Allometric scaling law in a simple oxygen exchanging network: possible implications on the biological allometric scaling laws

2003 ◽  
Vol 223 (2) ◽  
pp. 249-257 ◽  
Author(s):  
Moisés Santillán
Keyword(s):  
Scaling Laws ◽  
Allometric Scaling ◽  
Scaling Law

scholarly journals A Hierarchical Allometric Scaling Analysis of Chinese Cities: 1991–2014

2017 ◽  
Vol 2017 ◽  
pp. 1-15 ◽  
Author(s):  
Yanguang Chen ◽  
Jian Feng
Keyword(s):  
Scaling Laws ◽  
City Planning ◽  
Allometric Scaling ◽  
Scaling Law ◽  
Urban Systems ◽  
Long Term Memory ◽  
Scaling Analysis ◽  
Scaling Exponent ◽  
Random Disturbance ◽  
Chinese Cities

The law of allometric scaling based on Zipf distributions can be employed to research hierarchies of cities in a geographical region. However, the allometric patterns are easily influenced by random disturbance from the noises in observational data. In theory, both the allometric growth law and Zipf’s law are related to the hierarchical scaling laws associated with fractal structure. In this paper, the scaling laws of hierarchies with cascade structure are used to study Chinese cities, and the method of R/S analysis is applied to analyzing the change trend of the allometric scaling exponents. The results show that the hierarchical scaling relations of Chinese cities became clearer and clearer from 1991 to 2014 year; the global allometric scaling exponent values fluctuated around 0.85, and the local scaling exponent approached 0.85. The Hurst exponent of the allometric parameter change is greater than 0.5, indicating persistence and a long-term memory of urban evolution. The main conclusions can be reached as follows: the allometric scaling law of cities represents an evolutionary order rather than an invariable rule, which emerges from self-organized process of urbanization, and the ideas from allometry and fractals can be combined to optimize spatial and hierarchical structure of urban systems in future city planning.

scholarly journals Asymmetric Unimodal Maps with Non-universal Period-Doubling Scaling Laws

2020 ◽  
Vol 379 (1) ◽  
pp. 103-143
Author(s):  
Oleg Kozlovski ◽  
Sebastian van Strien
Keyword(s):  
Scaling Laws ◽  
Scaling Law ◽  
Period Doubling ◽  
Cantor Sets ◽  
Unimodal Maps ◽  
Renormalization Theory

Abstract We consider a family of strongly-asymmetric unimodal maps $$\{f_t\}_{t\in [0,1]}$$ { f t } t ∈ [ 0 , 1 ] of the form $$f_t=t\cdot f$$ f t = t · f where $$f:[0,1]\rightarrow [0,1]$$ f : [ 0 , 1 ] → [ 0 , 1 ] is unimodal, $$f(0)=f(1)=0$$ f ( 0 ) = f ( 1 ) = 0 , $$f(c)=1$$ f ( c ) = 1 is of the form and $$\begin{aligned} f(x)=\left\{ \begin{array}{ll} 1-K_-|x-c|+o(|x-c|)&{} \text{ for } x<c, \\ 1-K_+|x-c|^\beta + o(|x-c|^\beta ) &{} \text{ for } x>c, \end{array}\right. \end{aligned}$$ f ( x ) = 1 - K - | x - c | + o ( | x - c | ) for x < c , 1 - K + | x - c | β + o ( | x - c | β ) for x > c , where we assume that $$\beta >1$$ β > 1 . We show that such a family contains a Feigenbaum–Coullet–Tresser $$2^\infty $$ 2 ∞ map, and develop a renormalization theory for these maps. The scalings of the renormalization intervals of the $$2^\infty $$ 2 ∞ map turn out to be super-exponential and non-universal (i.e. to depend on the map) and the scaling-law is different for odd and even steps of the renormalization. The conjugacy between the attracting Cantor sets of two such maps is smooth if and only if some invariant is satisfied. We also show that the Feigenbaum–Coullet–Tresser map does not have wandering intervals, but surprisingly we were only able to prove this using our rather detailed scaling results.

