Entropy

Research

16 pages, 1119 KiB

Open AccessArticle

by Serban Raicu, Eugen Rosca and Dorinela Costescu

Entropy 2019, 21(9), 886; https://doi.org/10.3390/e21090886 - 12 Sep 2019

Cited by 1 | Viewed by 2965

The need to overcome the insulated treatment of urban technical infrastructures according to the nature of the transferred flows is argued. The operation of urban technical networks is affected by endogenous and exogenous random events with consequences for users. By identifying these operational [...] Read more.

The need to overcome the insulated treatment of urban technical infrastructures according to the nature of the transferred flows is argued. The operation of urban technical networks is affected by endogenous and exogenous random events with consequences for users. By identifying these operational risks and the difficulties of estimating the impact on the performance of the urban technical networks, the authors chose to study the risk management through a concise expression—in relation to the engineering resilience and its connections with vulnerability. Further, the research is confined to the case of urban traffic networks for which the resilience is expressed by the capabilities of these networks of resistance and risk absorption (both motivated by the redundancy in design and execution). The dynamics of the network, in correlation with the resistance and absorption capacities, is introduced by three states for which the signal graph is built. In a stationary regime, the probability of each state is computed. These probabilities allow the calculation of the entropy of the network, relevant for assessing the preservation of the network functionality. Full article

(This article belongs to the Special Issue Entropy and Scale-Dependence in Urban Modelling)

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13 pages, 5176 KiB

Open AccessArticle

Delimitating the Natural City with Points of Interests Based on Service Area and Maximum Entropy Method

by Lingbo Liu, Binxin Xia, Hao Wu, Jie Zhao, Zhenghong Peng and Yang Yu

Entropy 2019, 21(5), 458; https://doi.org/10.3390/e21050458 - 2 May 2019

Cited by 12 | Viewed by 3924

Abstract

The natural city, which is essential to understand urban physical scale and identify urban sprawling in urban studies, represents the urban functional boundaries of the city defined by human activities rather than the administrative boundaries. Most studies tend to utilize physical environment data [...] Read more.

The natural city, which is essential to understand urban physical scale and identify urban sprawling in urban studies, represents the urban functional boundaries of the city defined by human activities rather than the administrative boundaries. Most studies tend to utilize physical environment data such as street networks and remote sensing data to delimitate the natural city, however, such data may not match the real distribution of human activity density in the new cities or even ghost cities in China. This paper suggests aggregating the natural city boundary from the service area polygons of points of interest based on Reilly’s Law of Retail Gravitation and the maximum entropy method, since most points of interests provide services for surrounding communities, reflecting the vitality in a bottom-up way. The results indicate that the natural city defined by points of interests shows a high resolution and accuracy, providing a method to define the natural city with POIs. Full article

(This article belongs to the Special Issue Entropy and Scale-Dependence in Urban Modelling)

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15 pages, 267 KiB

Open AccessArticle

Entropy and its Application to Urban Systems

by Ben Purvis, Yong Mao and Darren Robinson

Entropy 2019, 21(1), 56; https://doi.org/10.3390/e21010056 - 12 Jan 2019

Cited by 41 | Viewed by 8400

Abstract

Since its conception over 150 years ago, entropy has enlightened and confused scholars and students alike, from its origins in physics and beyond. More recently, it has been considered within the urban context in a rather eclectic range of applications. The entropy maximization [...] Read more.

Since its conception over 150 years ago, entropy has enlightened and confused scholars and students alike, from its origins in physics and beyond. More recently, it has been considered within the urban context in a rather eclectic range of applications. The entropy maximization approach, as applied by Alan Wilson and others from the 1960s, contrasts with considerations from the 1990s of the city as a thermodynamic dissipative system, in the tradition of Ilya Prigogine. By reviewing the relevant mathematical theory, we draw the distinction among three interrelated definitions of entropy, the thermodynamic, the figurative, and the information statistical. The applications of these definitions to urban systems within the literature are explored, and the conflation of the thermodynamic and figurative interpretations are disentangled. We close this paper with an outlook on future uses of entropy in urban systems analysis. Full article

(This article belongs to the Special Issue Entropy and Scale-Dependence in Urban Modelling)

12 pages, 15894 KiB

Open AccessArticle

Scaling Effects of Elevation Data on Urban Nonpoint Source Pollution Simulations

by Ying Dai, Lei Chen, Pu Zhang, Yuechen Xiao and Zhenyao Shen

Entropy 2019, 21(1), 53; https://doi.org/10.3390/e21010053 - 11 Jan 2019

Cited by 2 | Viewed by 3237

Abstract

The scale effects of digital elevation models (DEM) on hydrology and nonpoint source (NPS) pollution simulations have been widely reported for natural watersheds but seldom studied for urban catchments. In this study, the scale effect of DEM data on the rainfall-runoff and NPS [...] Read more.

