Relevant bibliographies by topics / Fractal scaling

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Academic literature on the topic 'Fractal scaling'

Author: Grafiati
Published: 7 June 2025
Last updated: 13 July 2025

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Journal articles on the topic "Fractal scaling"

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Anitas, Eugen Mircea, Giorgia Marcelli, Zsolt Szakacs, Radu Todoran, and Daniela Todoran. "Structural Properties of Vicsek-like Deterministic Multifractals." Symmetry 11, no. 6 (2019): 806. http://dx.doi.org/10.3390/sym11060806.

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Deterministic nano-fractal structures have recently emerged, displaying huge potential for the fabrication of complex materials with predefined physical properties and functionalities. Exploiting the structural properties of fractals, such as symmetry and self-similarity, could greatly extend the applicability of such materials. Analyses of small-angle scattering (SAS) curves from deterministic fractal models with a single scaling factor have allowed the obtaining of valuable fractal properties but they are insufficient to describe non-uniform structures with rich scaling properties such as fractals with multiple scaling factors. To extract additional information about this class of fractal structures we performed an analysis of multifractal spectra and SAS intensity of a representative fractal model with two scaling factors—termed Vicsek-like fractal. We observed that the box-counting fractal dimension in multifractal spectra coincide with the scattering exponent of SAS curves in mass-fractal regions. Our analyses further revealed transitions from heterogeneous to homogeneous structures accompanied by changes from short to long-range mass-fractal regions. These transitions are explained in terms of the relative values of the scaling factors.
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Chen, Yanguang. "Fractal Modeling and Fractal Dimension Description of Urban Morphology." Entropy 22, no. 9 (2020): 961. http://dx.doi.org/10.3390/e22090961.

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The conventional mathematical methods are based on characteristic length, while urban form has no characteristic length in many aspects. Urban area is a scale-dependence measure, which indicates the scale-free distribution of urban patterns. Thus, the urban description based on characteristic lengths should be replaced by urban characterization based on scaling. Fractal geometry is one powerful tool for the scaling analysis of cities. Fractal parameters can be defined by entropy and correlation functions. However, the question of how to understand city fractals is still pending. By means of logic deduction and ideas from fractal theory, this paper is devoted to discussing fractals and fractal dimensions of urban landscape. The main points of this work are as follows. Firstly, urban form can be treated as pre-fractals rather than real fractals, and fractal properties of cities are only valid within certain scaling ranges. Secondly, the topological dimension of city fractals based on the urban area is 0; thus, the minimum fractal dimension value of fractal cities is equal to or greater than 0. Thirdly, the fractal dimension of urban form is used to substitute the urban area, and it is better to define city fractals in a two-dimensional embedding space; thus, the maximum fractal dimension value of urban form is 2. A conclusion can be reached that urban form can be explored as fractals within certain ranges of scales and fractal geometry can be applied to the spatial analysis of the scale-free aspects of urban morphology.
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Chen, Yanguang. "Characterizing Growth and Form of Fractal Cities with Allometric Scaling Exponents." Discrete Dynamics in Nature and Society 2010 (2010): 1–22. http://dx.doi.org/10.1155/2010/194715.

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Fractal growth is a kind of allometric growth, and the allometric scaling exponents can be employed to describe growing fractal phenomena such as cities. The spatial features of the regular fractals can be characterized by fractal dimension. However, for the real systems with statistical fractality, it is incomplete to measure the structure of scaling invariance only by fractal dimension. Sometimes, we need to know the ratio of different dimensions rather than the fractal dimensions themselves. A fractal-dimension ratio can make an allometric scaling exponent (ASE). As compared with fractal dimension, ASEs have three advantages. First, the values of ASEs are easy to be estimated in practice; second, ASEs can reflect the dynamical characters of system's evolution; third, the analysis of ASEs can be made through prefractal structure with limited scale. Therefore, the ASEs based on fractal dimensions are more functional than fractal dimensions for real fractal systems. In this paper, the definition and calculation method of ASEs are illustrated by starting from mathematical fractals, and, then, China's cities are taken as examples to show how to apply ASEs to depiction of growth and form of fractal cities.
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IGNATOWICH, MICHAEL J., DANIEL J. KELLEHER, CATHERINE E. MALONEY, DAVID J. MILLER, and KHRYSTYNA SERHIYENKO. "RESISTANCE SCALING FACTOR OF THE PILLOW AND FRACTALINA FRACTALS." Fractals 23, no. 02 (2015): 1550018. http://dx.doi.org/10.1142/s0218348x15500188.

