolo, Denis

2017-10-01

Combining experiments and theory, we address the dynamics of self-propelled particles in crowded environments. We first demonstrate that motile colloids cruising at constant speed through random lattices undergo a smooth transition from diffusive to subdiffusive to localized dynamics upon increasing the obstacle density. We then elucidate the nature of these transitions by performing extensive simulations constructed from a detailed analysis of the colloid-obstacle interactions. We evidence that repulsion at a distance and hard-core interactions both contribute to slowing down the long-time diffusion of the colloids. In contrast, the localization transition stems solely from excluded-volume interactions and occurs at the void-percolation threshold. Within this critical scenario, equivalent to that of the random Lorentz gas, genuine asymptotic subdiffusion is found only at the critical density where the motile particles explore a fractal maze.
A Stochastic Approach For Extending The Dimensionality Of Observed Datasets

NASA Technical Reports Server (NTRS)

Varnai, Tamas

2002-01-01

This paper addresses the problem that in many cases, observations cannot provide complete fields of the measured quantities, because they yield data only along a single cross-section through the examined fields. The paper describes a new Fourier-adjustment technique that allows existing fractal models to build realistic surroundings to the measured cross-sections. This new approach allows more representative calculations of cloud radiative processes and may be used in other areas as well.
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.
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.
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.
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.
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.
Phase ordering in disordered and inhomogeneous systems

NASA Astrophysics Data System (ADS)

Corberi, Federico; Zannetti, Marco; Lippiello, Eugenio; Burioni, Raffaella; Vezzani, Alessandro

2015-06-01

We study numerically the coarsening dynamics of the Ising model on a regular lattice with random bonds and on deterministic fractal substrates. We propose a unifying interpretation of the phase-ordering processes based on two classes of dynamical behaviors characterized by different growth laws of the ordered domain size, namely logarithmic or power law, respectively. It is conjectured that the interplay between these dynamical classes is regulated by the same topological feature that governs the presence or the absence of a finite-temperature phase transition.
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
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.
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.
Scaling Laws in Turbulence: Their Manifestation and Utility.

NASA Astrophysics Data System (ADS)

Juneja, Anurag

1995-01-01

It has long been hypothesized that small-scale features in turbulence possess some form of scale-invariance leading to several interesting predictions about related flow quantities. In the present work, we examine the scaling features and scaling exponents of various quantities in turbulence and the relationship they bear to Kolmogorov and multifractal scaling theories. A related goal (which is the inverse problem) is to synthesize stochastic fields which faithfully reproduce the observed scaling features of velocity fluctuations in high-Reynolds-number turbulence. First, we obtain, for structure functions of arbitrary order, an expression which is uniformly valid for the inertial and dissipation range. This enables a more definitive determination of scaling exponents than has been possible in the past. Next, we examine the scaling properties of circulation around contours of various sizes, as it is suggested that a better way to study the small-scale features might be to focus on the vortical component of the velocity field. We then utilize a quantity called the cancellation exponent to characterize the singular nature of vorticity fluctuations, whose trace exhibits an oscillation in sign on arbitrary fine scales. We note that the inter-relationships which can be established among the aforementioned scaling exponents for velocity structure functions, circulation and vorticity provide support for the multifractal formalism of turbulence. Next, we examine the fractal structure of self -affine time series data in turbulent flows. It is shown that the fractal dimension of velocity and temperature signals in atmospheric turbulence is 1.65 +/- 0.05 implying that the dimension of iso-velocity or iso-temperature surfaces in fully developed turbulence is about 2.65 +/- 0.05 in agreement with previous theoretical predictions. The Reynolds number dependence of the measured dimensions is also explored by examining laboratory data at moderate Reynolds numbers. Using simple ideas from turbulence physics underlying the observed scaling features, we outline a family of schemes for generating artificial velocity fields, dubbed synthetic turbulence, which mimic velocity fluctuations in high-Reynolds -number turbulence to various degrees of detail. In the case of one-dimensional implementation of these schemes, we provide comparisons with experimental turbulence data and note that analytical predictions from the model allow us to relate the parameters of synthetic turbulence to those of real turbulence. Finally, we show that, compared to random initial conditions, an artificial velocity field in three-dimensions generated using a simplified synthetic turbulence scheme may be better suited for use as the initial condition for direct numerical simulation of homogeneous isotropic turbulence.
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.
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.
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.
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)
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
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.
Multispectral image fusion based on fractal features

