Fractal properties of inertial-range turbulence with implications for aircraft response

1988 ◽  
Vol 92 (918) ◽  
pp. 301-308 ◽  
Author(s):  
J. G. Jones ◽  
G. W. Foster ◽  
A. Haynes
Keyword(s):  
Probability Distributions ◽  
Scale Dependence ◽  
Self Similarity ◽  
Scale Invariant ◽  
First Approximation ◽  
Fractal Properties ◽  
Fractal Process ◽  
Measured Probability ◽  
Turbulence Velocity ◽  
Gust Response

Summary Fractal geometry provides a method for modelling the scale dependence of fluctuations in atmospheric-turbulence velocity. In this paper the basic concepts are outlined and illustrated by a method of data analysis which, for a fractal process, displays measured probability distributions in scale-invariant form. To a first approximation the data exhibit statistical self-similarity, consistent with the classical theory of Kolmogorov. However, on more detailed analysis, the more intense fluctuations show systematic departures from self-similarity, consistent with recent theoretical estimates of the fractal dimension of the support of turbulence. Implications for aircraft gust response are discussed.

scholarly journals Graph fractal dimension and the structure of fractal networks

2020 ◽  
Vol 8 (4) ◽  
Author(s):  
Pavel Skums ◽  
Leonid Bunimovich
Keyword(s):  
Complex Networks ◽  
Evolutionary Biology ◽  
Real Life ◽  
Fractal Dimensions ◽  
Network Models ◽  
Self Similarity ◽  
Descriptive Complexity ◽  
Network Communities ◽  
Fractal Properties ◽  
Continuous Objects

Abstract Fractals are geometric objects that are self-similar at different scales and whose geometric dimensions differ from so-called fractal dimensions. Fractals describe complex continuous structures in nature. Although indications of self-similarity and fractality of complex networks has been previously observed, it is challenging to adapt the machinery from the theory of fractality of continuous objects to discrete objects such as networks. In this article, we identify and study fractal networks using the innate methods of graph theory and combinatorics. We establish analogues of topological (Lebesgue) and fractal (Hausdorff) dimensions for graphs and demonstrate that they are naturally related to known graph-theoretical characteristics: rank dimension and product dimension. Our approach reveals how self-similarity and fractality of a network are defined by a pattern of overlaps between densely connected network communities. It allows us to identify fractal graphs, explore the relations between graph fractality, graph colourings and graph descriptive complexity, and analyse the fractality of several classes of graphs and network models, as well as of a number of real-life networks. We demonstrate the application of our framework in evolutionary biology and virology by analysing networks of viral strains sampled at different stages of evolution inside their hosts. Our methodology revealed gradual self-organization of intra-host viral populations over the course of infection and their adaptation to the host environment. The obtained results lay a foundation for studying fractal properties of complex networks using combinatorial methods and algorithms.

scholarly journals On the fractal nature of complex syntax and the timescale problem

2020 ◽  
Vol 10 (4) ◽  
pp. 697-721
Author(s):  
D. Reid Evans
Keyword(s):  
Complex Systems ◽  
Dynamic Systems Theory ◽  
Self Similarity ◽  
Scale Invariant ◽  
Complex Dynamic Systems ◽  
Complex Syntax ◽  
Dynamic Relationship ◽  
Self Similar ◽  
Multiple Component ◽  
Dynamic Relationships

Fundamental to complex dynamic systems theory is the assumption that the recursive behavior of complex systems results in the generation of physical forms and dynamic processes that are self-similar and scale-invariant. Such fractal-like structures and the organismic benefit that they engender has been widely noted in physiology, biology, and medicine, yet discussions of the fractal-like nature of language have remained at the level of metaphor in applied linguistics. Motivated by the lack of empirical evidence supporting this assumption, the present study examines the extent to which the use and development of complex syntax in a learner of English as a second language demonstrate the characteristics of self-similarity and scale invariance at nested timescales. Findings suggest that the use and development of syntactic complexity are governed by fractal scaling as the dynamic relationship among the subconstructs of syntax maintain their complexity and variability across multiple temporal scales. Overall, fractal analysis appears to be a fruitful analytic tool when attempting to discern the dynamic relationships among the multiple component parts of complex systems as they interact over time.