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Much is known in the analysis of a finitely ramified self-similar fractal when the fractal has a harmonic structure: a Dirichlet form which respects the self-similarity of a fractal. What is still an open question is when such a structure exists in general. In this paper, we introduce two fractals, the fractalina and the pillow, and compute their resistance scaling factor. This is the factor which dictates how the Dirichlet form scales with the self-similarity of the fractal. By knowing this factor one can compute the harmonic structure on the fractal. The fractalina has scaling factor [Formula: see text], and the pillow fractal has scaling factor [Formula: see text].
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PERFECT, E., and B. DONNELLY. "BI-PHASE BOX COUNTING: AN IMPROVED METHOD FOR FRACTAL ANALYSIS OF BINARY IMAGES." Fractals 23, no. 01 (2015): 1540010. http://dx.doi.org/10.1142/s0218348x15400101.

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Many natural systems are irregular and/or fragmented, and have been interpreted to be fractal. An important parameter needed for modeling such systems is the fractal dimension, D. This parameter is often estimated from binary images using the box-counting method. However, it is not always apparent which fractal model is the most appropriate. This has led some researchers to report different D values for different phases of an analyzed image, which is mathematically untenable. This paper introduces a new method for discriminating between mass fractal, pore fractal, and Euclidean scaling in images that display apparent two-phase fractal behavior when analyzed using the traditional method. The new method, coined "bi-phase box counting", involves box-counting the selected phase and its complement, fitting both datasets conjointly to fractal and/or Euclidean scaling relations, and examining the errors from the resulting regression analyses. Use of the proposed technique was demonstrated on binary images of deterministic and stochastic fractals with known D values. Traditional box counting was unable to differentiate between the fractal and Euclidean phases in these images. In contrast, bi-phase box counting unmistakably identified the fractal phase and correctly estimated its D value. The new method was also applied to three binary images of soil thin sections. The results indicated that two of the soils were pore-fractals, while the other was a mass fractal. This outcome contrasted with the traditional box counting method which suggested that all three soils were mass fractals. Reclassification has important implications for modeling soil structure since different fractal models have different scaling relations. Overall, bi-phase box counting represents an improvement over the traditional method. It can identify the fractal phase and it provides statistical justification for this choice.
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Chauhan, Mahak Singh, Abhey Ram Bansal, and V. P. Dimri. "Scaling Laws and Fractal Geometry: Insights into Geophysical Data Interpretations." Journal Of The Geological Society Of India 101, no. 6 (2025): 983–89. https://doi.org/10.17491/jgsi/2025/174196.

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ABSTRACT Fractals, characterised by self-similarity and scale invariance, have emerged as powerful tools for understanding complex systems in geophysics. This paper highlights the applications of fractal geometry in geophysical data interpretation. For instance, fractal analysis is used in seismology to understand the fault systems, earthquake distribution, and the scaling laws governing seismic events. In potential fields, fractals are used to find the source depth, to design the optimum grid size of the survey, to detect the source and to separate signal from noise. In this paper, we first highlight the basics of fractal theory and then show how fractals are useful in various geophysical studies by showing examples from potential fields and seismology and reservoir characterisation.
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Yu, Bo, Yifei Pu, Qiuyan He, and Xiao Yuan. "Circuit Implementation of Variable-Order Scaling Fractal-Ladder Fractor with High Resolution." Fractal and Fractional 6, no. 7 (2022): 388. http://dx.doi.org/10.3390/fractalfract6070388.

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Extensive research has been conducted on the scaling fractal fractor using various structures. The development of high-resolution emulator circuits to achieve a variable-order scaling fractal fractor with high resolution is a major area of interest. We present a scaling fractal-ladder circuit for achieving high-resolution variable-order fractor based on scaling expansion theory using a high-resolution multiplying digital-to-analog converter (HMDAC). Firstly, the circuit configuration of variable-order scaling fractal-ladder fractor (VSFF) is designed. A theoretical demonstration proves that VSFF exhibits the operational characteristics of variable-order fractional calculus. Secondly, a programmable resistor–capacitor series circuit and universal electronic component emulators are developed based on the HMDAC to adjust the resistance and capacitance in the circuit configuration. Lastly, the model, component parameters, approximation performance, and variable-order characteristics are analyzed, and the circuit is physically implemented. The experimental results demonstrate that the circuit exhibits variable-order characteristics, with an operational order ranging from −0.7 to −0.3 and an operational frequency ranging from 7.72Hz to 4.82kHz. The peak value of the input signal is 10V. This study also proposes a novel method for variable-order fractional calculus based on circuit theory. This study was the first attempt to implement feasible high-resolution continuous variable-order fractional calculus hardware based on VSFF.
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Potapov, Alexander A. "Fractal applications in radio electronics as fractal engineering." Radioelectronics. Nanosystems. Information Technologies. 14, no. 3 (2022): 215–32. http://dx.doi.org/10.17725/rensit.2022.14.215.