NASA Astrophysics Data System (ADS)

Tian, Jie; Chen, Jie; Zhang, Chunhua

2004-01-01

Imagery sensors have been one indispensable part of the detection and recognition systems. They are widely used to the field of surveillance, navigation, control and guide, et. However, different imagery sensors depend on diverse imaging mechanisms, and work within diverse range of spectrum. They also perform diverse functions and have diverse circumstance requires. So it is unpractical to accomplish the task of detection or recognition with a single imagery sensor under the conditions of different circumstances, different backgrounds and different targets. Fortunately, the multi-sensor image fusion technique emerged as important route to solve this problem. So image fusion has been one of the main technical routines used to detect and recognize objects from images. While, loss of information is unavoidable during fusion process, so it is always a very important content of image fusion how to preserve the useful information to the utmost. That is to say, it should be taken into account before designing the fusion schemes how to avoid the loss of useful information or how to preserve the features helpful to the detection. In consideration of these issues and the fact that most detection problems are actually to distinguish man-made objects from natural background, a fractal-based multi-spectral fusion algorithm has been proposed in this paper aiming at the recognition of battlefield targets in the complicated backgrounds. According to this algorithm, source images are firstly orthogonally decomposed according to wavelet transform theories, and then fractal-based detection is held to each decomposed image. At this step, natural background and man-made targets are distinguished by use of fractal models that can well imitate natural objects. Special fusion operators are employed during the fusion of area that contains man-made targets so that useful information could be preserved and features of targets could be extruded. The final fused image is reconstructed from the composition of source pyramid images. So this fusion scheme is a multi-resolution analysis. The wavelet decomposition of image can be actually considered as special pyramid decomposition. According to wavelet decomposition theories, the approximation of image (formula available in paper) at resolution 2j+1 equal to its orthogonal projection in space , that is, where Ajf is the low-frequency approximation of image f(x, y) at resolution 2j and , , represent the vertical, horizontal and diagonal wavelet coefficients respectively at resolution 2j. These coefficients describe the high-frequency information of image at direction of vertical, horizontal and diagonal respectively. Ajf, , and are independent and can be considered as images. In this paper J is set to be 1, so the source image is decomposed to produce the son-images Af, D1f, D2f and D3f. To solve the problem of detecting artifacts, the concepts of vertical fractal dimension FD1, horizontal fractal dimension FD2 and diagonal fractal dimension FD3 are proposed in this paper. The vertical fractal dimension FD1 corresponds to the vertical wavelet coefficients image after the wavelet decomposition of source image, the horizontal fractal dimension FD2 corresponds to the horizontal wavelet coefficients and the diagonal fractal dimension FD3 the diagonal one. These definitions enrich the illustration of source images. Therefore they are helpful to classify the targets. Then the detection of artifacts in the decomposed images is a problem of pattern recognition in 4-D space. The combination of FD0, FD1, FD2 and FD3 make a vector of (FD0, FD1, FD2, FD3), which can be considered as a united feature vector of the studied image. All the parts of the images are classified in the 4-D pattern space created by the vector of (FD0, FD1, FD2, FD3) so that the area that contains man-made objects could be detected. This detection can be considered as a coarse recognition, and then the significant areas in each son-images are signed so that they can be dealt with special rules. There has been various fusion rules developed with each one aiming at a special problem. These rules have different performance, so it is very important to select an appropriate rule during the design of an image fusion system. Recent research denotes that the rule should be adjustable so that it is always suitable to extrude the features of targets and to preserve the pixels of useful information. In this paper, owing to the consideration that fractal dimension is one of the main features to distinguish man-made targets from natural objects, the fusion rule was defined that if the studied region of image contains man-made target, the pixels of the source image whose fractal dimension is minimal are saved to be the pixels of the fused image, otherwise, a weighted average operator is adopted to avoid loss of information. The main idea of this rule is to store the pixels with low fractal dimensions, so it can be named Minimal Fractal dimensions (MFD) fusion rule. This fractal-based algorithm is compared with a common weighted average fusion algorithm. An objective assessment is taken to the two fusion results. The criteria of Entropy, Cross-Entropy, Peak Signal-to-Noise Ratio (PSNR) and Standard Gray Scale Difference are defined in this paper. Reversely to the idea of constructing an ideal image as the assessing reference, the source images are selected to be the reference in this paper. It can be deemed that this assessment is to calculate how much the image quality has been enhanced and the quantity of information has been increased when the fused image is compared with the source images. The experimental results imply that the fractal-based multi-spectral fusion algorithm can effectively preserve the information of man-made objects with a high contrast. It is proved that this algorithm could well preserve features of military targets because that battlefield targets are most man-made objects and in common their images differ from fractal models obviously. Furthermore, the fractal features are not sensitive to the imaging conditions and the movement of targets, so this fractal-based algorithm may be very practical.
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.
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
Characterizing Fractures in Geysers Geothermal Field by Micro-seismic Data, Using Soft Computing, Fractals, and Shear Wave Anisotropy