The scale effects of digital elevation models (DEM) on hydrology and nonpoint source (NPS) pollution simulations have been widely reported for natural watersheds but seldom studied for urban catchments. In this study, the scale effect of DEM data on the rainfall-runoff and NPS pollution was studied in a typical urban catchment in China. Models were constructed based on the DEM data of nine different resolutions. The conventional model performance indicators and the information entropy method were applied together to evaluate the scale effects. Based on the results, scaling effects and a resolution threshold of DEM data exist for urban NPS pollution simulations. Compared with natural watersheds, the urban NPS pollution simulations were primarily affected by the local terrain due to the overall flat terrain and dense sewer inlet distribution. The overland process simulation responded more sensitively than the catchment outlet, showing prolonged times of concentration for impervious areas with decreasing DEM resolution. The diverse spatial distributions and accumulation magnitudes of pollutants could lead to different simulation responses to scaling effects. This paper provides information about the specific characteristics of the scale effects of DEM data in a typical urban catchment, and these results can be extrapolated to other similar catchments as a reference for data collection. Full article

(This article belongs to the Special Issue Entropy and Scale-Dependence in Urban Modelling)

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13 pages, 1699 KiB

Open AccessArticle

Spatio–Temporal Pattern of the Urban System Network in the Huaihe River Basin Based on Entropy Theory

by Yong Fan, Renzhong Guo, Zongyi He, Minmin Li, Biao He, Hao Yang and Nu Wen

Entropy 2019, 21(1), 20; https://doi.org/10.3390/e21010020 - 27 Dec 2018

Cited by 9 | Viewed by 3577

Abstract

As complex systems, the spatial structure of urban systems can be analyzed by entropy theory. This paper first calculates the interaction force between cities based on the gravity model, the spatial relationship matrix between cities is constructed using the method of network modeling, [...] Read more.

As complex systems, the spatial structure of urban systems can be analyzed by entropy theory. This paper first calculates the interaction force between cities based on the gravity model, the spatial relationship matrix between cities is constructed using the method of network modeling, and the spatial network modeling of urban system can be calculated. Secondly, the Efficiency Entropy (EE), Quality Entropy (QE), and System Entropy (SE) of urban system network are calculated and analyzed by information entropy. Finally, taking the Huaihe River Basin (HRB) as a case study, model verification and empirical analysis are performed. It is found that the spatio–temporal pattern of the urban system network structure in the basin is uneven: in space, the urban system network in the HRB presents a layer-by-layer spatial distribution centered on the core city of Xuzhou; meanwhile, the overall urban system network in the basin presents an orderly development trend. This study has certain theoretical and practical value for the planning of urban and urban systems and the coordinated development of regions. Full article

(This article belongs to the Special Issue Entropy and Scale-Dependence in Urban Modelling)

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21 pages, 2734 KiB

Open AccessArticle

Spatial Measures of Urban Systems: from Entropy to Fractal Dimension

by Yanguang Chen and Linshan Huang

Entropy 2018, 20(12), 991; https://doi.org/10.3390/e20120991 - 19 Dec 2018

Cited by 19 | Viewed by 4968

Abstract

One type of fractal dimension definition is based on the generalized entropy function. Both entropy and fractal dimensions can be employed to characterize complex spatial systems such as cities and regions. Despite the inherent connection between entropy and fractal dimensions, they have different [...] Read more.