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The use of the fractal paradigm is presented - the main directions for introducing textures, fractals, fractional operators, dynamic chaos and methods of nonlinear dynamics for the design and creation of real technical projects in radio electronics - fractal radio systems, taking into account the hereditarity, non-Gaussianity and scaling of physical signals and fields. The substantiation of the use of fractal-scaling and texture methods for the synthesis of fundamentally new topological texture-fractal methods for detecting signals in the space-time channel of scattering waves (a new type of radar) is discussed. It is shown that the use of fractal systems, sensors and nodes is a fundamentally new solution that significantly changes the principles of constructing intelligent radio engineering systems and devices. It is shown that the use of computational dielectric metasurfaces brings to a new level all the functional characteristics of a multifunctional system of topological texture-fractal processing of signals and fields in solving classical problems of detection, measurement, recognition and classification by intelligent radio engineering systems and devices. The concept of "fractal engineering" is introduced, the methodology of its use is discussed.
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NAIR, PRADEEP R., and MUHAMMAD A. ALAM. "KINETIC RESPONSE OF SURFACES DEFINED BY FINITE FRACTALS." Fractals 18, no. 04 (2010): 461–76. http://dx.doi.org/10.1142/s0218348x10005032.

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Historically, fractal analysis has been remarkably successful in describing wide ranging kinetic processes on (idealized) scale invariant objects in terms of elegantly simple universal scaling laws. However, as nanostructured materials find increasing applications in energy storage, energy conversion, healthcare, etc., one must reexamine the premise of traditional fractal scaling laws as it only applies to physically unrealistic infinite systems, while all natural/engineered systems are necessarily finite. In this article, we address the consequences of the 'finite-size' problem in the context of time dependent diffusion towards fractal surfaces via the novel technique of Cantor-transforms to (i) illustrate how finiteness modifies its classical scaling exponents; (ii) establish that for finite systems, the diffusion-limited reaction is decelerated below a critical dimension [Formula: see text] and accelerated above it; and (iii) to identify the crossover size-limits beyond which a finite system can be considered (practically) infinite and redefine the very notion of 'finiteness' of fractals in terms of its kinetic response. Our results have broad implications regarding dynamics of systems defined by the same fractal dimension, but differentiated by degree of scaling iteration or morphogenesis, e.g. variation in lung capacity between a child and adult.
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Pacheco, Julio César Ramırez, Homero Toral Cruz, and David Ernesto Troncoso Romero. "Rényi wavelet extropy of scaling signals." Parana Journal of Science and Education 10, no. 6 (2024): 21–25. https://doi.org/10.5281/zenodo.14232536.

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Recently, wavelet based informations tools are being used for fractals to unveil their complexities and providemore elaborate analyses. In this article, the time-domain definition of R&eacute;nyi extropy is extended to the waveletdomain and a closed-form expression of this extropy for scaling signals of parameter (alfa) is obtained. Based on&nbsp;the theoretical results, wavelet R&eacute;nyi <em>q</em>-extropy planes are obtained for various <em>q </em>and a range of the fractality&nbsp;parameter and, based on these, a complete characterization of the complexities of fractal signals based on R&eacute;nyi&nbsp;extropies are obtained. Moreover, potential applications for fractal signal analysis are highlighted and useful&nbsp;relations amongst different wavelet R&eacute;nyi extropy planes are provided.
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Dissertations / Theses on the topic "Fractal scaling"

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Price, Charles Anthony. "Scaling the Diversity of Botanical Form and Function." Diss., The University of Arizona, 2006. http://hdl.handle.net/10150/194373.

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Recent theoretical and empirical advances, in particular the fractal branching model of West, Brown and Enquist (WBE model), have highlighted the importance of exchange surfaces in understanding the integration of whole plant form, and functional traits. Key insights have arisen from an increased understanding of how the properties of distributive vessel networks influence whole plant metabolic and physiological traits. Here I show that an extension of WBE model, one in which network geometry is continuously variable, provides a robust foundation to understand the diversity of scaling relationships in plants and the organs of which they are composed. Central to the original WBE model has been the assumption of energy minimization as a selective force shaping the evolution of internal and external plant surface areas and morphology. Here I demonstrate how additional selection on traits not detailed in the original WBE formulation can lead to departures from strict energy minimization, and can thus explain much of the variation and covariation in observed scaling central tendencies in plant gross morphology observed within, and across natural plant communities. I test the predictions from this model extension with data from both regional and global datasets, from the leaf to whole plant level, across herbaceous, succulent, woody, annual and perennial taxa. These data demonstrate that the model extension is quite robust and should serve as a foundation upon which more detailed future models can be constructed.
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HUANG, KUAN-YU. "Fractal or Scaling Analysis of Natural Cities Extracted from Open Geographic Data Sources." Thesis, Högskolan i Gävle, Avdelningen för Industriell utveckling, IT och Samhällsbyggnad, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:hig:diva-19386.

