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The new version includes all figures in the correct order and addresses the figure issues noted in the previous Formal Correction. Originally published, uncorrected article. https://doi.org/10.1371/journal.pone.0093244.s001 (PDF) File S2.

Citation: Koyama K, Hidaka Y, Ushio M (2012) Correction: Dynamic Scaling in the Growth of a Non-Branching Plant, Cardiocrinum cordatum. PLoS ONE 7(11): 10.1371/annotation/adf4e7b0-d177-4d01-9419-1642f9a1318a. https://doi.org/10.1371/annotation/adf4e7b0-d177-4d01-9419-1642f9a1318a

Most of the planet’s population currently lives in urban areas, and urban land expansion is one of the most dramatic forms of land conversion. Understanding how cities evolve temporally, spatially, and organizationally in a rapidly urbanizing world is critical for sustainable development. However, few studies have examined the coevolution of urban attributes in time and space simultaneously and the adequacy of power law scaling across cities and through time, particularly in countries that have experienced abrupt, widespread, political and economic changes. Here, we show the temporal coevolution of multiple physical, demographic, socioeconomic, and environmental attributes in individual cities, and the cross-city scaling of urban attributes at six time points (i.e., 1978, 1990, 1995, 2000, 2005, and 2010) in 32 major Chinese cities. We found that power law scaling could adequately characterize both the cross-city scaling of urban attributes across cities and the longitudinal scaling describing the temporal coevolution of urban attributes within individual cities. The cross-city scaling properties demonstrated substantial changes over time signifying evolved social and economic forces. A key finding was that the cross-city linear or superlinear scaling of urban area with population contradicts the theoretical sublinear power law scaling proposed between infrastructure and population. Furthermore, the cross-city scaling between area and population transitioned from linear to superlinear over time, and the superlinear scaling in recent times suggests decreased infrastructure efficiency. Our results demonstrate a diseconomy of scale in urban areal expansion that indicates a significant waste of land resources in the urbanization process. Future planning efforts should focus on policies that increase urban land use efficiency before continuing expansion.

Fluid‐rock dissolution occurs ubiquitously in geological systems. Surface‐volume scaling is central to predicting overall dissolution rate R involved in modeling dissolution processes. Previous works focused on single‐phase environments but overlooked the multiphase‐flow effect. Here, through limestone‐based microfluidics experiments, we establish a fundamental link between dissolution regimes and scaling laws. In regime I (uniform), the scaling is consistent with classic law, and a satisfactory prediction of R can be obtained. However, the scaling for regime II (localized) deviates significantly from classic law. The underlying mechanism is that the reaction‐induced gas phase forms a layer, acting as a barrier that hinders contact between the acid and rock. Consequently, the error between measurement and prediction continuously amplifies as dissolution proceeds; the predictability is poor. We propose a theoretical model that describes the regime transition, exhibiting excellent agreement with experimental results. This work offers guidance on the usage of scaling law in multiphase flow environments. Plain Language Summary Fluid‐rock dissolution is ubiquitous in natural and engineered systems, including karst formation, geological carbon sequestration, and acid stimulation. Recent developed method for CO2 sequestration relies on mineralization, which transforms CO2 into carbonate minerals through geochemical reactions involving dissolution. The precise modeling of dissolution processes at the continuum‐scale is dependent on the estimation of the overall dissolution rate using surface‐volume scaling laws. This important scaling law is always established in a single‐phase system. Here, through limestone‐based microfluidics experiments, we find that the scaling is significantly affected by the dissolution regime in a multiphase flow environment. When the injection rate is lower, and the geometry is more homogeneous, the dissolution regime adheres to classic law. On the other hand, when the flow is stronger and the heterogeneity exhibits, the dissolution scaling significantly diverges. Our discovery indicates that a layer of CO2 gas attaches to the uneven surface, causing a shielding effect on the dissolution and resulting in a notable deviation. Through establishing a theoretical model for the regime transition, this work offers guidance on the usage of scaling law across various dissolution scenarios. The newly developed scaling can enhance dissolution modeling precision in multiphase flow‐dissolution systems such as geologic carbon sequestration. Key Points We observe two regimes, and the scaling in regime II deviates significantly from classic law, with a poor predictability of dissolution rate We identify a barrier effect in real rock samples that inhibits the contact of acid and rock for the deviation of scaling in regime II We propose a theoretical model for regime transition that offers guidance on the usage of scaling law in multiphase environments

Two key global seismic quantities are relevant to estimate the fundamental properties of a star: the frequency of maximum power (νmax) and the large frequency separation (Δν). The focus of this work is to test the νmax scaling relation in order to ascertain it’s level of accuracy. Here we report our results using artificial data and real Kepler data, based on a grid-modelling approach.

Scaling laws relating body mass to species characteristics are among the most universal quantitative patterns in biology. Within major taxonomic groups, the 4 key ecological variables of metabolism, abundance, growth, and mortality are often well described by power laws with exponents near 3/4 or related to that value, a commonality often attributed to biophysical constraints on metabolism. However, metabolic scaling theories remain widely debated, and the links among the 4 variables have never been formally tested across the full domain of eukaryote life, to which prevailing theory applies. Here we present datasets of unprecedented scope to examine these 4 scaling laws across all eukaryotes and link them to test whether their combinations support theoretical expectations. We find that metabolism and abundance scale with body size in a remarkably reciprocal fashion, with exponents near ±3/4 within groups, as expected from metabolic theory, but with exponents near ±1 across all groups. This reciprocal scaling supports “energetic equivalence” across eukaryotes, which hypothesizes that the partitioning of energy in space across species does not vary significantly with body size. In contrast, growth and mortality rates scale similarly both within and across groups, with exponents of ±1/4. These findings are inconsistent with a metabolic basis for growth and mortality scaling across eukaryotes. We propose that rather than limiting growth, metabolism adjusts to the needs of growth within major groups, and that growth dynamics may offer a viable theoretical basis to biological scaling.

In this note, we revisit the scaling relations among “hatted critical exponents”, which were first derived by Ralph Kenna, Des Johnston, and Wolfhard Janke, and we propose an alternative derivation for some of them. For the scaling relation involving the behavior of the correlation function, we will propose an alternative form since we believe that the expression is erroneous in the work of Ralph and his collaborators.

In this study, the behavior of permeate flux decline due to scale precipitation of calcium sulfate on reverse osmosis membranes was investigated. The proposed scaling-based flux model is able to explain that permeate fluxes attributed to three mechanisms of scale precipitation—cake formation, surface blockage, and mixed crystallization—converge to the same newly defined scaling-based critical flux. In addition, a scaling index is defined, which determines whether scale precipitates on the membrane. The experimental results were analyzed based on this index. The mass-transfer coefficients of flat membrane cells used in the experiments were measured and, although the coefficients differed, they could be summarized in the same form as the Leveque equation. Considering the results of the scale precipitation experiments, where the operating conditions of pressure, solute concentration, temperature, and Reynolds number were varied, the convergent values of the permeate fluxes are explained by the scaling-based critical fluxes and the scale precipitation zones by the scaling indexes.