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The isothermal compressibility (i.e., related to the asymptotic number variance) of equilibrium liquid water as a function of temperature is minimal under near-ambient conditions. This anomalous non-monotonic temperature dependence is due to a balance between thermal fluctuations and the formation of tetrahedral hydrogen-bond networks. Since tetrahedrality is a many-body property, it will also influence the higher-order moments of density fluctuations, including the skewness and kurtosis. To gain a more complete picture, we examine these higher-order moments that encapsulate many-body correlations using a recently developed, advanced platform for local density fluctuations. We study an extensive set of simulated phases of water across a range of temperatures (80–1600 K) with various degrees of tetrahedrality, including ice phases, equilibrium liquid water, supercritical water, and disordered nonequilibrium quenches. We find clear signatures of tetrahedrality in the higher-order moments, including the skewness and excess kurtosis, which scale for all cases with the degree of tetrahedrality. More importantly, this scaling behavior leads to non-monotonic temperature dependencies in the higher-order moments for both equilibrium and non-equilibrium phases. Specifically, under near-ambient conditions, the higher-order moments vanish most rapidly for large length scales, and the distribution quickly converges to a Gaussian in our metric. However, under non-ambient conditions, higher-order moments vanish more slowly and hence become more relevant, especially for improving information-theoretic approximations of hydrophobic solubility. The temperature non-monotonicity that we observe in the full distribution across length scales could shed light on water’s nested anomalies, i.e., reveal new links between structural, dynamic, and thermodynamic anomalies.
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My, how you've grown: A practical guide to modeling size transitions for integral projection model ( IPM ) applications
Abstract Integral projection models (IPMs) are widely used for studying continuously size‐structured populations. IPMs require a growth sub‐model that describes the probability of future size conditional on current size and any covariates. Most IPM studies assume that this distribution is Gaussian, despite calls for non‐Gaussian models that accommodate skewness and excess kurtosis. We provide a general workflow for accommodating non‐Gaussian growth patterns while retaining important covariates and random effects. Our approach emphasizes visual diagnostics from pilot Gaussian models and quantile‐based metrics of skewness and kurtosis that guide selection of a non‐Gaussian alternative, if necessary. Across six case studies, skewness and excess kurtosis were common features of growth data, and non‐Gaussian models consistently generated simulated data that were more consistent with real data than pilot Gaussian models. However, effects of “improved” growth modeling on IPM results were moderate to weak and differed in direction or magnitude between different outputs from the same model. Using tools not available when IPMs were first developed, it is now possible to fit non‐Gaussian models to growth data without sacrificing ecological complexity. Doing so, as guided by careful interrogation of the data, will result in models that better represent the populations for which they are intended.
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- PAR ID:
- 10609729
- Publisher / Repository:
- Ecological Society of America
- Date Published:
- Journal Name:
- Ecology
- Volume:
- 106
- Issue:
- 5
- ISSN:
- 0012-9658
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript
- Journal Article:
- https://doi.org/10.1002/ecy.70088