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A city consists of many elements such as humans, buildings, and roads. The complexity of cities is difficult to measure using Euclidean geometry. In this study, we use fractal geometry (scaling analysis) to measure the complexity of urban areas. We observe urban development from different perspectives using the bottom-up approach. In a bottom-up approach, we observe an urban region from a basic to higher level from our daily life perspective to an overall view. Furthermore, an urban environment is not constant, but it is complex; cities with greater complexity are more prosperous. There are many disciplines that analyze changes in the Earth’s surface, such as urban planning, detection of melting ice, and deforestation management. Moreover, these disciplines can take advantage of remote sensing for research. This study not only uses satellite imaging to analyze urban areas but also uses check-in and points of interest (POI) data. It uses straightforward means to observe an urban environment using the bottom-up approach and measure its complexity using fractal geometry.   Web 2.0, which has many volunteers who share their information on different platforms, was one of the most important tools in this study. We can easily obtain rough data from various platforms such as the Stanford Large Network Dataset Collection (SLNDC), the Earth Observation Group (EOG), and CloudMade. The check-in data in this thesis were downloaded from SLNDC, the POI data were obtained from CloudMade, and the nighttime lights imaging data were collected from EOG. In this study, we used these three types of data to derive natural cities representing city regions using a bottom-up approach. Natural cities were derived from open geographic data without human manipulation. After refining data, we used rough data to derive natural cities. This study used a triangulated irregular network to derive natural cities from check-in and POI data.   In this study, we focus on the four largest US natural cities regions: Chicago, New York, San Francisco, and Los Angeles. The result is that the New York City region is the most complex area in the United States. Box-counting fractal dimension, lacunarity, and ht-index (head/tail breaks index) can be used to explain this. Box-counting fractal dimension is used to represent the New York City region as the most prosperous of the four city regions. Lacunarity indicates the New York City region as the most compact area in the United States. Ht-index shows the New York City region having the highest hierarchy of the four city regions. This conforms to central place theory: higher-level cities have better service than lower-level cities. In addition, ht-index cannot represent hierarchy clearly when data distribution does not fit a long-tail distribution exactly. However, the ht-index is the only method that can analyze the complexity of natural cities without using images.
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Zhou, Xiaobo. "Fractal and Multifractal Analysis of Runoff Time Series and Stream Networks in Agricultural Watersheds." Diss., Virginia Tech, 2004. http://hdl.handle.net/10919/11287.

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The usefulness of watershed hydrological process models is considerably increased when they can be extrapolated across spatial and temporal scales. This scale transfer problem, meaning the description and prediction of characteristics and processes at a scale different from the one at which observations and measurements are made, and has become the subject of much current research in hydrology and other areas. Quantitative description of fractal scaling behavior of runoff and stream network morphometry in agricultural watersheds has not been previously reported. In the present study, fractal and multifractal scaling of daily runoff rate in four experimental agricultural watersheds and their associated sub-watersheds (32 in total) were investigated. The time series of daily runoff rate were obtained from the database (comprising about 16,600 station years of rainfall and runoff data for small agricultural watersheds across the U.S.) developed by the Hydrological and Remote Sensing Laboratory, Agricultural Research Service, US Department of Agriculture (HRSL/ARS/USDA). Fractal scaling patterns of the Digital Elevation Model (DEM)-extracted stream network morphometry for these four watersheds were also examined. The morphometry of stream networks of four watersheds were obtained by Geographic Information System (GIS) manipulation of digital elevation data downloaded from the most recent (July 2004) U.S. Geological Survey (USGS) National Elevation Dataset (NED). Several threshold values of contribution area for stream initiation were used to extract stream networks for each of the four watersheds. The principal measures of fractal scaling determined for the runoff series were the Hurst exponent obtained by rescaled range (R/S) analysis, the fractal dimension estimated by the shifted box-counting method, and the multifractal scaling function parameters (a and C1) of the Universal Multifractal Model (UMM). Corresponding measures for the DEM-extracted stream networks at each threshold value were the fractal dimension estimated using the box-counting technique and the Horton ratios of the network. Daily runoff rate exhibited strong long-term dependence and scale invariance over certain time scales. The same fractal dimensions and Hurst exponents were obtained for the sub-watersheds within each watershed. Runoff exhibited multifractal behavior that was well described by UMM. The multifractal parameters a (quantifies how far the process is from monofractality) and C1 (characterizes the sparseness or inhomogeneity of the mean of the process) were reasonably close to each other for sub-watersheds within a watershed and were generally similar among four watersheds. For the DEM-extracted networks, the morphometric attributes and Horton ratios as well as their fractal dimensions were dependent on the threshold values of contribution area used in the extraction process. The fractal dimensions were almost identical for DEM-extracted stream networks of the four watersheds. The DEM-extracted stream network displayed a single scaling pattern, rather than multifractal behavior. Explanation of the physical significance of fractal characteristics of the stream network in relation to runoff time series would require more data than were available in this study.<br>Ph. D.
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Rai, Durgesh K. "Quantification of Fractal Systems using Small Angle Scattering." University of Cincinnati / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1377870724.

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Vasko, Erik S. "Power Scaling of the Mainland Shoreline of the Contiguous United States." Wright State University / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=wright1527259316331524.

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Jaskowak, Daniel Joseph. "Detecting Transient Changes in Gait Using Fractal Scaling of Gait Variability in Conjunction with Gaussian Continuous Wavelet Transform." Thesis, Virginia Tech, 2019. http://hdl.handle.net/10919/87393.

