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A Sourcebook for the Worldwide Discovery of a Creative Organic Universe
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Genesis Vision
Learning Planet
Organic Universe
Earth Life Emerge
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III. Ecosmos: A Revolutionary Fertile, Habitable, Solar-Bioplanet, Incubator Lifescape

4. Geosphere, Hydrosphere, Atmosphere as Complex, Network Systems

Karimova, L., et al. Fractal and Topological Dynamics for the Analysis of Paleoclimatic Records. Physica A. 373/737, 2006. A team from Kazakhstan, England, and Finland composed of a geologist, mathematicians, and climate scientists find that data readings from ice cores and tree rings of past North Atlantic climes exemplify a natural self-similarity. What kind of creation then, one might wonder, achieves its own retrospective description. Whom is doing this and for what purpose?

Paleoclimatic proxy records are analyzed with the help of multifractal formalism, wavelet analysis and topological dynamics methods to reveal scaling features as well as their nonlinear dynamics and interrelationship. (737)

Kleidon, Axel, et al. Thermodynamics, Maximum Power, and the Dynamics of Preferential River Flow Structures at the Continental Scale. Hydrology and Earth System Sciences. 17/225, 2013. An Interactive Open Access Journal of the European Geosciences Union. As the Abstract explains, MPI, Biogeochemistry, and Karlsruhe Institute of Technology, scientists proceed to articulate living nature’s constant riverine form and flow. See also in this journal series Biogeosciences, Climates of the Past, Earth Surface Dynamics, and Nonlinear Processes in Geophysics, for similar understandings of common, ever recurrent, dynamic vitalities.

The organization of drainage basins shows some reproducible phenomena, as exemplified by self-similar fractal river network structures and typical scaling laws, and these have been related to energetic optimization principles, such as minimization of stream power, minimum energy expenditure or maximum "access". Here we describe the organization and dynamics of drainage systems using thermodynamics, focusing on the generation, dissipation and transfer of free energy associated with river flow and sediment transport. We argue that the organization of drainage basins reflects the fundamental tendency of natural systems to deplete driving gradients as fast as possible through the maximization of free energy generation, thereby accelerating the dynamics of the system. This effectively results in the maximization of sediment export to deplete topographic gradients as fast as possible and potentially involves large-scale feedbacks to continental uplift. We illustrate this thermodynamic description with a set of three highly simplified models related to water and sediment flow and describe the mechanisms and feedbacks involved in the evolution and dynamics of the associated structures. We close by discussing how this thermodynamic perspective is consistent with previous approaches and the implications that such a thermodynamic description has for the understanding and prediction of sub-grid scale organization of drainage systems and preferential flow structures in general. (Abstract)

Klinger, Lee. Gaia and Complexity. Schneider, Stephen, et al, eds. Scientists Debate Gaia. Cambridge: MIT Press, 2004. Noted more in A Living Planet, the paper also discusses self-organizing, fractal landscapes.

L’Heureux, Ivan. Self-Organized Rhythmic Patterns in Geochemical Systems. Philosophical Transactions of the Royal Society A. 371/20120356, 2013. In this issue on Pattern Formation in the Geosciences (Goehring above), a University of Ottawa “condensed matter physicist” details how rock formations, such as “periodic precipitation of pyrite bands,” express the same dynamical topologies and behaviors as everywhere else in nature. In regard, as an increasing number of similar reports confirm, as strongly implied, it can be realized that these recurrent phenomena spring from universal, “intrinsic” material spontaneities.

Chemical oscillating patterns are ubiquitous in geochemical systems. Although many such patterns result from systematic variations in the external environmental conditions, it is recognized that some patterns are due to intrinsic self-organized processes in a non-equilibrium nonlinear system with positive feedback. In rocks and minerals, periodic precipitation (Liesegang bands) and oscillatory zoning constitute good examples of patterns that can be explained using concepts from nonlinear dynamics. (Abstract)

We hope that we have convinced the reader that, in order to understand the origin of geochemical rhythmic patterns exhibited by a variety of rocks and minerals, the tools used in the study of nonlinear dynamical systems and the concepts of self-organization are essential. Thus, not only do these examples provide beautiful illustrations of the manifestation of nonlinear dynamics in nature, but they allow Earth scientists to better understand the genesis conditions under which these patterns are formed. In this manner, Earth scientists can obtain more information on the past history of the Earth and, perhaps, better understand its future evolution. (8)

Lofta, Nastaran, et al. Centrality in Earthquake Multiplex Networks. Chaos. 28/063113, 2018. University of Zanjan, Iran and University of Sao Paulo physicists achieve a detailed global complex systems analysis of these spurious geological calamities. To reflect, out of this arduous planetary evolution and human history a collective, cumulative knowledge at last arises which then might be fed back to give better warnings, and maybe mitigate. What could its cosmic identity and purpose be?

