Relevant bibliographies by topics / Power-law scaling

Academic literature on the topic 'Power-law scaling'

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Published: 11 March 2023

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Journal articles on the topic "Power-law scaling"

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Tatlıer, M. "Power-law scaling behavior of membranes." Journal of Membrane Science 182, no. 1-2 (February 15, 2001): 183–93. http://dx.doi.org/10.1016/s0376-7388(00)00565-2.

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BURROUGHS, STEPHEN M., and SARAH F. TEBBENS. "UPPER-TRUNCATED POWER LAW DISTRIBUTIONS." Fractals 09, no. 02 (June 2001): 209–22. http://dx.doi.org/10.1142/s0218348x01000658.

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Power law cumulative number-size distributions are widely used to describe the scaling properties of data sets and to establish scale invariance. We derive the relationships between the scaling exponents of non-cumulative and cumulative number-size distributions for linearly binned and logarithmically binned data. Cumulative number-size distributions for data sets of many natural phenomena exhibit a "fall-off" from a power law at the largest object sizes. Previous work has often either ignored the fall-off region or described this region with a different function. We demonstrate that when a data set is abruptly truncated at large object size, fall-off from a power law is expected for the cumulative distribution. Functions to describe this fall-off are derived for both linearly and logarithmically binned data. These functions lead to a generalized function, the upper-truncated power law, that is independent of binning method. Fitting the upper-truncated power law to a cumulative number-size distribution determines the parameters of the power law, thus providing the scaling exponent of the data. Unlike previous approaches that employ alternate functions to describe the fall-off region, an upper-truncated power law describes the data set, including the fall-off, with a single function.
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Ton, Robert, and Andreas Daffertshofer. "Model selection for identifying power-law scaling." NeuroImage 136 (August 2016): 215–26. http://dx.doi.org/10.1016/j.neuroimage.2016.01.008.

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CAMPOS, PAULO R. A., VIVIANE M. DE OLIVEIRA, and LEONARDO P. MAIA. "EMERGENCE OF ALLOMETRIC SCALING IN GENEALOGICAL TREES." Advances in Complex Systems 07, no. 01 (March 2004): 39–46. http://dx.doi.org/10.1142/s0219525904000044.

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We investigate the emergence of power-law scalings in genealogical trees. Especially, we study the topological properties of genealogical trees both in the neutral evolution and the selective evolution. In all instances, we observe that the topologies of these trees are well described by a power-law scaling [Formula: see text], where Ak is the number of nodes which are direct or indirect descendants of node k and Ck=∑jAj where the sum is taken over all nodes that contribute to Ak. This relation is well known in transportation networks as well as in metabolic networks, and it is referred to as allometric scaling. Furthermore, we observe a slight dependence of the scaling exponent η on the intensity of selection.
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Chen, Bo, Chunying Ma, Witold F. Krajewski, Pei Wang, and Feipeng Ren. "Logarithmic transformation and peak-discharge power-law analysis." Hydrology Research 51, no. 1 (December 2, 2019): 65–76. http://dx.doi.org/10.2166/nh.2019.108.

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Abstract The peak-discharge and drainage area power-law relation has been widely used in regional flood frequency analysis for more than a century. The coefficients and can be obtained by nonlinear or log-log linear regression. To illustrate the deficiencies of applying log-transformation in peak-discharge power-law analyses, we studied 52 peak-discharge events observed in the Iowa River Basin in the United States from 2002 to 2013. The results show that: (1) the estimated scaling exponents by the two methods are remarkably different; (2) for more than 80% of the cases, the power-law relationships obtained by log-log linear regression produce larger prediction errors of peak discharge in the arithmetic scale than that predicted by nonlinear regression; and (3) logarithmic transformation often fails to stabilize residuals in the arithmetic domain, it assigns higher weight to data points representing smaller peak discharges and drainage areas, and it alters the visual appearance of the scatter in the data. The notable discrepancies in the scaling parameters estimated by the two methods and the undesirable consequences of logarithmic transformation raise caution. When conducting peak-discharge scaling analysis, especially for prediction purposes, applying nonlinear regression on the arithmetic scale to estimate the scaling parameters is a better alternative.
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Luo, Liang, and Lei-Han Tang. "Sub-diffusive scaling with power-law trapping times." Chinese Physics B 23, no. 7 (July 2014): 070514. http://dx.doi.org/10.1088/1674-1056/23/7/070514.