Spatial Distribution and Fractal Properties of Aggregating Magnetic and Non-Magnetic Particles

Fractals ◽  
1998 ◽  
Vol 06 (03) ◽  
pp. 219-230 ◽  
Author(s):  
A. Provata ◽  
K. N. Trohidou
Keyword(s):  
Spatial Distribution ◽  
Fractal Dimension ◽  
Magnetic Particles ◽  
Composite System ◽  
System Size ◽  
Real Space ◽  
Magnetic Clusters ◽  
Self Similarity ◽  
Fractal Properties ◽  
Simple Connectivity

We study the spatial distribution in aggregating systems of mixtures of magnetic and non-magnetic particles using Monte-Carlo simulations together with scaling arguments. In particular, we show that (a) as the system size grows, the fractal dimension of the composite system is dominated by the smaller fractal dimension, (b) the system is realized as a back-bone consisting of magnetic particles (lower fractal dimension) with denser regions of non-magnetic particles attached to it at random positions. Using simple connectivity features observed in pure magnetic and non-magnetic clusters and self-similarity arguments we predict, via Real-Space-Renormalization, fractal exponents Dm = 1.25 ± 0.05 for the magnetic clusters and Dnm = 1.4 ± 0.1 for the non-magnetic clusters.

scholarly journals Family of probability distributions derived from maximal entropy principle with scale invariant restrictions

2013 ◽  
Vol 87 (1) ◽  
Author(s):  
Giorgio Sonnino ◽  
György Steinbrecher ◽  
Alessandro Cardinali ◽  
Alberto Sonnino ◽  
Mustapha Tlidi
Keyword(s):  
Probability Distributions ◽  
Maximal Entropy ◽  
Scale Invariant ◽  
Entropy Principle

scholarly journals The P-wave charmonium annihilation into two photons $$\chi _{c0, c2}\rightarrow \gamma \gamma $$ with high-order QCD corrections

2021 ◽  
Vol 81 (7) ◽  
Author(s):  
Hua Zhou ◽  
Qing Yu ◽  
Xu-Dong Huang ◽  
Xu-Chang Zheng ◽  
Xing-Gang Wu
Keyword(s):  
Perturbative Qcd ◽  
Scale Dependence ◽  
High Order ◽  
P Wave ◽  
Leading Order ◽  
Scale Invariant ◽  
Central Value ◽  
Setting Approach ◽  
Belle Ii ◽  
Principle Of Maximum

AbstractIn this paper, we present a new analysis on the P-wave charmonium annihilation into two photons up to next-to-next-to-leading order (NNLO) QCD corrections by using the principle of maximum conformality (PMC). The conventional perturbative QCD prediction shows strong scale dependence and deviates largely from the BESIII measurements. After applying the PMC, we obtain a more precise scale-invariant pQCD prediction, which also agrees with the BESIII measurements within errors, i.e. $$R={\Gamma _{\gamma \gamma }(\chi _{c2})} /{\Gamma _{\gamma \gamma }(\chi _{c0})}=0.246\pm 0.013$$ R = Γ γ γ ( χ c 2 ) / Γ γ γ ( χ c 0 ) = 0.246 ± 0.013 , where the error is for $$\Delta \alpha _s(M_\tau )=\pm 0.016$$ Δ α s ( M τ ) = ± 0.016 . By further considering the color-octet contributions, even the central value can be in agreement with the data. This shows the importance of a correct scale-setting approach. We also give a prediction for the ratio involving $$\chi _{b0, b2} \rightarrow \gamma \gamma $$ χ b 0 , b 2 → γ γ , which could be tested in future Belle II experiment.