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Accelerometer data can be analyzed using a variety of methods which are effective in the clinical setting. Time-series analysis is used to analyze spatiotemporal variables in various populations. More recently, investigators have focused on gait complexity and the structure of spatiotemporal variations during walking and running. This study evaluated the use of time-series analyses to determine gait parameters during running. Subjects were college-age female soccer players. Accelerometer data were collected using GPS-embedded trunk-mounted accelerometers. Customized Matlab® programs were developed that included Gaussian continuous wavelet transform (CWT) to determine spatiotemporal characteristics, detrended fluctuation analysis (DFA) to examine gait complexity and autocorrelation analyses (ACF) to assess gait regularity. Reliability was examined using repeated running efforts and intraclass correlation. Proof of concept was determined by examining differences in each variable between various running speeds. Applicability was established by examining gait before and after fatiguing activity. The results showed most variables had excellent reliability. Test-retest R2 values for these variables ranged from 0.8 to 1.0. Low reliability was seen in bilateral comparisons of gait symmetry. Increases in running speed resulted in expected changes in spatiotemporal and acceleration variables. Fatiguing exercise had minimal effects on spatiotemporal variables but resulted in noticeable declines in complexity. This investigation shows that GPS-embedded trunk-mounted accelerometers can be effectively used to assess running gait. CWT and DFA yield reliable measures of spatiotemporal characteristics of gait and gait complexity. The effects of running speed and fatigue on these variables provides proof of concepts and applicability for this analytical approach.<br>Master of Science<br>Fitness trackers have become widely accessible and easy to use. So much so that athletic teams have been using them to track activity throughout the season. Researchers are able to manipulate data generated from the fitness monitors to assess many different variables including gait. Monitoring gait may generate important information about the condition of the individual. As a person fatigues, running form is theorized to breakdown, which increases injury risk. Therefore the ability to monitor gait may be advantageous in preventing injury. The purpose of this study is to show that the methods in this study are reproducible, respond reasonably to changes in speed, and to observe the changes of gait in the presence of fatigue or on tired legs. Three analyses are used in this study. The first method called autocorrelation, overlays acceleration signals of consecutive foot strikes, and determines the similarity between them. The second method utilizes a wave transformation technique that is able to determine foot contact times. The final method attempts to determine any pattern in the running stride. This method looks for changes in the structure of the pattern. Less structure would indicate a stride that is fatigued. The results showed that the methods of gait analysis used in this study were reproducible and responded appropriately with changes in speed. Small changes in gait were observed due to the presence of fatigue. Further investigation into the use of these methods to determine changes in gait due to the presence of fatigue are warranted.
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Zhai, Chongpu. "Stress-dependent electrical conduction in granular materials." Thesis, The University of Sydney, 2017. http://hdl.handle.net/2123/17975.

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This dissertation is focused on electrical conduction behaviour in granular systems with the purpose of acquiring a fundamental understanding towards applications of granular materials. Performance in a range of engineering systems can be largely influenced by complex multi-physics interactions arising from microstructures of granular materials. The bulk of this dissertation is built on six published or submitted papers. After project background and related previous work introduced in Chapters 1 and 2, respectively, Chapters 3 and 4 deal primarily with the contact properties between rough surfaces. The obtained information at the interfacial scale serves as an experimental and numerical basis for modelling inter-particle contacts in granular media. Chapter 5 with the fifth paper presents the effects of network configuration on macroscopic network responses focussing on the dielectric universal scaling behaviour. In Chapter 6, the final paper shows a physical picture illustrating experimentally observed alternating-current universal scaling in conductive granular systems under different stress states. An effective numerical approach incorporating inter-particle interaction has been provided to simulate electrical responses of granular materials. The combination of the studies from macro-scale phenomena, network topologies, and inter-particle properties is presented leading to new physics-based constitutive models that contain lower scale information. This dissertation presents a new comprehensive understanding of conduction behaviour in granular materials by means of a physics-based framework combining features containing both experimental and numerical information obtained across various length scales, guiding design and optimisation of various granular materials.
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Rakonczay, Zoltán. "Characterizing the Respiration of Stems and Roots of Three Hardwood Tree Species in the Great Smoky Mountains." Diss., Virginia Tech, 1997. http://hdl.handle.net/10919/30624.

