scholarly journals Universal scaling of human flow remain unchanged during the COVID-19 pandemic

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Yohei Shida ◽  
Hideki Takayasu ◽  
Shlomo Havlin ◽  
Misako Takayasu
Keyword(s):  
Mobile Phone ◽  
Exponential Distribution ◽  
Scaling Laws ◽  
Drainage Basin ◽  
Transportation Network ◽  
Scaling Law ◽  
Basic Structure ◽  
Flow Patterns ◽  
Flow Features ◽  
Human Flow

AbstractTo prevent the spread of the COVID-19 pandemic, governments in various countries have severely restricted the movement of people. The large amount of detailed human location data obtained from mobile phone users is useful for understanding the change of flow patterns of people under the effect of pandemic. In this paper, we observe the synchronized human flow during the COVID-19 pandemic using Global Positioning System data of about 1 million people obtained from mobile phone users. We apply the drainage basin analysis method which we introduced earlier for characterization of macroscopic human flow patterns to observe the effect of the spreading pandemic. Before the pandemic the afternoon basin size distribution has been approximated by an exponential distribution, however, the distribution of Tokyo and Sapporo, which were most affected by the first wave of COVID-19, deviated significantly from the exponential distribution. On the other hand, during the morning rush hour, the scaling law holds universally, i.e., in all cities, even though the number of moving people in the basin has decreased significantly. The fact that these scaling laws, which are closely related to the three-dimensionality structure of the city and the fractal structure of the transportation network, have not changed indicates that the macroscopic human flow features are determined mainly by the means of transport and the basic structure of cities which are invariant of the pandemic.

scholarly journals Universal scaling laws of collective human flow patterns in urban regions

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Yohei Shida ◽  
Hideki Takayasu ◽  
Shlomo Havlin ◽  
Misako Takayasu
Keyword(s):  
Mobile Phones ◽  
Scaling Laws ◽  
River Flow ◽  
Drainage Basin ◽  
Flow Patterns ◽  
Dimensional Structure ◽  
3 Dimensional ◽  
Universal Scaling ◽  
Urban Regions ◽  
Human Flow

AbstractDetail observation of human locations became available recently by the development of information technology such as mobile phones with GPS (Global Positioning System). We analyzed temporal changes of global human flow patterns in urban regions based on mobile phones’ GPS data in 9 large cities in Japan. By applying a new concept of drainage basins in analogous to river flow patterns, we discovered several universal scaling relations. These include, the number of moving people in a drainage basin of diameter L is proportional to $$L^3$$ L 3 in the morning rush hour, which is surprisingly different from reasonable intuition of proportionality to the 2 dimensional area, $$L^2$$ L 2 . We show that this unexpected 3 dimensional feature is related to the strong attraction of the city center to become a 3 dimensional structure due skyscrapers.

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 Can We Map-Match Individual Cellular Network Signaling Trajectories in Urban Environments? Data-Driven Study

2019 ◽  
Vol 2673 (7) ◽  
pp. 74-88 ◽  
Author(s):  
Loïc Bonnetain ◽  
Angelo Furno ◽  
Jean Krug ◽  
Nour-Eddin El Faouzi
Keyword(s):  
Mobile Phone ◽  
Cellular Network ◽  
Travel Demand ◽  
Transportation Network ◽  
Urban Environments ◽  
Network Control ◽  
Mobile Phone Data ◽  
Transport Systems ◽  
Spatiotemporal Scales ◽  
Temporal Dimensions

Mobile phone data collected by network operators can provide fundamental insights into individual and aggregate mobility of people, at unprecedented spatiotemporal scales. However, traditional call detail records (CDR) have fundamental issues because of low accuracy in both spatial and temporal dimensions, which limits their applicability for detailed studies on mobility, especially in urban scenarios. This paper focuses on a new generation of mobile phone passive data, individual cellular network signaling data, characterized by higher spatiotemporal resolutions than traditional CDR. A framework based on unsupervised hidden Markov model is designed for map-matching such data on a multimodal transportation network, aimed at accurately inferring the complex multimodal travel itineraries and popular paths people follow in their urban daily mobility. This information, especially if computed at large spatiotemporal scales, can represent a solid basis for studying actual and dynamic travel demand, to properly dimension multimodal transport systems and even perform anomaly detection and adaptive network control. The approach is evaluated in a case study based on real cellular traces collected by a major French operator in the city of Lyon, and a validation study at both microscopic and macroscopic levels proposed. The results show that this approach can properly handle sparse and noisy cell phone trajectories in complex urban environments. Moreover, the results are promising concerning popular paths detection and reconstruction of origin–destination matrices.

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.

scholarly journals Modelled fracture and calving on the Totten Ice Shelf

2018 ◽  
Vol 12 (7) ◽  
pp. 2401-2411 ◽  
Author(s):  
Sue Cook ◽  
Jan Åström ◽  
Thomas Zwinger ◽  
Benjamin Keith Galton-Fenzi ◽  
Jamin Stevens Greenbaum ◽  
...  
Keyword(s):  
Sea Level ◽  
Drainage Basin ◽  
Element Model ◽  
Fracture Pattern ◽  
Current Position ◽  
Ice Shelf ◽  
Wide Range ◽  
Grounding Line ◽  
Flow Features ◽  
Calving Rate

Abstract. The Totten Ice Shelf (IS) has a large drainage basin, much of which is grounded below sea level, leaving the glacier vulnerable to retreat through the marine ice sheet instability mechanism. The ice shelf has also been shown to be sensitive to changes in calving rate, as a very small retreat of the calving front from its current position is predicted to cause a change in flow at the grounding line. Therefore understanding the processes behind calving on the Totten IS is key to predicting its future sea level rise contribution. Here we use the Helsinki Discrete Element Model (HiDEM) to show that not all of the fractures visible at the front of the Totten IS are produced locally, but that the across-flow basal crevasses, which are part of the distinctive cross-cutting fracture pattern, are advected into the calving front area from upstream. A separate simulation of the grounding line shows that re-grounding points may be key areas of basal crevasse production, and can produce basal crevasses in both an along- and across-flow orientation. The along-flow basal crevasses at the grounding line may be a possible precursor to basal channels, while we suggest the across-flow grounding-line fractures are the source of the across-flow features observed at the calving front. We use two additional models to simulate the evolution of basal fractures as they advect downstream, demonstrating that both strain and ocean melt have the potential to deform narrow fractures into the broad basal features observed near the calving front. The wide range of factors which influence fracture patterns and calving on this glacier will be a challenge for predicting its future mass loss.

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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