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Bhattacharyya, Gautam, Anindya Datta, Swarup Kumar Majee, and Amitava Raychaudhuri. "Power law scaling in universal extra dimension scenarios." Nuclear Physics B 760, no. 1-2 (January 2007): 117–27. http://dx.doi.org/10.1016/j.nuclphysb.2006.10.018.

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Gupta, Hari M., and José R. Campanha. "Firms growth dynamics, competition and power-law scaling." Physica A: Statistical Mechanics and its Applications 323 (May 2003): 626–34. http://dx.doi.org/10.1016/s0378-4371(03)00017-7.

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Kitzes, Justin. "Evidence for power‐law scaling in species aggregation." Ecography 42, no. 6 (February 8, 2019): 1224–25. http://dx.doi.org/10.1111/ecog.04159.

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Ferree, Thomas C., and Rudolph C. Hwa. "Power-law scaling in human EEG: relation to Fourier power spectrum." Neurocomputing 52-54 (June 2003): 755–61. http://dx.doi.org/10.1016/s0925-2312(02)00760-9.

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Dissertations / Theses on the topic "Power-law scaling"

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Ayalew, Tibebu Bekele. "Physical basis of the power-law spatial scaling structure of peak discharges." Diss., University of Iowa, 2015. https://ir.uiowa.edu/etd/1537.

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Key theoretical and empirical results from the past two decades have established that peak discharges exhibit power-law, or scaling, relation with drainage area across multiple scales of time and space. This relationship takes the form Q(A)= $#945;AΘ where Q is peak discharge, A is the drainage area, Θ is the flood scaling exponent, and α is the intercept. Motivated by seminal empirical studies that show that the flood scaling parameters α and Θ change from one rainfall-runoff event to another, this dissertation explores how certain rainfall and catchment physical properties control the flood scaling exponent and intercept at the rainfall-runoff event scale using a combination of extensive numerical simulation experiments and analysis of observational data from the Iowa River basin, Iowa. Results show that Θ generally decreases with increasing values of rainfall intensity, runoff coefficient, and hillslope overland flow velocity, whereas its value generally increases with increasing rainfall duration. Moreover, while the flood scaling intercept is primarily controlled by the excess rainfall intensity, it increases with increasing runoff coefficient and hillslope overland flow velocity. Results also show that the temporal intermittency structure of rainfall has a significant effect on the scaling structure of peak discharges. These results highlight the fact that the flood scaling parameters are able to be estimated from the aforementioned catchment rainfall and physical variables, which can be measured either directly or indirectly using in situ or remote sensing techniques. The dissertation also proposes and demonstrates a new flood forecasting framework that is based on the scaling theory of floods. The results of the study mark a step forward to provide a physically meaningful framework for regionalization of flood frequencies and hence to solve the long standing hydrologic problem of flood prediction in ungauged basins.
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Coey, Charles A. "Complexity and Coordination: Power-Law Scaling in the Temporal Coordination of Complex Systems." University of Cincinnati / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1439282201.

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Miao, Yufan. "Exploring Spatio-Temporal Patterns of Volunteered Geographic Information : A Case Study on Flickr Data of Sweden." Thesis, Högskolan i Gävle, Avdelningen för Industriell utveckling, IT och Samhällsbyggnad, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:hig:diva-15031.