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Carbon dioxide efflux rates (CER) of stems and roots of overstory and understory black cherry (<i>Prunus serotina</i> Ehrh., BC), red maple (<i>Acer rubrum</i> L., RM) and northern red oak (<i>Quercus rubra</i> L., RO) trees were monitored over two growing seasons at two contrasting sites in the Great Smoky Mountains to investigate diurnal and seasonal patterns in respiration and to develop prediction models based on environmental and plant parameters. CER of small roots (d<0-8 mm) was measured with a newly developed system which allows periodic <i>in situ</i> measurements by using permanently installed flexible cuvettes. Temperature-adjusted CER of roots showed no diel variation. The moderate long-term changes occurred simultaneously in all species and size classes, suggesting that they were driven mostly by environmental factors. Mean root CER ranged from 0.5 to 4.0 nmol g⁻¹ d.w. s⁻¹. Rates were up to six times higher for fine roots (d<2.0 mm) than for coarse roots. CER (per unit length) of boles (d>10 cm) and twigs (d<2 cm) was related to diameter by the function lnCER = a+<i>D</i>·lnd, with <i>D</i> between 1.2 and 1.8. A new, scale-invariant measure of CER, based on <i>D</i>, facilitated comparisons across diameters. Q₁₀ varied with the method of determination, and it was higher in spring (1.8-2.5) than in autumn (1.4-1.5) for all species. Daytime bole CER often fell below temperature-based predictions, likely due to transpiration. The reduction (usually <10%) was less pronounced at the drier site. Twig CER showed more substantial (often >±50%) deviations from the predictions. Deviations were higher in the canopy than in the understory. Mean bole maintenance respiration (at 20°C and d=20 cm) was 0.66, 0.43 and 0.50 μMol m⁻¹, while the volume-based growth coefficient was around 5, 6 and 8 mol cm⁻³ for BC, RM and RO, respectively. In a controlled study, BC and RM seedlings were fumigated in open-top chambers with sub-ambient, ambient and twice-ambient levels of ozone. The twice-ambient treatment reduced stem CER in BC by 50% (p=0.05) in July, but there was no treatment effect in September or in RM. Ozone reduced root/shoot ratio and diameter growth in BC, and P<sub>max</sub> in both species.<br>Ph. D.
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Lamorlette, Aymeric. "Caractérisation macroscopique du milieu végétal pour les modèles physiques de feux de forêts." Thesis, Vandoeuvre-les-Nancy, INPL, 2008. http://www.theses.fr/2008INPL044N/document.

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La description aux échelles macroscopiques et gigascopiques des feux de forêts permet l'établissement de modèles physiques aptes à représenter l'évolution d'un feu avec une meilleure précision que les modèles empiriques de type Rothermel développés jusqu'alors. Cependant ces modèles nécessitent l'ajustement de paramètres dont la mesure directe est impossible, car les équations associées à ces modèles ne sont pas relatives à l'air et à la matière végétale mais aux milieux équivalents à la végétation pour l'échelle considérée. Les propriétés des milieux équivalents sont alors liées aux propriétés des milieux les constituant, mais la connaissance des propriétés des milieux constitutifs ne permet pas de connaître directement les propriétés du milieu équivalent. Ce travail consistera tout d'abord en la reconstruction du milieu végétal à l'aide d'outils issus de la géométrie fractale. Des méthodes de mesures de paramètres géométriques venant de la foresterie ont ensuite été utilisées pour valider nos modèles de végétation. Enfin, des expériences numériques ont été menées sur nos structures reconstruites afin d'identifier les paramètres macroscopiques qui nous intéressent. Ces expériences permettent également de valider ou non les hypothèses effectuées lors de l'établissement des équations du milieu équivalent. Les paramètres ajustés sont la viscosité du milieu équivalent, le coefficient d'échange convectif et le coefficient d'extinction<br>The macroscopic and gigascopic scale description of forest fires allows physical modelings of the propagation which can predict the fire evolution with a better accuracy than usually developed empirical Rothermel-like models. However, those models need fitting for their parameters which cannot be measured directly as the models equations are related to the equivalent media at the considered scale and not related to the air and the vegetal material. The equivalent media properties are related to the inner media properties, but the inner media properties knowledge does not allow directly the equivalent media properties knowledge. This work is then aiming on the vegetal medium reconstruction using fractal geometry. Geometrical parameters measurement methods used in forestry sciences are applied for the vegetal modeling validation. Numerical studies are finally done on the reconstructed structures to fit the relevant macroscopic scale parameters. Those studies also allow us to validate or invalidate the assumptions which have been done for the equivalent medium equation development. Those parameters are: the equivalent medium viscosity, the convective heat transfer coefficient and the extinction coefficient
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Warren, Patrick Bewick. "Scaling laws in cluster-cluster aggregation." Thesis, University of Cambridge, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.386210.

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Books on the topic "Fractal scaling"

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Nottale, Laurent. Fractal space-time and microphysics: Towards a theory of scale relativity. World Scientific, 1992.

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Nottale, Laurent. Fractal space-time and microphysics: Towards a theory of scale relativity. World Scientific, 1993.

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Abry, Patrice, Paulo Gonalves, and Jacques Lvy Vhel, eds. Scaling, Fractals and Wavelets. ISTE, 2009. http://dx.doi.org/10.1002/9780470611562.

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Patrice, Abry, Gonçalves Paulo 1967-, and Lévy Véhel Jacques 1960-, eds. Scaling, fractals and wavelets. ISTE Ltd, 2007.

