III. Ecosmos: A Revolutionary Fertile, Habitable, Solar-Bioplanet, Incubator Lifescape

E. Systems Cosmology: Fractal SpaceTimeMatter

Ramos, F. M., et al. Multiscaling and Nonextensivity of Large-Scale Structures in the Universe. Physica D. 168/404, 2002. Whereby the problem of the transition from multifractal galaxies and clusters to an overall homogeneous universe is resolved by a generalized thermostatistics method.

Rohringer, Wolfgang, et al. Non-equilibrium Scale Invariance and Shortcuts to Adiabaticity in a One-dimensional Bose Gas. Nature Scientific Reviews. 5/9820, 2015. This brief note by Vienna Center for Quantum Science and Technology researchers is another indication of an inherent, universal self-similarity across every possible domain. When and how might these many disparate findings become a worldwise discovery of a creative organic universe?

We present experimental evidence for scale invariant behaviour of the excitation spectrum in phase-fluctuating quasi-1d Bose gases after a rapid change of the external trapping potential. Probing density correlations in free expansion, we find that the temperature of an initial thermal state scales with the spatial extension of the cloud as predicted by a model based on adiabatic rescaling of initial eigenmodes with conserved quasiparticle occupation numbers. Based on this result, we demonstrate that shortcuts to adiabaticity for the rapid expansion or compression of the gas do not induce additional heating. (Abstract)

A systematic understanding of non-equilibrium dynamics in many-body quantum systems is a longstanding goal, with far-reaching applicability for many different fields of physics. Ultracold atom experiments offer clean implementations of systems that are tunable, well isolated from the environment and theoretically tractable1,2. In particular, the profound understanding available for the one-dimensional (1d) Bose gas makes it an ideal test bed for quantum many-body dynamics. (1)

Roukema, B. F., et al. A Hint of Poincare Dodecahedral Topology in the WMAP First Year Sky Map. Astronomy & Astrophysics. 423/821, 2004. Appropriately from the Nicolas Copernicus University in Torun, Poland, a further analysis of temperature fluctuations in the cosmic microwave background CMB as measured by the Wilkinson Microwave Anisotropy Probe WMAP satellite is seen to support the hypothesis that the overall universe is shaped as a dodecahedron rather than an infinite flat plane.

Rusin, D., et al. Self-Similar Models for the Mass Profiles of Early-Type Lens Galaxies. The Astrophysical Journal. 595/29, 2003. An example of how cosmologists are finding that scale-free power law profiles can describe the structure of the galactic clusters.

Sanchez, Nestor and Emilio Alfaro. The Fractal Distribution of H II Regions in Disk Galaxies. Astrophysical Journal. 178/1, Supplement, 2008. “H II” means areas of interstellar hydrogen that is ionized, sans an electron. Instituto de Astrofísica de Andalucía astronomers here find these domains to likewise possess a constant fractal structure over galactic reaches.

Sanchez, Nestor, et al. Fractal Dimension of Interstellar Clouds. Astrophysical Journal. 656/222, 2007. This conclusion is reached by studies of the opacity and noise of these celestial reaches.

There exists observational evidence that the interstellar medium has a fractal structure in a wide range of spatial scales. (222)

Sendker, Franziska, et al.. Emergence of fractal geometries in the evolution of a metabolic enzyme. Nature. April 10, 2024. MPI Terrestrial Microbiology researchers report finding what is considered to be the first actual notice of such self-similar topologies in organismic biological phenomena. The work became science news because it attests to much how nature’s infinite strata does manifest itself everywhere.

Fractals are patterns that are self-similar across multiple length-scales. Macroscopic fractals are common in nature; however, so far, molecular assembly into fractals is restricted to synthetic systems. Here we report the discovery of a natural protein, citrate synthase, which self-assembles into Sierpiński triangles. We use ancestral sequence reconstruction to retrace how the citrate synthase fractal evolved from non-fractal precursors. Our findings expand the space of protein complexes and show that intricate assemblies can evolve in a single substitution.

Slobodrian, R. Fractal Cosmogony. Chaos, Solitons and Fractals. 23/3, 2005. The structure of the early universe is noticed to exhibit a fractional self-similarity akin to microbial aggregates.

Smet, Jurgen. Wheels within Wheels. Nature. 422/391, 2003. A report on the discovery that when electrons constrained to move in a plane are exposed to a perpendicular magnetic field, known as the Quantum Hall effect, the curve of voltage vs. field strength takes on an iterative, fractal self-similarity.

Smolin, Lee. Three Roads to Quantum Gravity. New York: Basic Books, 2001. Noted earlier in Quantum Cosmology, the work entertains theories of the grainy, fractal, and holographic character of an integral universe.

We realized during that work that one way of making such a fractal spacetime is to build it up from a network of interacting loops. (124)

Sole, Ricard and A. Munteanu. The Large-Scale Organization of Chemical Reaction Networks in Astrophysics. EPL Europhysics Letters. 68/2, 2004. Universitat Pompeu, Fabra, Spain, systems theorists make an early, prescient notice that small world, scale-free topologies appear in astrochemical complexities. This reference is cited in a 2016 Nature Scientific Reports paper Multilayer Network Analysis of Nuclear Reactions (6/31882, 2016, see Liang Zhu in Systems Chemistry) whence a dozen years later this organic physiology and anatomy is robustly verified from cosmos to culture.

The large-scale organization of complex networks, both natural and artificial, has shown the existence of highly heterogeneous patterns of organization. Such patterns typically involve scale-free degree distributions and small-world, modular architectures. One example is provided by chemical reaction networks, such as the metabolic pathways. The chemical reactions of the Earth's atmosphere have also been shown to give rise to a scale-free network. Here we present novel data analysis on the structure of several astrophysical networks including the chemistry of the planetary atmospheres and the interstellar medium. Our work reveals that Earth's atmosphere displays a hierarchical organization, close to the one observed in cellular webs. Instead, the other astrophysical reaction networks reveal a much simpler pattern consistent with an equilibrium state. (Abstract)

Sowmya, G., et al. Supergranular Fractal Dimension and Solar Radiation. arXiv:2207.10490. In these 2020s, CSSS Institute of Engineering and Technology for Women, Karnataka, Poornaprajna Institute of Scientific Research, Devanahalli, and Bangalore University astrophysicists proceed to find and quantify evidence of deep self-similarities even in the sun’s rays.

In regard, see The Sun’s Supergranulation by Francois Rincon and Michel Rieutord in Living Reviews in Solar Physics (15/6, 2018) whence Supergranulation is a fluid-dynamical phenomenon in the solar photosphere in the form of a vigorous cellular flow pattern.

We present findings from an analysis of the fractal dimension of solar supergranulation as a function of latitude, cell size and solar rotation, by way of spectroheliographic data. We find that the fractal dimension tends to decrease from about 1.37 at the equator to about 1 at 20 degree latitude in either hemisphere, suggesting that solar rotation rate has the effect of augmenting the irregularity of supergranular boundaries. (Excerpt)

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