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This thesis aims to seek interesting patterns from massive amounts of Flickr data in Sweden with pro- posed new clustering strategies. The aim can be further divided into three objectives. The first one is to acquire large amount of timestamped geolocation data from Flickr servers. The second objective is to develop effective and efficient methods to process the data. More specifically, the methods to be developed are bifold, namely, the preprocessing method to solve the “Big Data” issue encountered in the study and the new clustering method to extract spatio-temporal patterns from data. The third one is to analyze the extracted patterns with scaling analysis techniques in order to interpret human social activities underlying the Flickr Data within the urban envrionment of Sweden. During the study, the three objectives were achieved sequentially. The data employed for this study was vector points downloaded through Flickr Application Programming Interface (API). After data ac- quisition, preprocessing was performed on the raw data. The whole dataset was firstly separated by year based on the temporal information. Then data of each year was accumulated with its former year(s) so that the evovling process can be explored. After that, large datasets were splitted into small pieces and each piece was clipped, georeferenced, and rectified respectively. Then the pieces were merged together for clustering. With respect to clustering, the strategy was developed based on the Delaunay Triangula- tion (DT) and head/tail break rule. After that, the generated clusters were analyzed with scaling analysis techniques and spatio-temporal patterns were interpreted from the analysis results. It has been found that the spatial pattern of the human social activities in the urban environment of Sweden generally follows the power-law distribution and the cities defined by human social activities are evolving as time goes by. To conclude, the contributions of this research are threefold and fulfill the objectives of this study, respectively. Firstly, large amount of Flickr data is acquired and collated as a contribution to other aca- demic researches related to Flickr. Secondly, the clustering strategy based on the DT and head/tail break rule is proposed for spatio-temporal pattern seeking. Thirdly, the evolving of the cities in terms of human activities in Sweden is detected from the perspective of scaling. Future work is expected in major two aspects, namely, data and data processing. For the data aspect, the downloaded Flickr data is expected to be employed by other studies, especially those closely related to human social activities within urban environment. For the processing aspect, new algorithms are expected to either accelerate the processing process or better fit machines with super computing capacities.
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Zang, Xin. "Over-the-air Computation for Large-scale Wireless Data Fusion." Thesis, The University of Sydney, 2021. https://hdl.handle.net/2123/25100.

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For future Internet-of-Things based Big Data applications, sensors need to collect a vast volume of data from sensors and the environment. To interpret the meaning behind the collected data, it is challenging for an edge fusion center running extensive computing tasks over large data sets with limited computation capacity. To tackle the challenge, by exploiting the superposition property of the multiple-access channel and the functional decomposition, the recently proposed over-the-air computation (AirComp) technique, enables an effective joint data collection and computation from concurrent sensor transmissions. In this thesis, we first consider a single-antenna AirComp system consisting of K sensors and one receiver. We formulate an optimization problem to minimize the computation mean-squared error (MSE) of the K sensors' signals at the receiver by optimizing the transmission and receiver processing policy, under the peak power constraint of each sensor. Although the problem is not convex, we derive the computation-optimal policy in a closed form. We comprehensively investigate the ergodic performance of the AirComp system, the scaling laws of the average computation MSE and the average power consumption of different policies with respect to K. For the computation-optimal policy, we show that the policy has a varnishing average computation MSE and a varnishing average power consumption with the increasing K. In most of the existing work on AirComp, the optimal system-parameter design is commonly considered under the peak-power constraint of each sensor. In my second work, we propose an optimal transmitter-receiver parameter design problem to minimize the computation MSE of an AirComp system under the sum-power constraint of the sensors. We solve the non-convex problem and obtain a closed-form solution. We investigate another problem that minimizes the sum power of the sensors under the constraint of computation MSE. Our results show that in both problems, the sensors with poor and good channel conditions should use less power than the ones with moderate channel conditions. Most existing work on AirComp assumes computation of spatial-and-temporal independent sensor signals, though in practice different sensor measurements are usually correlated and the current measurements are normally related to the previous ones. In my third work, we propose an AirComp system with spatial-and-temporal correlated sensor signals for the first time in the literature, and formulate the optimal AirComp policy design problem for achieving the minimum computation MSE. We derive the optimal AirComp policy to achieve the minimum computation MSE in each time step by utilizing the current and the previously received signals. We also propose and optimize a low-complexity AirComp policy in a closed form, which approaches the performance of the optimal policy.
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Kirk, Andrew J. "Seasonal Variation of Fish and Macroinvertebrate Biomass Spectra in Southern West Virginia Streams." VCU Scholars Compass, 2016. http://scholarscompass.vcu.edu/etd/4228.

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The biomass size spectrum - the power-law scaling relationship between average individual size and total biomass - has often been studied in lake and marine ecosystems, but rarely in lotic systems. The objective of this study was to test for characteristic biomass spectra in small temperate streams. Seasonal fish and macroinvertebrate data, including population abundance and biomass estimates, were collected in three wadeable, southern West Virginia streams from October 2013 to May 2015. Fish abundances were estimated with 3-pass electrofishing (depletion) surveys and individuals were weighed in the field. Macroinvertebrates were collected with a Hess sampler and returned to the lab for identification to the lowest practical level (usually genus). Published length-mass regressions were then used to estimate individual mass. All size spectra relationships (linear regression of log-log data) were highly significant (p<0.001). Size spectra intercepts were variable and may reflect seasonal differences in fish and invertebrate densities. Size spectra slopes were more consistent, with a mean slope of approximately -0.73, suggesting a common scaling relationship between stream consumers at differing trophic levels.
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Smigelski, Jeffrey Ralph. "Water Level Dynamics of the North American Great Lakes:Nonlinear Scaling and Fractional Bode Analysis of a Self-Affine Time Series." Wright State University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=wright1379087351.

