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 The effect of dragon-kings on the estimation of scaling law parameters

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Carmen Cabrera-Arnau ◽  
Steven R. Bishop
Keyword(s):  
Traffic Accidents ◽  
Scaling Laws ◽  
Road Traffic ◽  
House Prices ◽  
Scaling Law ◽  
Large Population ◽  
Estimation Procedure ◽  
Urban Systems ◽  
Scaling Analysis ◽  
Scaling Parameters

AbstractScaling laws are used to model how different quantifiable properties of cities, such as the number of road traffic accidents or average house prices, vary as a function of city population size, with parameters estimated from data. Arcaute et al. raised the issue of whether specific cities with extremely large population sizes, known as dragon-kings, should be considered separately from other smaller cities when estimating the scaling law parameters since the two types of cities tend to display different behaviour. Through the analysis of randomly generated samples, we find that the inclusion of dragon-kings in the scaling analysis does not affect the estimated values for the parameters but only provided that all the data points satisfy the same scaling law. We also analyse randomly generated samples where data corresponding to a particular city deviates from the scaling law followed by the rest of the cities. We then show that deviations corresponding to dragon-king cities have the most significant effect on the estimated values of the scaling parameters. The extent of this effect also depends on which estimation procedure is used. Our results have important implications on the suitability of scaling laws as a model for urban systems.

scholarly journals HYDRODYNAMIC SCALING ANALYSIS OF NUCLEAR FUSION DRIVEN BY ULTRA-INTENSE LASER-PLASMA INTERACTIONS

2012 ◽  
Vol 21 (12) ◽  
pp. 1250102 ◽  
Author(s):  
SACHIE KIMURA ◽  
ALDO BONASERA
Keyword(s):  
Laser Plasma ◽  
Laser Power ◽  
Scaling Laws ◽  
Scaling Law ◽  
Intense Laser ◽  
Scaling Analysis ◽  
Plasma Interactions ◽  
Laser Plasma Interactions ◽  
Hydrodynamic Scaling ◽  
Fusion Yield

We discuss scaling laws of fusion yields generated by laser-plasma interactions. The yields are found to scale as a function of the laser power. The origin of the scaling law in the laser driven fusion yield is derived in terms of hydrodynamic scaling. We point out that the scaling properties can be attributed to the laser power dependence of three terms: the reaction rate, the density of the plasma and the projected range of the plasma particle in the target medium. The resulting scaling relations have a predictive power that enables estimating the fusion yield for a nuclear reaction which has not been investigated by means of the laser accelerated ion beams.

Elimination of an isolated pore: Effect of grain size

1995 ◽  
Vol 10 (4) ◽  
pp. 1000-1015 ◽  
Author(s):  
Wan Y. Shih ◽  
Wei-Heng Shih ◽  
Ilhan A. Aksay
Keyword(s):  
Grain Size ◽  
Monte Carlo ◽  
Sample Size ◽  
Scaling Laws ◽  
Pore Diameter ◽  
Scaling Law ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Scaling Analysis ◽  
Scaling Relationships

The effect of grain size on the elimination of an isolated pore was investigated both by the Monte Carlo simulations and by a scaling analysis. The Monte Carlo statistical mechanics model for sintering was constructed by mapping microstructures onto domains of vectors of different orientations as grains and domains of vacancies as pores. The most distinctive feature of the simulations is that we allow the vacancies to move. By incorporating the outer surfaces of the sample in the simulations, sintering takes place via vacancy diffusion from the pores to the outer sample surfaces. The simulations were performed in two dimensions. The results showed that the model is capable of displaying various sintering phenomena such as evaporation and condensation, rounding of a sharp corner, pore coalescence, thermal etching, neck formation, grain growth, and growth of large pores. For the elimination of an isolated pore, the most salient result is that the scaling law of the pore elimination time tp with respect to the pore diameter dp changes as pore size changes from larger than the grains to smaller than the grains. For example, in sample-size-fixed simulations, tp ∼ d3p for dp < G and tp ∼ d2p for dp > G with the crossover pore diameter dc increasing linearly with G where G is the average grain diameter. For sample-size-scaled simulations, tp ∼ d4p for dp < G and tp ∼ d3p for dp > G. That tp has different scaling laws in different grain-size regimes is a result of grain boundaries serving as diffusion channels in a fine-grain microstructure such as those considered in the simulations. A scaling analysis is provided to explain the scaling relationships among tp, dp, and G obtained in the simulations. The scaling analysis also shows that these scaling relationships are independent of the dimensionality. Thus, the results of the two-dimensional simulations should also apply in three dimensions.