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

Aminzadeh, Fred; Sammis, Charles; Sahimi, Mohammad

The ultimate objective of the project was to develop new methodologies to characterize the northwestern part of The Geysers geothermal reservoir (Sonoma County, California). The goal is to gain a better knowledge of the reservoir porosity, permeability, fracture size, fracture spacing, reservoir discontinuities (leaky barriers) and impermeable boundaries.
Viscoelastic and fractal characteristics of a supramolecular hydrogel hybridized with clay nanoparticles.

PubMed

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

2010-12-01

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

NASA Astrophysics Data System (ADS)

Swapna, M. S.; Saritha Devi, H. V.; Raj, Vimal; Sankararaman, S.

2018-03-01

Today diesel engines are used worldwide for various applications and very importantly in transportation. Hydrocarbons are the most widespread precursors among carbon sources employed in the production of carbon nanotubes (CNTs). The aging of internal combustion engine is an important parameter in deciding the carbon emission and particulate matter due to incomplete combustion of fuel. In the present work, an attempt has been made for the effective utilization of the aged engines for potential applicationapplications in fuel cells and nanoelectronics. To analyze the impact of aging, the particulate matter rich in carbon content areis collected from diesel engines of different ages. The soot with CNTs is purified by the liquid phase oxidation method and analyzed by Field Emission Scanning Electron Microscopy, High-Resolution Transmission Electron Microscopy, Energy Dispersive Spectroscopy, UV-Visible spectroscopy, Raman spectroscopy and Thermogravimetric analysis. The SEM image contains self-similar patterns probing fractal analysis. The fractal dimensions of the samples are determined by the box counting method. We could find a greater amount of single-walled carbon nanotubes (SWCNTs) in the particulate matter emitted by aged diesel engines and thereby giving information about the combustion efficiency of the engine. The SWCNT rich sample finds a wide range of applicationapplications in nanoelectronics and thereby pointing a potential use of these aged engines.
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.
Human development VIII: a theory of "deep" quantum chemistry and cell consciousness: quantum chemistry controls genes and biochemistry to give cells and higher organisms consciousness and complex behavior.

PubMed

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

2006-11-14

Deep quantum chemistry is a theory of deeply structured quantum fields carrying the biological information of the cell, making it able to remember, intend, represent the inner and outer world for comparison, understand what it "sees", and make choices on its structure, form, behavior and division. We suggest that deep quantum chemistry gives the cell consciousness and all the qualities and abilities related to consciousness. We use geometric symbolism, which is a pre-mathematical and philosophical approach to problems that cannot yet be handled mathematically. Using Occam's razor we have started with the simplest model that works; we presume this to be a many-dimensional, spiral fractal. We suggest that all the electrons of the large biological molecules' orbitals make one huge "cell-orbital", which is structured according to the spiral fractal nature of quantum fields. Consciousness of single cells, multi cellular structures as e.g. organs, multi-cellular organisms and multi-individual colonies (like ants) and human societies can thus be explained by deep quantum chemistry. When biochemical activity is strictly controlled by the quantum-mechanical super-orbital of the cell, this orbital can deliver energetic quanta as biological information, distributed through many fractal levels of the cell to guide form and behavior of an individual single or a multi-cellular organism. The top level of information is the consciousness of the cell or organism, which controls all the biochemical processes. By this speculative work inspired by Penrose and Hameroff we hope to inspire other researchers to formulate more strict and mathematically correct hypothesis on the complex and coherence nature of matter, life and consciousness.
Human Development VIII: A Theory of “Deep” Quantum Chemistry and Cell Consciousness: Quantum Chemistry Controls Genes and Biochemistry to Give Cells and Higher Organisms Consciousness and Complex Behavior