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Siena, Martina. "Caratterizzazione della permeabilità in mezzi porosi sintetici e naturali." Doctoral thesis, Università degli studi di Trieste, 2013. http://hdl.handle.net/10077/8661.

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2011/2012
La presente tesi ha come principale obiettivo lo studio della variabilità di proprietà idrologiche in mezzi porosi, con particolare attenzione alla permeabilità. A tal fine, ci si avvale di un approccio che combina l'analisi di proprietà statistiche e di scaling applicata a dataset di permeabilità, con lo studio di risultati numerici di simulazioni di flusso alla microscala in mezzi porosi. Con la prima analisi è possibile caratterizzare variazioni di permeabilità alla scala di misura (tipicamente dell'ordine del centimetro), mentre la seconda analisi dà una descrizione dell'eterogeneità di permeabilità ad una scala inferiore (nell'ordine del millimetro), ottenuta risolvendo processi fisici alla scala dei pori e derivando le quantità integrali di interesse. L'analisi statistica e di scaling, effettuata sia su distribuzioni di permeabilità sintetiche, sia su dataset raccolti su campioni reali, avvalora la validità dei modelli truncated fractional Brownian motion (tfBm) e truncated fractional Gaussian noise (tfGn), o di processi random sub-Gaussiani ad essi subordinati, per l'interpretazione della variabilità di proprietà idrologiche. Soluzioni numeriche di campi di flusso (i.e. velocità e pressione) alla scala dei pori sono ottenute sia per campioni sintetici, sia per campioni reali, la cui geometria è ricostruita mediante micro-tomografia a raggi X. Diverse metodologie di applicazione delle condizioni al contorno in corrispondenza dell'interfaccia liquido-solido forniscono risultati qualitativamente simili sia in termini di quantità microscopiche, sia in termini di quantità medie.
The work is aimed at providing some insights on the variability of hydrological properties in porous media, focusing in particular on permeability. We consider an approach which combines scaling and statistical analyses of air-permeability datasets with pore-scale numerical simulations of flow through porous media. The former investigation allows to characterize permeability heterogeneity at the centimeter observation scale; the latter provides a description of heterogeneity on a millimeter scale by resolving physical processes occurring at the microscopic scale and deriving up-scaled quantities. Scaling and statistical analyses performed on synthetic permeability distributions as well as on datasets collected on real media support the identification of truncated fractional Brownian motion (tfBm) or truncated fractional Gaussian noise (tfGn) and of sub-Gaussian random processes subordinated to tfBm (or tfGn) as viable models for the interpretation of hydrological properties variability. Pore-scale numerical solutions of flow (i.e., in terms of velocity and pressure distributions) are performed on both randomly generated samples and real porous media reconstructed via X-ray Micro-Tomography. Different approaches for the enforcement of boundary conditions at the fluid-solid interface provide qualitatively similar results in terms of both microscopic and averaged quantities.
XXV Ciclo
1984
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Ding, Tuan Ji, and 丁團吉. "The Theoretical Research of Scaling Law for Maanshan Nuclear Power Plant Scaling-down Test Facility." Thesis, 1994. http://ndltd.ncl.edu.tw/handle/59426337427247709369.

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Hooker, John Noel. "Fracture scaling and diagenesis." 2012. http://hdl.handle.net/2152/19573.