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Mandelbrot, Benoit B. Fractals and Scaling in Finance. Springer New York, 1997. http://dx.doi.org/10.1007/978-1-4757-2763-0.

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Mandelbrot, Benoit B. Fractals and scaling in finance: Discontinuity, concentration, risk. Springer, 1997.

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D, Schertzer, and Lovejoy S. 1956-, eds. Non-linear variability in geophysics: Scaling and fractals. Kluwer Academic Publishers, 1991.

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1949-, Novak M. M., ed. Emergent nature: Patterns, growth and scaling in the sciences. World Scientific, 2001.

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Lovejoy, S. The weather and climate: Emergent laws and multifractal cascades. Cambridge University Press, 2012.

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Mandelbrot, Benoit B. Fractals and scaling in finance: Discontinuity, concentration, risk : selecta volume E. Springer, 1997.

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Book chapters on the topic "Fractal scaling"

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Borodich, Feodor M. "Fractals and fractal scaling in fracture mechanics." In Fracture Scaling. Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4659-3_13.

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Southern, B. W., and A. R. Douchant. "Phonon-Fracton Crossover on Fractal Lattices." In Scaling Phenomena in Disordered Systems. Springer US, 1991. http://dx.doi.org/10.1007/978-1-4757-1402-9_29.

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Padhy, Simanchal, and Vijay P. Dimri. "Fractal Scaling of Earthquakes." In Encyclopedia of Solid Earth Geophysics. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-10475-7_274-1.

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Bakunin, Oleg G. "Fractal Objects and Scaling." In Chaotic Flows. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-20350-3_8.

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Padhy, Simanchal, and Vijay P. Dimri. "Fractal Scaling of Earthquakes." In Encyclopedia of Solid Earth Geophysics. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-58631-7_274.

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Blumenfeld, Rafael, and Amnon Aharony. "Nonlinear Resistor Fractal Networks." In Scaling Phenomena in Disordered Systems. Springer US, 1991. http://dx.doi.org/10.1007/978-1-4757-1402-9_33.

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Chen, Yanguang. "Geographical space based on urban allometry and fractal dimension." In Urban Scaling. Routledge, 2024. http://dx.doi.org/10.4324/9781003288312-32.

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Bassingthwaighte, James B., Larry S. Liebovitch, and Bruce J. West. "The Fractal Dimension: Self-Similar and Self-Affine Scaling." In Fractal Physiology. Springer New York, 1994. http://dx.doi.org/10.1007/978-1-4614-7572-9_3.

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Daoud, Mohamed, H. Eugene Stanley, and Dietrich Stauffer. "Scaling, Exponents, and Fractal Dimensions." In Physical Properties of Polymers Handbook. Springer New York, 2007. http://dx.doi.org/10.1007/978-0-387-69002-5_6.

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Orbach, R. "Excitations of/on Fractal Networks." In Scaling Phenomena in Disordered Systems. Springer US, 1991. http://dx.doi.org/10.1007/978-1-4757-1402-9_27.

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Conference papers on the topic "Fractal scaling"

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Potapov, A. A. "Topological Texture-Fractal Processing of Signals and Fields in Radio Physics, Radio Engineering and Radiolocation: Developed Methods and Technologies (1979 – 2022) – Fractal Engineering." In 32nd International Conference on Computer Graphics and Vision. Keldysh Institute of Applied Mathematics, 2022. http://dx.doi.org/10.20948/graphicon-2022-741-755.

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The report discusses the main directions of the introduction of textures, fractals, fractional operators, dynamic chaos and methods of nonlinear dynamics to create new information (breakthrough) technologies. The research is carried out in the fundamental scientific direction "Fractal radio physics and fractal radio electronics: design of fractal radio systems", initiated and developed by the author in V. A. Kotel’nikov IREE RAS from 1979 to the present. The relevance of these studies is related to the need for a more accurate description of all real processes occurring in radio physical and radio engineering systems: taking into account the hereditarity (memory), nonGaussianity and scaling of physical signals and fields. The use of fractal systems, sensors and nodes is a fundamentally new solution that significantly changes the principles of building intelligent radio engineering systems and devices. The performed studies are priority ones in the world and serve as a basis for further development and justification of the practical application of fractal-scaling and texture methods in the synthesis of fundamentally new topological texture-fractal methods for detecting signals in the space-time channel of waves propagation with scattering (a new type of radar). The concepts of fractal engineering are introduced for the first time.
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Peng, C. K., S. Havlin, H. E. Stanley, and A. L. Goldberger. "Fractal scaling properties in nonstationary heartbeat time series." In Chaotic, fractal, and nonlinear signal processing. AIP, 1996. http://dx.doi.org/10.1063/1.51000.

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Potapov, A. A. "Fractal paradigm and fractal-scaling methods in fundamentally new dynamic fractal signal detectors." In 2013 International Kharkov Symposium on Physics and Engineering of Microwaves, Millimeter and Submillimeter Waves (MSMW). IEEE, 2013. http://dx.doi.org/10.1109/msmw.2013.6622151.