Allometric scaling of wall shear stress from mice to humans: quantification using cine phase-contrast MRI and computational fluid dynamics

2006 ◽  
Vol 291 (4) ◽  
pp. H1700-H1708 ◽  
Author(s):  
Joan M. Greve ◽  
Andrea S. Les ◽  
Beverly T. Tang ◽  
Mary T. Draney Blomme ◽  
Nathan M. Wilson ◽  
...  
Keyword(s):  
Shear Stress ◽  
Magnetic Resonance ◽  
Wall Shear Stress ◽  
Cardiovascular System ◽  
Phase Contrast ◽  
Scaling Laws ◽  
Allometric Scaling ◽  
Scaling Exponent ◽  
Infrarenal Aorta ◽  
Wall Shear

Allometric scaling laws relate structure or function between species of vastly different sizes. They have rarely been derived for hemodynamic parameters known to affect the cardiovascular system, e.g., wall shear stress (WSS). This work describes noninvasive methods to quantify and determine a scaling law for WSS. Geometry and blood flow velocities in the infrarenal aorta of mice and rats under isoflurane anesthesia were quantified using two-dimensional magnetic resonance angiography and phase-contrast magnetic resonance imaging at 4.7 tesla. Three-dimensional models constructed from anatomic data were discretized and used for computational fluid dynamic simulations using phase-contrast velocity imaging data as inlet boundary conditions. WSS was calculated along the infrarenal aorta and compared between species to formulate an allometric equation for WSS. Mean WSS along the infrarenal aorta was significantly greater in mice and rats compared with humans (87.6, 70.5, and 4.8 dyn/cm2, P < 0.01), and a scaling exponent of −0.38 ( R2 = 0.92) was determined. Manipulation of the murine genome has made small animal models standard surrogates for better understanding the healthy and diseased human cardiovascular system. It has therefore become increasingly important to understand how results scale from mouse to human. This noninvasive methodology provides the opportunity to serially quantify changes in WSS during disease progression and/or therapeutic intervention.

Urban scaling in rapidly urbanising China

Urban Studies ◽  
2021 ◽  
pp. 004209802110178
Author(s):  
Weiqian Lei ◽  
Limin Jiao ◽  
Gang Xu ◽  
Zhengzi Zhou
Keyword(s):  
Urban Population ◽  
Economies Of Scale ◽  
Scaling Laws ◽  
Temporal Evolution ◽  
Urban System ◽  
Scaling Analysis ◽  
Scaling Exponent ◽  
Scaling Exponents ◽  
Economic Output ◽  
Urban Scaling

Understanding the scaling characteristics in China is critical for perceiving the development process of rapidly urbanising countries. This paper conducts a comprehensive scaling analysis with quantitative assessment of a large number of diverse urban indicators of 275 Chinese cities. Our findings confirm that urban scaling laws can also be applied to rapidly urbanising China but demonstrate some unique features echoing its distinct urbanisation. Chinese urban population agglomeration results in more effective economic production but the economies of scale for infrastructure are less obvious. Some urban indicators associated with infrastructure and living facilities surprisingly scale super-linearly with urban population size, contrary to expected sublinear scaling behaviours. In developing countries, different-sized cities have diverse agglomeration, industrial and resource allocation advantages, which can be reflected by scaling exponents. We characterise these unique features in detail, exploring the spatial disparities and temporal evolution of scaling exponents ( β). Strong regional variations and differences are particularly pronounced in Northeast China and the Beijing-Tianjin-Hebei Urban Agglomeration. Scaling exponent variations over time reflect the temporal evolution of the urban system and measure the coordination and balance of urbanisation. Economic output was most efficient in 2009 and β of GDP was slightly greater than 1.15 in recent years. Urban land expansion has been accelerating since 2000 with β remaining around 0.85–0.90. The study of urban scaling in China is enlightening in elaborating the uniqueness and coordination of urban development in rapidly urbanising countries and provides support in formulating differentiated urban planning for different-sized cities to promote coordinated development.

SCALING LAW OF SUPERFLUID–INSULATOR TRANSITION IN THE 1D BOSE–HUBBARD MODEL

2012 ◽  
Vol 26 (04) ◽  
pp. 1250014 ◽  
Author(s):  
SHI-JIAN GU ◽  
JUNPENG CAO ◽  
SHU CHEN ◽  
HAI-QING LIN
Keyword(s):  
Hubbard Model ◽  
Critical Point ◽  
Scaling Laws ◽  
Scaling Law ◽  
Finite Size ◽  
Superfluid Density ◽  
Insulator Transition ◽  
Scaling Analysis ◽  
Finite Size Scaling ◽  
Size Scaling

The finite size scaling behavior of superfluid–insulator transition in the one-dimensional Bose–Hubbard model is studied. It is shown that the superfluid density of the system with finite size has a maximum at a certain interaction Um and the derivative of superfluid density has a minimum at a certain interaction Ud. The critical point Uc can be quantified by the scaling analysis of either Um or Ud. The transition point Um tends to the critical point Uc from the region of U < Uc, while the Ud tends to the Uc from the region of U > Uc. The transition points Um and Ud satisfy different finite size scaling laws and have the different critical exponents. The divergence speed of the superfluid density is much smaller than that of its derivative at the critical point.