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Sets of natural opening-mode fractures in sedimentary rocks may show a variety of types of aperture-size distributions. A frequently documented size distribution type, in the literature and in data presented here, is the power law. The emergence of power-law distributions of fracture aperture and length sizes has been simulated using various quasi-mechanical fracture-growth routines but models based on linear-elastic fracture mechanics rarely produce such patterns. I collected a fracture-size dataset of unprecedented size and resolution using core and field methods and scanning electron microscope-based cathodoluminescence (SEM-CL) images. This dataset confirms the prevalence of power laws with a narrow range of power-law exponents among fractures that contain synkinematic cement. Organized microfractures are ubiquitous in sandstones. A fracture-growth simulation I devised reproduces observed size-scaling patterns by distributing fracture-opening increments among actively growing fractures. The simulated opening increments have a uniform size, which can be specified; uniform opening size is consistent with observations of narrow ranges of micron-scale widths of opening increments within crack-seal texture in natural fractures. Thus power-law size scaling of natural fractures can be explained using non-power-law (uniform-sized) opening increments, arranged using rules designed to simulate the effects of cement precipitation during fracture opening. A fundamental shortcoming of previous models of fracture-set evolution is the absence of a test because only natural fracture end states, not growth histories, could be measured. Using a technique to constrain fracture timing based on fluid inclusion microthermometry and thermal history modeling, I tested growth models by reconstructing the opening history of a set of natural fractures in the Triassic El Alamar Formation in northeast Mexico. The natural-fracture data show that, consistent with simulations, new microscopic fractures are continually introduced during natural fracture pattern evolution. As well, larger fractures represent sites of concentrated reactivation, although smaller fractures may be reactivated after long periods of quiescence. The pattern likely arises through feedback between fracture growth and the mechanically adhesive effects of contemporaneous fracture cement deposition. The narrow range in power-law exponents documented among fractures can help improve estimates of meter-scale large-fracture spacing where limited fracture samples are available.
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"Distributed estimation in wireless sensor networks under a semi-orthogonal multiple access technique." Thesis, 2014. http://hdl.handle.net/10388/ETD-2014-09-1753.

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This thesis is concerned with distributed estimation in a wireless sensor network (WSN) with analog transmission. For a scenario in which a large number of sensors are deployed under a limited bandwidth constraint, a semi-orthogonal multiple-access channelization (MAC) approach is proposed to provide transmission of observations from K sensors to a fusion center (FC) via N orthogonal channels, where K≥N. The proposed semi-orthogonal MAC can be implemented with either fixed sensor grouping or adaptive sensor grouping. The mean squared error (MSE) is adopted as the performance criterion and it is first studied under equal power allocation. The MSE can be expressed in terms of two indicators: the channel noise suppression capability and the observation noise suppression capability. The fixed version of the semi-orthogonal MAC is shown to have the same channel noise suppression capability and two times the observation noise suppression capability when compared to the orthogonal MAC under the same bandwidth resource. For the adaptive version, the performance improvement of the semi-orthogonal MAC over the orthogonal MAC is even more significant. In fact, the semi-orthogonal MAC with adaptive sensor grouping is shown to perform very close to that of the hybrid MAC, while requiring a much smaller amount of feedback. Another contribution of this thesis is an analysis of the behavior of the average MSE in terms of the number of sensors, namely the scaling law, under equal power allocation. It is shown that the proposed semi-orthogonal MAC with adaptive sensor grouping can achieve the optimal scaling law of the analog WSN studied in this thesis. Finally, improved power allocations for the proposed semi-orthogonal MAC are investigated. First, the improved power allocations in each sensor group for different scenarios are provided. Then an optimal solution of power allocation among sensor groups is obtained by the convex optimization theory, and shown to outperform equal power allocation. The issue of balancing between the performance improvement and extra feedback required by the improved power allocation is also thoroughly discussed.
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Books on the topic "Power-law scaling"

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Brisbin, Richard A. Justice Antonin Scalia and the Conservative revival. Baltimore, Md: Johns Hopkins University Press, 1997.

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Justice Antonin Scalia and the Conservative revival. Baltimore, Md: Johns Hopkins University Press, 1998.

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Thurner, Stefan, Rudolf Hanel, and Peter Klimekl. Scaling. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198821939.003.0003.

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Scaling appears practically everywhere in science; it basically quantifies how the properties or shapes of an object change with the scale of the object. Scaling laws are always associated with power laws. The scaling object can be a function, a structure, a physical law, or a distribution function that describes the statistics of a system or a temporal process. We focus on scaling laws that appear in the statistical description of stochastic complex systems, where scaling appears in the distribution functions of observable quantities of dynamical systems or processes. The distribution functions exhibit power laws, approximate power laws, or fat-tailed distributions. Understanding their origin and how power law exponents can be related to the particular nature of a system, is one of the aims of the book.We comment on fitting power laws.
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Zeitlin, Vladimir. Wave Turbulence. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198804338.003.0013.