Seismic time series has been mapped as a complex network, where a geographical region is divided into square cells that represent the nodes and connections are defined according to the sequence of earthquakes. In this paper, we map a seismic time series to a multiplex network, and characterize the evolution of the network structure in terms of the eigenvector centrality measure. We generalize previous works that considered the single layer representation of earthquake networks. Our results suggest that the multiplex representation captures better earthquake activity than methods based on single layer networks. We also verify that the regions with highest seismological activities in Iran and California can be identified from the network centrality analysis. The temporal modeling of seismic data provided here may open new possibilities for a better comprehension of the physics of earthquakes. (Abstract)

Ma, Hongbo, et al. Universal Relation with Regime Transition for Sediment Transport in Fine-Grained Rivers. Proceedings of the National Academy of Sciences. 117/171, 2020. A thirteen member team of geoscientists from across China and the USA, with a global cast of names, uncover and quantify a common mathematical basis which underlie and guide such sediment flows and depositions across the world’s waterways. We also cite as more current proof that a natural genesis is graced by an independent generative source code across land, sea, air and space.

Fine-grained sediment transport systems (grain size under 2,000 μm) are ubiquitous over time and space on Earth and extraplanetary surfaces, and include rivers, deltaic coastal settings, and submarine, subglacial systems. Forecasting the evolution of Earth’s surface requires a predictive algorithm for sediment transport. Herein we provide a universal relation for sediment transport in fine-grained rivers. Surprisingly, it is shown that sediment flux differs by up to 2 orders of magnitude as grain size changes only slightly near the boundary between very fine sand and fine sand. The universal applicability of the sediment transport formulation enables quantitative understanding of the sedimentology and morphology of fine-grained rivers. (Significance)

Mann, Daniel. On Patterned Ground. Science. 299/354, 2003. A report on how intricate, ever changing landscape patterns are being understood through complex systems theory.

The (geomorphology) field is experiencing a paradigm shift from a reductionist approach towards concepts such as universality and self-organization. (355)

Martin, Miguel Angel, et al. Fractal Modeling and Scaling in Natural Systems. Ecological Complexity. 6/3, 2009. An introduction to a special section as an update to the wealth of findings across nature, noted herein, from snowy surfaces and rainfall amounts to Amazonian meteorology and fishery biomass, that evidence the same scale invariant geometries and dynamics. A number of these papers about soil complexities are drawn from a series of PEDOFRACT international seminars, see, e.g., J. Ibanez, et al.

The development and application of fractal models has become an important part of the ongoing quest to quantify, analyze, and manage the complexity of natural systems. Such models can help to reveal underlying relationships between structure and function, provide a succinct representation of scaling properties, and improve parameterization of natural variability and heterogeneity. (219)

Martin, Miguel Angel, et al, eds. Scaling, Fractals and Diversity in Soils and Ecohydrology. Ecological Modelling. 182/3-4, 2005. An introduction to a dedicated issue on self-similar, invariant spatial and temporal geometries that characterize hydrated earth. An example studied is the Aegean islands.

Scaling relations in ecosystems can be interpreted as the result of self-organization. (220)

Matthews, Robert. And Now the Forecast: Cloudy with a Chance of Fractals. New Scientist. November 7, 2009. Whereby the 1920s climate models of British mathematician Lewis Fry Richardson that were graced by cascades of similar weather patterns are being rediscovered and confirmed by the latest satellite data. Indeed, multifractal power laws abound in repetitive scales from local rainfalls to planetwide currents. A prime technical reference cited in this regard is Shaun Lovejoy, et al. Atmospheric Complexity or Scale by Scale Simplicity? in Geophysical Research Letters (36/L36801, 2009), see also Lovejoy above.

Meng, Fanzhen, et al. Power Law Relations in Earthquakes from Microscopic to Macroscopic Scales. Nature Scientific Reports. 9/10705, 2019. University of Hong Kong, and Chinese Academy of Sciences, Wuhan systems geologists provide a latest technical analysis of Earth shaking catastrophic events by way of self-similar complexity theories. As they become more common in China, Iran and the USA, these insights can aid better warning systems.

Understanding the physics of earthquakes is a crucial step towards improving their prediction accuracy. Scale invariance or fractal features are often reported in earthquakes, such as the size distribution, the spatial distribution of hypocenters, and the frequency of aftershocks. Here we assess whether other key parameters and quantities involved in earthquakes also conform to the power law. By analyzing a large amount of data collected from the laboratory experiments and field monitoring of earthquakes, we find that the crack density on the two sides of small scale fracture or large scale fault decreases with increasing distance following the power law, and the crack number-crack length distribution is also scale invariant like natural faults. (Abstract excerpt)

Menon, Anirudha and Banasri Basu.. Uncovering the Fractal Nature of Water Vapor Distribution above the Surface of the Earth. arXiv:2211.04106. When these scientific postings began in the early 2000s, evident perceptions such as this were rarely noticed anywhere. But two decades later every realm from Earth to ecosystems is found to be inherently graced with invariant patternings. Here Indian Association for the Cultivation of Science and Indian Statistical Institute mathematicians even find a moist atmosphere to exhibit their presence.

Fractals have recently become a major aspect of geophysical and geospatial studies. We examine the emergent fractal character of water vapor distributions on Earth’s surface as a function of pixel image resolution and moisture content percentile. We calculate physically relevant quantities such as fractal dimension, number of clusters, and size of the largest cluster with varying vapor percentile using computational methods and algorithms. We show that the self-similarity distribution is exact as a function of image resolution and approximate in some regimes as a function of the vapor percentiles. (Excerpt)

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