One type of fractal dimension definition is based on the generalized entropy function. Both entropy and fractal dimensions can be employed to characterize complex spatial systems such as cities and regions. Despite the inherent connection between entropy and fractal dimensions, they have different application scopes and directions in urban studies. This paper focuses on exploring how to convert entropy measurements into fractal dimensions for the spatial analysis of scale-free urban phenomena using the ideas from scaling. Urban systems proved to be random prefractal and multifractal systems. The spatial entropy of fractal cities bears two properties. One is the scale dependence: the entropy values of urban systems always depend on the linear scales of spatial measurement. The other is entropy conservation: different fractal parts bear the same entropy value. Thus, entropy cannot reflect the simple rules of urban processes and the spatial heterogeneity of urban patterns. If we convert the generalized entropies into multifractal spectrums, the problems of scale dependence and entropy homogeneity can be solved to a degree for urban spatial analysis. Especially, the geographical analyses of urban evolution can be simplified. This study may be helpful for students in describing and explaining the spatial complexity of urban evolution. Full article

(This article belongs to the Special Issue Entropy and Scale-Dependence in Urban Modelling)

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22 pages, 4749 KiB

Open AccessArticle

Cities, from Information to Interaction

by Vinicius M. Netto, Edgardo Brigatti, João Meirelles, Fabiano L. Ribeiro, Bruno Pace, Caio Cacholas and Patricia Sanches

Entropy 2018, 20(11), 834; https://doi.org/10.3390/e20110834 - 31 Oct 2018

Cited by 16 | Viewed by 11352

Abstract

From physics to the social sciences, information is now seen as a fundamental component of reality. However, a form of information seems still underestimated, perhaps precisely because it is so pervasive that we take it for granted: the information encoded in the very [...] Read more.

From physics to the social sciences, information is now seen as a fundamental component of reality. However, a form of information seems still underestimated, perhaps precisely because it is so pervasive that we take it for granted: the information encoded in the very environment we live in. We still do not fully understand how information takes the form of cities, and how our minds deal with it in order to learn about the world, make daily decisions, and take part in the complex system of interactions we create as we live together. This paper addresses three related problems that need to be solved if we are to understand the role of environmental information: (1) the physical problem: how can we preserve information in the built environment? (2) The semantic problem: how do we make environmental information meaningful? and (3) the pragmatic problem: how do we use environmental information in our daily lives? Attempting to devise a solution to these problems, we introduce a three-layered model of information in cities, namely environmental information in physical space, environmental information in semantic space, and the information enacted by interacting agents. We propose forms of estimating entropy in these different layers, and apply these measures to emblematic urban cases and simulated scenarios. Our results suggest that ordered spatial structures and diverse land use patterns encode information, and that aspects of physical and semantic information affect coordination in interaction systems. Full article

(This article belongs to the Special Issue Entropy and Scale-Dependence in Urban Modelling)

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21 pages, 6417 KiB

Open AccessArticle

Morphogenesis of Urban Water Distribution Networks: A Spatiotemporal Planning Approach for Cost-Efficient and Reliable Supply

by Jonatan Zischg, Wolfgang Rauch and Robert Sitzenfrei

Entropy 2018, 20(9), 708; https://doi.org/10.3390/e20090708 - 14 Sep 2018

Cited by 19 | Viewed by 4679

Abstract

Cities and their infrastructure networks are always in motion and permanently changing in structure and function. This paper presents a methodology for automatically creating future water distribution networks (WDNs) that are stressed step-by-step by disconnection and connection of WDN parts. The associated effects [...] Read more.

Cities and their infrastructure networks are always in motion and permanently changing in structure and function. This paper presents a methodology for automatically creating future water distribution networks (WDNs) that are stressed step-by-step by disconnection and connection of WDN parts. The associated effects of demand shifting and flow rearrangements are simulated and assessed with hydraulic performances. With the methodology, it is possible to test various planning and adaptation options of the future WDN, where the unknown (future) network is approximated via the co-located and known (future) road network, and hence different topological characteristics (branched vs. strongly looped layout) can be investigated. The reliability of the planning options is evaluated with the flow entropy, a measure based on Shannon’s informational entropy. Uncertainties regarding future water consumption and water loss management are included in a scenario analysis. To avoid insufficient water supply to customers during the transition process from an initial to a final WDN state, an adaptation concept is proposed where critical WDN components are replaced over time. Finally, the method is applied to the drastic urban transition of Kiruna, Sweden. Results show that without adaptation measures severe performance drops will occur after the WDN state 2023, mainly caused by the disconnection of WDN parts. However, with low adaptation efforts that consider 2–3% pipe replacement, sufficient pressure performances are achieved. Furthermore, by using an entropy-cost comparison, the best planning options are determined. Full article

(This article belongs to the Special Issue Entropy and Scale-Dependence in Urban Modelling)

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