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Main notions and ideas of wave (weak) turbulence theory are explained with the help of Hamiltonian approach to wave dynamics, and are applied to waves in RSW model. Derivation of kinetic equations under random-phase approximation is explained. Short inertia–gravity waves on the f plane, short equatorial inertia–gravity waves, and Rossby waves on the beta plane are then considered along these lines. In all of these cases, approximate solutions of kinetic equation, annihilating the collision integral, can be obtained by scaling arguments, giving power-law energy spectra. The predictions of turbulence of inertia–gravity waves on the f plane are compared with numerical simulations initialised by ensembles of random waves. Energy spectra much steeper than theoretical are observed. Finite-size effects, which prevent energy transfer from large to short scales, provide a plausible explanation. Long waves thus evolve towards breaking and shock formation, yet the number of shocks is insufficient to produce shock turbulence.
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Book chapters on the topic "Power-law scaling"

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Mochizuki, Shinsuke, Takatsugu Kameda, and Hideo Osaka. "An Experimental Study af a Self-Preserving Boundary Layer with a Power-Law Variation of Free-Stream Velocity." In IUTAM Symposium on Reynolds Number Scaling in Turbulent Flow, 297–300. Dordrecht: Springer Netherlands, 2004. http://dx.doi.org/10.1007/978-94-007-0997-3_51.

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Perez, Gabriel, Ricardo Mantilla, and Witold F. Krajewski. "Spatial Patterns of Peak Flow Quantiles Based on Power-Law Scaling in the Mississippi River Basin." In Advances in Nonlinear Geosciences, 497–518. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-58895-7_23.

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Samura, Toshikazu, Yasuomi D. Sato, Yuji Ikegaya, Hatsuo Hayashi, and Takeshi Aihara. "Power-Law Scaling of Synchronization Robustly Reproduced in the Hippocampal CA3 Slice Culture Model with Small-World Topology." In Neural Information Processing, 152–59. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-34481-7_19.

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El Boudouti, El Houssaine, Bahram Djafari-Rouhani, Abdellatif Akjouj, and Leonard Dobrzyński. "Fibonacci loop structures: bandgaps, power law, scaling law, confined and surface modes." In Photonics, 333–71. Elsevier, 2021. http://dx.doi.org/10.1016/b978-0-12-819388-4.00023-x.

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André, Maina, and Rudy Calif. "Temporal Fluctuations Scaling Analysis: Power Law of Ramp Rate’s Variance for PV Power Output." In Solar Radiation - Measurement, Modeling and Forecasting Techniques for Photovoltaic Solar Energy Applications [Working Title]. IntechOpen, 2022. http://dx.doi.org/10.5772/intechopen.99072.

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The characterization of irradiance variability needs tools to describe and quantify variability at different time scales in order to optimally integrate PV onto electrical grids. Recently in the literature, a metric called nominal variability defines the intradaily variability by the ramp rate’s variance. Here we will concentrate on the quantification of this parameter at different short time scales for tropical measurement sites which particularly exhibit high irradiance variability due to complex microclimatic context. By analogy with Taylor law performed on several complex processes, an analysis of temporal fluctuations scaling properties is proposed. The results showed that the process of intradaily variability obeys Taylor’s power law for every short time scales and several insolation conditions. The Taylor power law for simulated PV power output has been verified for very short time scale (30s sampled data) and short time scale (10 min sampled data). The exponent λ presents values between 0.5 and 0.8. Consequently, the results showed a consistency of Taylor power law for simulated PV power output. These results are a statistical perspective in solar energy area and introduce intradaily variability PV power output which are key properties of this characterization, enabling its high penetration.
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Schulman, L. S. "Power laws." In When Things Grow Many, 76–88. Oxford University PressOxford, 2022. http://dx.doi.org/10.1093/oso/9780198861881.003.0007.

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Abstract A power law is [a frequency or probability] ≡ f(x) = ax−b, where x is a variable and a and b are constants. Many distributions are alleged to have this property: words (where x is the rank), city size (where x is the rank and f the population), music, genes, and so on. Scaling properties of power laws are explored and competing distributions (e.g. log-normal) are examined. Origins of power laws are found in diffusion, “rich get richer” distributions, self-organized criticality, and many other sources.
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Sinha, Sanjeet Kumar, and Sweta Chander. "Reliability of CNTFET and NW-FET Devices." In AI Techniques for Reliability Prediction for Electronic Components, 55–66. IGI Global, 2020. http://dx.doi.org/10.4018/978-1-7998-1464-1.ch003.