scholarly journals Scaling and Similarity of the Anisotropic Coherent Eddies in Near-Surface Atmospheric Turbulence

2018 ◽  
Vol 75 (3) ◽  
pp. 943-964 ◽  
Author(s):  
Khaled Ghannam ◽  
Gabriel G. Katul ◽  
Elie Bou-Zeid ◽  
Tobias Gerken ◽  
Marcelo Chamecki
Keyword(s):  
Scaling Laws ◽  
Velocity Structure ◽  
Scaling Law ◽  
Longitudinal Velocity ◽  
Structure Functions ◽  
Length Scale ◽  
Near Surface ◽  
Vegetation Canopies ◽  
Velocity Spectra ◽  
Attached Eddies

Abstract The low-wavenumber regime of the spectrum of turbulence commensurate with Townsend’s “attached” eddies is investigated here for the near-neutral atmospheric surface layer (ASL) and the roughness sublayer (RSL) above vegetation canopies. The central thesis corroborates the significance of the imbalance between local production and dissipation of turbulence kinetic energy (TKE) and canopy shear in challenging the classical distance-from-the-wall scaling of canonical turbulent boundary layers. Using five experimental datasets (two vegetation canopy RSL flows, two ASL flows, and one open-channel experiment), this paper explores (i) the existence of a low-wavenumber k−1 scaling law in the (wind) velocity spectra or, equivalently, a logarithmic scaling ln(r) in the velocity structure functions; (ii) phenomenological aspects of these anisotropic scales as a departure from homogeneous and isotropic scales; and (iii) the collapse of experimental data when plotted with different similarity coordinates. The results show that the extent of the k−1 and/or ln(r) scaling for the longitudinal velocity is shorter in the RSL above canopies than in the ASL because of smaller scale separation in the former. Conversely, these scaling laws are absent in the vertical velocity spectra except at large distances from the wall. The analysis reveals that the statistics of the velocity differences Δu and Δw approach a Gaussian-like behavior at large scales and that these eddies are responsible for momentum/energy production corroborated by large positive (negative) excursions in Δu accompanied by negative (positive) ones in Δw. A length scale based on TKE dissipation collapses the velocity structure functions at different heights better than the inertial length scale.

scholarly journals An allometric scaling law in plants

2008 ◽  
Vol 96 ◽  
pp. 012179 ◽  
Author(s):  
J H He ◽  
L-F Mo
Keyword(s):  
Allometric Scaling ◽  
Scaling Law

scholarly journals Origin of the scaling laws of sediment transport

2017 ◽  
Vol 473 (2197) ◽  
pp. 20160785 ◽  
Author(s):  
Sk Zeeshan Ali ◽  
Subhasish Dey
Keyword(s):  
Sediment Transport ◽  
Froude Number ◽  
Scaling Laws ◽  
Scaling Law ◽  
Bedload Transport ◽  
Inertial Range ◽  
Channel Width ◽  
Densimetric Froude Number ◽  
Relative Roughness ◽  
Contraction Ratio

In this paper, we discover the origin of the scaling laws of sediment transport under turbulent flow over a sediment bed, for the first time, from the perspective of the phenomenological theory of turbulence. The results reveal that for the incipient motion of sediment particles, the densimetric Froude number obeys the ‘(1 +  σ )/4’ scaling law with the relative roughness (ratio of particle diameter to approach flow depth), where σ is the spectral exponent of turbulent energy spectrum. However, for the bedforms, the densimetric Froude number obeys a ‘(1 +  σ )/6’ scaling law with the relative roughness in the enstrophy inertial range and the energy inertial range. For the bedload flux, the bedload transport intensity obeys the ‘3/2’ and ‘(1 +  σ )/4’ scaling laws with the transport stage parameter and the relative roughness, respectively. For the suspended load flux, the non-dimensional suspended sediment concentration obeys the ‘ − Z ’ scaling law with the non-dimensional vertical distance within the wall shear layer, where Z is the Rouse number. For the scour in contracted streams, the non-dimensional scour depth obeys the ‘4/(3 −  σ )’, ‘−4/(3 −  σ )’ and ‘−(1 +  σ )/(3 −  σ )’ scaling laws with the densimetric Froude number, the channel contraction ratio (ratio of contracted channel width to approach channel width) and the relative roughness, respectively.