Urban scaling and the geographic concentration of inequalities by city size

2018 ◽  
Vol 46 (9) ◽  
pp. 1627-1644 ◽  
Author(s):  
Somwrita Sarkar
Keyword(s):  
Urban Policy ◽  
Scaling Laws ◽  
City Size ◽  
Urban Systems ◽  
Scaling Analysis ◽  
Middle Income ◽  
Income Distributions ◽  
Spatial Inequalities ◽  
Housing Costs ◽  
Urban Scaling

Urban scaling laws summarise how socio-economic behaviours of urban systems may be predicted from city size. While most scaling analysis rests on using aggregate quantities (total incomes, GDP, etc.), examining distributions of these aggregate quantities (e.g. income distributions) could shed light on how socio-economic inequalities may correlate or be causally linked to city size. In this direction, this paper examines how geographic distributions and spatial inequalities of income and housing costs vary by city size. The paper presents three principal results. First, it brings out qualitative implications of quantitative scaling by relating scaling of the distributions of income and housing costs to their specific geographic concentrations. Second, it shows that some small and medium sized cities are clear outliers, showing behaviour similar to the largest cities and starkly different from the behaviours of the bulk of small and medium sized cities. Third, this above observation explains why heteroscedasticity, or large and heterogeneous fluctuations, are frequently observed in urban indicator data when plotted as a function of city size. Putting together these three results, overall, it is shown that income distributions and housing costs scale and concentrate in cities by size in a predictable way, where the largest cities superlinearly/disproportionately agglomerate the highest income earners and the highest housing costs, and show relatively lower concentrations of low-middle income earners and low-medium housing costs. In contrast, most of the smaller and medium sized cities show a ‘flipped’ opposite trend. A few small and medium sized cities are outliers: they show trends that match those of the largest cities, due to specialisations of economic functions or concentrations of high-paying occupations in these cities. The empirical findings lead to a discussion on the objective and normative relationships between city size and urban inequalities. It is suggested that due to the concentrations of high income and high housing costs, largest cities may have a resulting housing market structure that will push out lower and medium income earners, thereby making affordability, diversity, and socio-spatial justice emerge as important urban policy issues.

SCALING ANALYSIS OF THE A-PHASE DYNAMICS DURING SLEEP

Fractals ◽  
2020 ◽  
Vol 28 (02) ◽  
pp. 2050050
Author(s):  
V. E. ARCE-GUEVARA ◽  
M. O. MENDEZ ◽  
J. S. MURGUÍA ◽  
A. ALBA ◽  
H. GONZÁLEZ-AGUILAR ◽  
...  
Keyword(s):  
Binary Sequence ◽  
Fluctuation Analysis ◽  
Scaling Analysis ◽  
Scaling Exponent ◽  
Sleep State ◽  
Phase Dynamics ◽  
A Value ◽  
Sleep Condition ◽  
Detrended Fluctuation

In this work, the scaling behavior of the sleep process is evaluated by using detrended fluctuation analysis based on wavelets. The analysis is carried out from arrivals of short and recurrent cortical events called A-phases, which in turn build up the Cyclic Alternating Pattern phenomenon, and are classified in three types: A1, A2 and A3. In this study, 61 sleep recordings corresponding to healthy, nocturnal frontal lobe epilepsy patients and sleep-state misperception subjects, were analyzed. From the A-phase annotations, the onsets were extracted and a binary sequence with one second resolution was generated. An item in the sequence has a value of one if an A-phase onset occurs in the corresponding window, and a value of zero otherwise. In addition, we consider other different temporal resolutions from 2[Formula: see text]s to 256[Formula: see text]s. Furthermore, the same analysis was carried out for sequences obtained from the different types of A-phases and their combinations. The results of the numerical analysis showed a relationship between the time resolutions and the scaling exponents; specifically, for higher time resolutions a white noise behavior is observed, whereas for lower time resolutions a behavior towards to [Formula: see text]-noise is exhibited. Statistical differences among groups were observed by applying various wavelet functions from the Daubechies family and choosing the appropriate sequence of A-phase onsets. This scaling analysis allows the characterization of the free-scale dynamic of the sleep process that is specific for each sleep condition. The scaling exponent could be useful as a diagnosis parameter in clinics when sleep macrostructure does not offer enough information.

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