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The scaling of devices is a fundamental step for advancing technology in the semiconductor industry. The device scaling allows extra components as well as devices on a single chip, which provides large functionality and application for each integrated circuit (IC). The ultimate goal of device scaling is to make each IC smaller, faster, cheaper, and consumes low power. In today's nanoscale technology, the scaling has been continued and follows Moore's law in the initial phase of fabrication and also shows an exponential growth in ICs. The silicon-based semiconductor industry has reached its scaling limits due to tunneling and quantum-mechanical effects in deep nanometer level. The physics of such devices is not going to continue and hold true. This makes nanoelectronics the leading future of the semiconductor industry. The carbon nanotubes and nanowires are the most promising candidates to make illustrated devices.
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Martin, Jeffrey T. "Holding Things Together." In Sentiment, Reason, and Law, 113–32. Cornell University Press, 2019. http://dx.doi.org/10.7591/cornell/9781501740046.003.0006.

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This chapter takes up the issue of how a police power defined, in practice, by the dialogical accommodation of disorder can effectively uphold a solidary political community. It gives insight of an ideal of balance among sentiment, reason, and law, and uses this ideal to continually renew attunement to the potentialities of worldhood that is emergent from human togetherness. The chapter also explores police involvement in “order maintenance” work. It explains how the police engage certain issues through an idiom of a balance among sentiment, reason, and law. It also shows how patrolmen rely on this idiom to do their job, and how it provides a scaling logic for reconciling the localized concerns of “paichusuo” policing with more abstract ideas about state-based order.
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Zapperi, Stefano. "Outlook." In Crackling Noise, 187–89. Oxford University PressOxford, 2022. http://dx.doi.org/10.1093/oso/9780192856951.003.0012.

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Abstract In this book, we have presented an overview of crackling noise and have discussed its interpretation in terms of underlying avalanche phenomena. We have seen that the statistical properties of crackling noise are characterized by a set of power-law distributions which can be related by scaling laws in analogy with similar relations derived for equilibrium- and non-equilibrium-critical systems. This suggests that crackling noise is a manifestation of some for of criticality of the avalanches that produce the noise. While in this book we followed the general idea that power-law distributions in crackling noise are due to critical avalanches, several other mechanisms not involving critical points have been proposed in the literature. However, none of these mechanisms of power-law generation have gained much traction in the context of crackling noise. While not all power laws in nature are a signature of a critical point, avalanche phenomena have been consistently and quantitatively interpreted using critical phenomena.
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Lyra, Marcelo L. "Nonextensive Entropies and Sensitivity to Initial Conditions of Complex Systems." In Nonextensive Entropy. Oxford University Press, 2004. http://dx.doi.org/10.1093/oso/9780195159769.003.0009.

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Tsallis generalized statistics has been successfully applied to describe some relevant features of several natural systems exhibiting a nonextensive character. It is based on an extended form for the entropy, namely S<sub>q</sub> = (1 — Σ<sub>q</sub>p<sup>Q</sup><sub>q</sub>)/(Q —1), where q is a parameter that measures the degre of nonextensivity (q→1 for the traditional Boltzmann-Gibbs statistics). A series of recent works have shown that the power-law sensitivity to initial conditions in a complex state provides a natural link between the g-entropic parameter and the scaling properties of dynamical attractors. These results contribute to the growing set of theoretical and experimental evidences that Tsallis statistics can be a natural frame for studying systems with a fractal-like structure in phase space. Here, the main ideas underlying this relevant aspect are reviewed. The starting point is the weak sensitivity to initial conditions exhibited by low-dimensional dynamical systems at the onset of chaos. It is shown how general scaling arguments can provide a direct relation between the entropic index q and the scaling exponents associated with the multifractal critical attractor. These works shed light in the elusive problem concerning the connection between the g-entropic parameter of Tsallis statistics and the underlying microscopic dynamics of nonextensive systems.... Inspired on the scaling properties of multifractals, Tsallis introduced a generalized entropy with the aim of extending the usual statistical mechanics and thermodynamics [37].
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Conference papers on the topic "Power-law scaling"

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Su, Q., Joseph H. Eberly, and W. G. Greenwood. "Channel closing and power-law scaling in multiphoton ionization." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1989. http://dx.doi.org/10.1364/oam.1989.fu3.