scholarly journals Scaling laws and warning signs for bifurcations of SPDEs

2018 ◽  
Vol 30 (5) ◽  
pp. 853-868
Author(s):  
CHRISTIAN KUEHN ◽  
FRANCESCO ROMANO
Keyword(s):  
Differential Equations ◽  
Scaling Laws ◽  
Scaling Law ◽  
Warning Signs ◽  
Covariance Operator ◽  
Large Classes ◽  
Practical Applications ◽  
Critical Transitions ◽  
Degenerate Eigenvalues ◽  
Adjoint Operators

Critical transitions (or tipping points) are drastic sudden changes observed in many dynamical systems. Large classes of critical transitions are associated with systems, which drift slowly towards a bifurcation point. In the context of stochastic ordinary differential equations, there are results on growth of variance and autocorrelation before a transition, which can be used as possible warning signs in applications. A similar theory has recently been developed in the simplest setting for stochastic partial differential equations (SPDEs) for self-adjoint operators in the drift term. This setting leads to real discrete spectrum and growth of the covariance operator via a certain scaling law. In this paper, we develop this theory substantially further. We cover the cases of complex eigenvalues, degenerate eigenvalues as well as continuous spectrum. This provides a fairly comprehensive theory for most practical applications of warning signs for SPDE bifurcations.

Scaling Laws From Statistical Data and Dimensional Analysis

2004 ◽  
Vol 72 (5) ◽  
pp. 648-657 ◽  
Author(s):  
Patricio F. Mendez ◽  
Fernando Ordóñez
Keyword(s):  
Dimensional Analysis ◽  
Scaling Laws ◽  
Ad Hoc ◽  
Scaling Law ◽  
Engineering Systems ◽  
User Input ◽  
Backward Elimination ◽  
Dimensionless Groups ◽  
Complex Engineering ◽  
Complex Engineering Systems

Scaling laws provide a simple yet meaningful representation of the dominant factors of complex engineering systems, and thus are well suited to guide engineering design. Current methods to obtain useful models of complex engineering systems are typically ad hoc, tedious, and time consuming. Here, we present an algorithm that obtains a scaling law in the form of a power law from experimental data (including simulated experiments). The proposed algorithm integrates dimensional analysis into the backward elimination procedure of multivariate linear regressions. In addition to the scaling laws, the algorithm returns a set of dimensionless groups ranked by relevance. We apply the algorithm to three examples, in each obtaining the scaling law that describes the system with minimal user input.

Determination method of dynamic distorted scaling laws and applicable structure size intervals of a rotating thin-wall short cylindrical shell

2014 ◽  
Vol 229 (5) ◽  
pp. 806-817 ◽  
Author(s):  
Z Luo ◽  
YP Zhu ◽  
XY Zhao ◽  
DY Wang
Keyword(s):  
Cylindrical Shell ◽  
Scaling Laws ◽  
Good Accuracy ◽  
Scaling Law ◽  
Thin Wall ◽  
Determination Method ◽  
Governing Equations ◽  
7050 Aluminum Alloy ◽  
Boundary Functions

This study investigates the applicability of distortion models for predicting dynamic characteristics of a rotating thin-wall short cylindrical shell. The significance of this study is that it provides a necessary scaling law, applicable structure size intervals, and its boundary functions, which can guide the design of distortion models. Sensitivity analysis and governing equations are employed to establish the scaling law between the model and the prototype. Then a commonly used 7050 aluminum alloy cylindrical shell is analyzed as a prototype. The determination of applicable structure size intervals is discussed, and the boundary functions of the applicable structure size intervals are investigated. The applicability of the scaling law and the applicable intervals of rotating thin-wall short cylindrical shell are verified numerically. The results indicate that distortion models that satisfy the structure size applicable intervals can predict the characteristics of the prototype with good accuracy.

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