Discrimination performance of single neurons: rate and temporal-pattern information

1991 ◽  
Vol 66 (1) ◽  
pp. 334-362 ◽  
Author(s):  
W. S. Geisler ◽  
D. G. Albrecht ◽  
R. J. Salvi ◽  
S. S. Saunders
Keyword(s):  
Visual Cortex ◽  
Auditory Nerve ◽  
Probability Distributions ◽  
Discrimination Performance ◽  
Counting Method ◽  
Phase Discrimination ◽  
Temporal Phase ◽  
Measured Probability ◽  
Pattern Information ◽  
Temporal Offset

1. A new method of measuring the performance of neurons in sensory discrimination tasks was developed and then applied to single-neuron responses recorded in the auditory nerve of chinchilla and in the striate visual cortex of cat. 2. Most previous methods of measuring discrimination performance have employed decision rules that involve comparing the total counts of action potentials (spikes) produced by two different stimuli. Such measures ignore response pattern and hence may not reflect all the information transmitted by a neuron. The proposed method attempts to measure all (or most) of the transmitted information by constructing descriptive models of the neuron's response to each stimulus in the discrimination experiment; these descriptive models consist of measured probability distributions of the spike counts in small time bins. The measured probability distributions are then used to define an optimal decision rule (an ideal observer) for discriminating the two stimuli. Finally, discrimination performance is measured by applying this decision rule to novel presentations of the same two stimuli. 3. Intensity and temporal-phase discrimination were measured for three neurons in the auditory nerve of chinchilla. The discrimination stimuli were low-frequency pure tones of 70-ms duration. Intensity thresholds were found to be 5–20 dB lower at low intensities using the new pattern method compared with the traditional counting method. The pattern method led to better performance because it utilized both rate and temporal pattern information. Phase discrimination performance using the counting method was at chance because the average spike rate did not change with phase. On the other hand, using the pattern method, phase discrimination thresholds were found to decrease with intensity, often reaching values equivalent to 30–40 microseconds of temporal offset. These thresholds are as good as or better than behavioral thresholds in chinchilla. 4. Contrast and temporal-phase discrimination were measured for three neurons in the striate visual cortex of cat. The discrimination stimuli were drifting sine-wave gratings of 100- to 160-ms duration. Contrast discrimination functions measured by the pattern method and the counting method were found to be essentially identical. Phase discrimination using the counting method was at chance. However, using the pattern method, phase thresholds were found to decrease with contrast, reaching values equivalent to 7 ms of temporal offset for the two simple cells. 5. Our results suggest that temporal response pattern carries substantial information for intensity and phase discrimination in the auditory nerve and for phase discrimination in the striate visual cortex.(ABSTRACT TRUNCATED AT 400 WORDS)

scholarly journals A nonextensive entropy path to probability distributions in solar wind turbulence

2005 ◽  
Vol 12 (2) ◽  
pp. 171-180 ◽  
Author(s):  
M. P. Leubner ◽  
Z. Vörös
Keyword(s):  
Solar Wind ◽  
Long Range ◽  
Large Scale ◽  
Probability Distributions ◽  
Spatial Separation ◽  
Scale Dependence ◽  
Small Scale ◽  
Time Lags ◽  
Turbulent Fluctuations ◽  
Long Range Interactions

Abstract. The observed scale dependence of the probability distributions of the differences of characteristic solar wind variables is analyzed. Intermittency of the turbulent fluctuations at small-scale spatial separations is accompanied by strongly non-Gaussian distributions that turn into a normal distribution for large-scale separation. Conventional theoretical models are subject to insufficient physical justification since nonlocality in turbulence should be based on long-range interactions, provided recently by the bi-kappa distribution in the context of nonextensive thermo-statistics. Observed WIND and ACE probability distributions are accurately reproduced for different time lags by the one-parameter bi-kappa functional, a core-halo convolution, where kappa measures the degree of nonlocality or nonextensivity in the system. Gradual decoupling is obtained by enhancing the spatial separation scale corresponding to increasing kappa values, where a Gaussian is approached for infinite kappa. Consequently, long-range interactions introduced on the fundamental level of entropy generalization, are able to provide physically the source of the observed scale dependence of the turbulent fluctuations in the intermittent interplanetary medium.

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