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We present numerical data giving the intensity dependence of the multiphoton ionization rate for two different model atoms. As the intensity increases, the pon-deromotive shift causes peaks in the electron energy spectrum to disappear, one by one, at the threshold. We carefully examine the ionization rate near to and between the intensities at which these ponderomotive channel closings occur. The data have been obtained from ab initio wave functions calculated for 1-D atoms in the presence of intense laser fields. In the first model the potential V ( x ) = − 1 / 1 + x 2 is used to simulate the one-electron binding potential of a typical atom, and in the second model the potential V ( x ) = − exp ( − | x | ) / x 2 + α 2 is used to simulate the binding potential of the extra electron in the H– negative ion. The first potential is quasicoulombic1 with long tails at large ±x and supports a Rydberg series of bound levels near the continuum limit, while the second potential is short range in nature and supports only a single bound state. Both potentials are enclosed in a box (terminated at x = ±L by rigid walls) that is large enough to support a relatively dense set of positive energy states.
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Shahidi, Ghavam. "Slow-Down in Power Scaling and the End of Moore's Law?" In 2019 International Symposium on VLSI Design, Automation and Test (VLSI-DAT). IEEE, 2019. http://dx.doi.org/10.1109/vlsi-dat.2019.8741850.

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Shahidi, Ghavam. "Slow-Down in Power Scaling and the End of Moore's Law?" In 2019 International Symposium on VLSI Technology, Systems and Application (VLSI-TSA). IEEE, 2019. http://dx.doi.org/10.1109/vlsi-tsa.2019.8804705.

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Bjornson, Emil, and Luca Sanguinetti. "Demystifying the Power Scaling Law of Intelligent Reflecting Surfaces and Metasurfaces." In 2019 IEEE 8th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP). IEEE, 2019. http://dx.doi.org/10.1109/camsap45676.2019.9022637.

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Ajam, Hedieh, Marzieh Najafi, Vahid Jamali, and Robert Schober. "Power Scaling Law for Optical IRSs and Comparison with Optical Relays." In GLOBECOM 2022 - 2022 IEEE Global Communications Conference. IEEE, 2022. http://dx.doi.org/10.1109/globecom48099.2022.10001121.

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Kolendo, Piotr, Bartosz Jaworski, and Roman Smierzchalski. "Power-law fitness function scaling in the evolutionary method of path planning." In Robotics (MMAR). IEEE, 2011. http://dx.doi.org/10.1109/mmar.2011.6031383.

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Xu, Wanyue, Yibin Sheng, Zuobai Zhang, Haibin Kan, and Zhongzhi Zhang. "Power-Law Graphs Have Minimal Scaling of Kemeny Constant for Random Walks." In WWW '20: The Web Conference 2020. New York, NY, USA: ACM, 2020. http://dx.doi.org/10.1145/3366423.3380093.

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Afzal, Noor. "Scaling of Power Law Velocity Profile in Wall-bounded Turbulent Shear Flows." In 43rd AIAA Aerospace Sciences Meeting and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2005. http://dx.doi.org/10.2514/6.2005-109.

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Murakami, Nao, and Robert Winglee. "Downstream Plasma Velocity Measurement and Scaling Law of High-Power Helicon Double Gun Thruster." In 51st AIAA/SAE/ASEE Joint Propulsion Conference. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2015. http://dx.doi.org/10.2514/6.2015-3722.

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Krapchev, Vladimir B. "Scaling laws for atmospheric thermal blooming." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1989. http://dx.doi.org/10.1364/oam.1989.ww1.

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The propagation of ground-based high energy lasers through the atmosphere leads to heating of the air due to molecular and aerosol absorption.1 This heating changes the local refractive index and the rays diverge from the center of the beam leading to thermal blooming. While the direct energy loss from absorption is small, the phase distortion from thermal blooming degrades the beam quality. To compensate for thermal blooming, one has to correct the beam phase at the transmitter. This is achieved by a closed loop adaptive optics. The conjugate of the incoming beacon phase is imposed on the outgoing laser beam. The phase compensation leads to instability, which places a limit on the critical HEL power (Pc) that can be transmitted through the atmosphere at a given beam diameter (D). The scaling law, Pc ~ Db is of critical importance for the design of a beam director. The role of the refractive index and velocity turbulence of the atmosphere have been studied. Without velocity turbulence the scaling law is Pc ~ D, and with velocity turbulence the result is Pc ~ D1.5.
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