PubMed Central

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

2006-01-01

Deep quantum chemistry is a theory of deeply structured quantum fields carrying the biological information of the cell, making it able to remember, intend, represent the inner and outer world for comparison, understand what it “sees”, and make choices on its structure, form, behavior and division. We suggest that deep quantum chemistry gives the cell consciousness and all the qualities and abilities related to consciousness. We use geometric symbolism, which is a pre-mathematical and philosophical approach to problems that cannot yet be handled mathematically. Using Occams razor we have started with the simplest model that works; we presume this to be a many-dimensional, spiral fractal. We suggest that all the electrons of the large biological molecules orbitals make one huge “cell-orbital”, which is structured according to the spiral fractal nature of quantum fields. Consciousness of single cells, multi cellular structures as e.g. organs, multi-cellular organisms and multi-individual colonies (like ants) and human societies can thus be explained by deep quantum chemistry. When biochemical activity is strictly controlled by the quantum-mechanical super-orbital of the cell, this orbital can deliver energetic quanta as biological information, distributed through many fractal levels of the cell to guide form and behavior of an individual single or a multi-cellular organism. The top level of information is the consciousness of the cell or organism, which controls all the biochemical processes. By this speculative work inspired by Penrose and Hameroff we hope to inspire other researchers to formulate more strict and mathematically correct hypothesis on the complex and coherence nature of matter, life and consciousness. PMID:17115084
Fractal-Inspired Subwavelength Geometric Inclusions for Improvement of High-Frequency Electromagnetic Devices

NASA Astrophysics Data System (ADS)

Smith, Kathryn Leigh

This dissertation presents research results demonstrating the efficacy of fractal-inspired subwavelength geometric inclusions for improvement of high-frequency electromagnetic devices. It begins with a review of the open literature in the area of fractal applications in antennas and metamaterials. This is followed by a detailed discussion of three high-frequency electromagnetic devices that demonstrate performance improvement through incorporation of subwavelength geometric design elements. The first of these devices is a spherical spiral metamaterial unit cell that was developed as a three-dimensional fractal expansion of the traditional split ring resonator, and is shown to be capable of producing broadband negative permeability, negative permittivity, or both, depending solely on the orientation of the unit cells with respect to the incident electric field. The second device is a ringed rectangular patch antenna that has four resonant frequencies. All four of these operative frequencies are shown to produce similar radiation patterns, which also closely match the pattern of a traditional patch antenna. Several minor geometric modifications of the basic shape of the device are also presented, and are shown to enable modification of the number of resonances, as well as tuning of frequencies of resonance. The third and final topic is a modified horn antenna that incorporates a spiral metamaterial as a phase-shifting device in order to achieve circularly polarized radiation. The handedness of the radiated wave is shown to be tunable through simple reorientation of the loading unit cells. In each of these cases, electrically-small geometric modification of existing device geometries is shown to greatly affect performance, either by increasing bandwidth, by inducing multiband behavior, or by enabling exotic radiation characteristics.
Diversity of Poissonian populations.

PubMed

Eliazar, Iddo I; Sokolov, Igor M

2010-01-01

Populations represented by collections of points scattered randomly on the real line are ubiquitous in science and engineering. The statistical modeling of such populations leads naturally to Poissonian populations-Poisson processes on the real line with a distinguished maximal point. Poissonian populations are infinite objects underlying key issues in statistical physics, probability theory, and random fractals. Due to their infiniteness, measuring the diversity of Poissonian populations depends on the lower-bound cut-off applied. This research characterizes the classes of Poissonian populations whose diversities are invariant with respect to the cut-off level applied and establishes an elemental connection between these classes and extreme-value theory. The measures of diversity considered are variance and dispersion, Simpson's index and inverse participation ratio, Shannon's entropy and Rényi's entropy, and Gini's index.
Friction and universal contact area law for randomly rough viscoelastic contacts.

PubMed

Scaraggi, M; Persson, B N J

2015-03-18

We present accurate numerical results for the friction force and the contact area for a viscoelastic solid (rubber) in sliding contact with hard, randomly rough substrates. The rough surfaces are self-affine fractal with roughness over several decades in length scales. We calculate the contribution to the friction from the pulsating deformations induced by the substrate asperities. We also calculate how the area of real contact, A(v, p), depends on the sliding speed v and on the nominal contact pressure p, and we show how the contact area for any sliding speed can be obtained from a universal master curve A(p). The numerical results are found to be in good agreement with the predictions of an analytical contact mechanics theory.

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