Organization and scaling in water supply networks

Superlinear urban scaling by functional organization: A metabolic interpretation of sectoral water consumption

Prevailing view asserts that the disproportionately greater productivities of larger cities, or superlinear urban scaling, are the result of human interactions channeled by urban networks. But this view was established by considering the spatial organization of urban infrastructure and social networks-the urban "arteries" effects-but neglecting the functional organization of urban production and consumption entities-the urban "organs" effects. Here, adopting a metabolic view and using water consumption as a proxy for metabolism, we empirically quantify the scaling of entity number, size, and metabolic rate for the functionally specific urban residential, commercial, public or institutional, and industrial sectors. Sectoral urban metabolic scaling is highlighted by a disproportionate coordination between residential and enterprise metabolic rates, attributable to the functional mechanisms of mutualism, specialization, and entity size effect. The resultant whole-city metabolic scaling exhibits a constant superlinear exponent for water-abundant regions in numerical agreement with superlinear urban productivity, with varying exponent deviations for water-deficient regions explainable as adaptations to climate-driven resource constraints. These results present a functional organizational, non-social-network explanation of superlinear urban scaling.

Scaling of Energy, Water, and Waste Flows in China's Prefecture-Level and Provincial Cities

Cities have been envisioned as biological organisms as the integral part of nature's energy and material flows. Recent advances in urban scaling research have uncovered systematic changes in socioeconomic rates and infrastructural networks as urban population increases, providing predictive contents for the comparison between cities and organisms. However, it is still unclear how and why larger and smaller cities may differ in their per capita environmental impacts. Here, we study scaling patterns of urban energy, water, and waste flows as well as other relevant measures in Chinese cities. We divide cities into different groups using an algorithm that automatically assigns cities to clusters with distinct scaling patterns. Despite superlinear scaling of urban GDP, as predicted by urban scaling theories, resource consumption, such as the supply of electricity and water, and waste generation, such as wastewater and domestic waste, do not show significant deviations from linear scaling. The lengths of resource pipelines scale linearly in most cases, as opposed to sub-linearity predicted by theory. Furthermore, we show two competing forces underlying the overall observed effects of scale: a higher population density tends to decrease per capita resource consumption and infrastructure provisions, while intensified socioeconomic activities have the opposite effect.

Scaling Analysis of Energy in Great Lakes Water Supplies

Resource-scale quantification of energy in water supplies is important for local-scale sustainability and for regional-, national-, and global-scale assessments of the water-energy nexus. Water supply systems within a resource region are characterized by a homogeneity in system type but a heterogeneity in system size. Size heterogeneity has traditionally imposed large challenges to energy quantification because of nonlinearities. Recently, an analytical approach for quantifying nonlinear size effects in water supplies was developed based on the complex system phenomena of skewed size abundance (decreasing abundance with increasing size in a population of systems) and allometric energy scaling (decreasing energy intensity with increasing size in an individual system). Here, building on this advance and using new, resource-scope data on Great Lakes water supplies, we explore the interaction between energy allometry and size abundance and demonstrate the application of scaling for making energy predictions in water supplies. We show that communities are driven by the allometric effect to form "large get larger" supply systems, but ultimately spatial distances impose limits on the effect, resulting in delegation of tasks to local systems to preserve energy optimality. This cross-scale, interaction perspective of scaling and the application of scaling for energy prediction together may lead to a more functional understanding of supply size abundance and more integrative quantification of supply energy and environmental impacts at the water resource scale.

Optimizing biologically inspired transport networks by control

Transportation networks with intrinsic flow dynamics governed by the Kirchhoff's current law are ubiquitous in natural and engineering systems. There has been recent work on designing optimal transportation networks based on biological principles with the goal to minimize the total dissipation associated with the flow. Despite being biologically inspired, e.g., adaptive network design based on slime mold Physarum polycephalum, such methods generally lead to suboptimal networks due to the difficulty in finding a global or nearly global optimum of the nonconvex optimization function. Here we articulate a design paradigm that combines engineering control and biological principles to realize optimal transportation networks. In particular, we show how small control signals applied only to a fraction of edges in an adaptive network can lead to solutions that are far more optimal than those based solely on biological principles. We also demonstrate that control signals, if not properly designed, can lead to networks that are less optimal. Incorporating control principle into biology-based optimal network design has broad applications not only in biomedical science and engineering but also in other disciplines such as civil engineering for designing resilient infrastructure systems.