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Hargreaves, N. "Some geophysical consequences of fractal scaling." In 58th EAEG Meeting. EAGE Publications BV, 1996. http://dx.doi.org/10.3997/2214-4609.201408614.

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Potapov, A. A., Wei Zhang, and Tianhua Feng. "Cognitive Radar in Fractal - Scaling Design." In 2018 International Conference on Sensing,Diagnostics, Prognostics, and Control (SDPC). IEEE, 2018. http://dx.doi.org/10.1109/sdpc.2018.8664932.

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Zhurkovsky, S. V., Andrei V. Lavrinenko, and Sergey V. Gaponenko. "Scaling properties of multilayer fractal structures." In Saratov Fall Meeting 2001, edited by Dmitry A. Zimnyakov. SPIE, 2002. http://dx.doi.org/10.1117/12.469000.

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Vega, S., and D. Arteaga. "Fractal Scaling Porosity: An Intriguing Approach." In First EAGE Rock Physics Workshop in Latin America. European Association of Geoscientists & Engineers, 2021. http://dx.doi.org/10.3997/2214-4609.202187015.

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Ortiz, Guillermo P., and W. Luis Mochan. "Optical properties and scaling in fractal aggregates." In IV Iberoamerican Meeting of Optics and the VII Latin American Meeting of Optics, Lasers and Their Applications, edited by Vera L. Brudny, Silvia A. Ledesma, and Mario C. Marconi. SPIE, 2001. http://dx.doi.org/10.1117/12.437199.

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Courtial, Johannes. "Fractal resonator modes." In The European Conference on Lasers and Electro-Optics. Optica Publishing Group, 1998. http://dx.doi.org/10.1364/cleo_europe.1998.cfc3.

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Physical approximations to fractal radiation patterns have been largely limited to essentially random distributions with fractal-like scaling behaviour and the generation of fractal radiation patterns using fractal arrays. Recently, a complex design for an all-optical device that generates fractal intensity patterns, based on the principle of the multiple reduction copy machine (Fig. 1 (a)) with feedback, has been introduced [1]. Within this work the resonator properties of a modified and simplified version of such a device are investigated.
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Mazumder, S., Abarrul Ikram, Agus Purwanto, et al. "Dynamical Scaling, Fractal Morphology and Small-angle Scattering." In NEUTRON AND X-RAY SCATTERING 2007: The International Conference. AIP, 2008. http://dx.doi.org/10.1063/1.2906085.

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Reports on the topic "Fractal scaling"

1

Meisel, Lawrence V., and Mark A. Johnson. Fractal Scaling in Cellular Automata Simulations of Dissipative Dynamical Systems. Defense Technical Information Center, 1996. http://dx.doi.org/10.21236/ada315392.

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Nechaev, V., Володимир Миколайович Соловйов, and A. Nagibas. Complex economic systems structural organization modelling. Politecnico di Torino, 2006. http://dx.doi.org/10.31812/0564/1118.

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One of the well-known results of the theory of management is the fact, that multi-stage hierarchical organization of management is unstable. Hence, the ideas expressed in a number of works by Don Tapscott on advantages of network organization of businesses over vertically integrated ones is clear. While studying the basic tendencies of business organization in the conditions of globalization, computerization and internetization of the society and the results of the financial activities of the well-known companies, the authors arrive at the conclusion, that such companies, as IBM, Boeing, Mercedes-Benz and some others companies have not been engaged in their traditional business for a long time. Their partner networks performs this function instead of them. The companies themselves perform the function of system integrators. The Tapscott’s idea finds its confirmation within the framework of a new powerful direction of the development of the modern interdisciplinary science – the theory of the complex networks (CN) [2]. CN-s are multifractal objects, the loss of multifractality being the indicator of the system transition from more complex state into more simple state. We tested the multifractal properties of the data using the wavelet transform modulus maxima approach in order to analyze scaling properties of our company. Comparative analysis of the singularity spectrumf(®), namely, the difference between maximum and minimum values of ® (∆ = ®max ¡ ®min) shows that IBM company is considerably more fractal in comparison with Apple Computer. Really, for it the value of ∆ is equal to 0.3, while for the vertically integrated company Apple it only makes 0.06 – 5 times less. The comparison of other companies shows that this dependence is of general character. Taking into consideration the fact that network organization of business has become dominant in the last 5-10 years, we carried out research for the selected companies in the earliest possible period of time which was determined by the availability of data in the Internet, or by historically later beginning of stock trade of computer companies. A singularity spectrum of the first group of companies turned out to be considerably narrower, or shifted toward the smaller values of ® in the pre-network period. The latter means that dynamic series were antipersistant. That is, these companies‘ management was rigidly controlled while the impact of market mechanisms was minimized. In the second group of companies if even the situation did changed it did not change for the better. In addition, we discuss applications to the construction of portfolios of stock that have a stable ratio of risk to return.
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