
III. Ecosmos: A Revolutionary Fertile, Habitable, SolarBioplanet, Incubator LifescapeE. Systems Cosmology: Fractal SpaceTimeMatter Sylos Labini, Francesco, et al. Persistent Fluctuations in the Distributions of Galaxies from the Twodegree Field Galaxy Redshift Survey. EPL. 85/29002, 2009. A team of Italian and Russian astronomers further quantify selfsimilar geometries across the celestial realms. We apply the scalelength method to several threedimensional samples of the Twodegree Field Galaxy Redshift Survey. This method allows us to map in a quantitative and powerful way large scale structures in the distribution of galaxies controlling systematic effects. By determining the probability density function of conditional fluctuations we show that largescale structures are quite typical and correspond to large fluctuations in the galaxy density field. We do not find a convergence to homogeneity up to the samples sizes, i.e. 75 Mpc/h. We then measure, at scales r Tatekawa, Takayuki and Keichi Maeda. Primordial Fractal Density Perturbations and Structure Formation in the Universe. The Astrophysical Journal. 547/531, 2001. A technical paper on how such recurrently ordered forms appear and ramify in the developing cosmos. One of the most plausible explanations is the nonlinear dynamics of the perturbations will provide such a scalefree structure during the evolution of the universe. (531) Teles, Sharon, et al. Fractal Analysis of the UltraVISTA Galaxy Survey. arXiv:2013.07164. In 2000, one could find inklings that selfsimilar geometries might be present across the celestial reaches. Two decades later, Valongo Observatory, Universidade Federal do Rio de Janeiro Observatório Nacional astronomers add another strong confirmation that all manner of spacescape phenomena is indeed arrayed in and sustained by fractal scales. This paper seeks to test if the largescale galaxy distribution can be characterized as fractal system. Tools appropriate for describing galaxy fractal structures with a single fractal dimension in relativistic settings are developed and applied to the UltraVISTA galaxy survey. A graph of volumelimited samples corresponding to the redshift limits in each redshift bins for absolute magnitude is presented. The results show two consecutive and distinct redshift ranges in both the reduced and complete samples where the data behave as a single fractal galaxy structure. (Abstract excerpt) Theel, Friethjof, et al. The Fractal Geometry of HartreeFock. Chaos. 27/12, 2017. When this section went online in 2004, scientific perceptions of a natural selfsimilarity from atomic depths to cosmic breadth were spurious and rudimentary, with a smattering of evidence. A decade and a half later, as this entry by University of Hamburg physicists, and many citations herein now testify, iterative fractal forms are quantified and known to array across these reaches, and everywhere in between. Circa 2018, by a natural philosophy view, our worldwide humankinder seems to be well finding a new genesis universe graced by these intrinsic phenomenal qualities. OK The HartreeFock method is an important approximation for the groundstate electronic wave function of atoms and molecules so that its usage is widespread in computational chemistry and physics. The HartreeFock method is an iterative procedure in which the electronic wave functions of the occupied orbitals are determined. The set of functions found in one step builds the basis for the next iteration step. In this work, we interpret the HartreeFock method as a dynamical system since dynamical systems are iterations where iteration steps represent the time development of the system, as encountered in the theory of fractals. The focus is put on the convergence behavior of the dynamical system as a function of a suitable control parameter. An investigation of the convergence behavior depending on the parameter λ is performed for helium, neon, and argon. We observe fractal structures in the complex λplane, which resemble the wellknown Mandelbrot set, determine their fractal dimension, and find that with increasing nuclear charge, the fragmentation increases as well. (Abstract) Toriumi, Shin and Vladimir Airapelian. Universal Scaling Laws for the Solar and Stellar Atmospheric Heating. arXiv:2202.01232. We cite this entry by Japan Aerospace Exploration Agency and NASA Goddard Space Flight Center researchers as a typical instance nowadays of how a global science is finding an infinite recurrence in kind across every celestial, and cultural scale and realm. See also Universal Scaling Law of Glass Rheology by Shuangxi, Song, et al. in Nature Materials (February 2022). The Sunlike stars commonly host multimillionKelvin coronae an 10,000Kelvin chromospheres. These hot gases generate Xray and Ultraviolet emissions that may influence the chemistry of (exo)planetary atmospheres, along the climate and habitability. However, the mechanism of coronal and chromospheric heating is poorly understood. To this end, we report on a systematic survey of the responses of solar and stellar atmospheres to surface magnetic flux over a wide range of temperatures. We reveal that the irradiance and magnetic flux show powerlaw relations with an exponent from above to subunity as the temperature decreases from the corona to the chromosphere. Our study provides observational evidence that the mechanism of atmospheric heating is universal among the Sun and sunlike stars, regardless of age or activity. (Abstract excerpt)
Venkataramani, Shankar and Alan Newell.
Pattern Dark Matter and Galaxy Scaling Relations.
European Physical Journal Special Topics.
June,
2021.
University of Arizona astrophysicists press on through 40 pages to express the latest mathematic verities of “universal equations” that distinguish and arrange these celestial reaches. Once again, we ought to reflect on how incredible it is that fraught human beings can yet achieve such cosmic quantifications, as if we are meant to perform necessary function of natural selfdescription. University of Arizona astrophysicists press on through 40 pages to express the latest mathematic verities of “universal equations” that distinguish and arrange these celestial reaches. Once again, we ought to reflect on how incredible it is that fraught human beings can yet achieve such cosmic quantifications, as if we are meant to perform necessary function of natural selfdescription. Vijar, Sagar, et al. A New Kind of Topological Quantum Order. arXiv:1505.02576. With a Dimensional Hierarchy of Quasiparticles Built from Stationary Excitations subtitle, by way of clever mathematics, MIT physicists SV, Jeongwan Haah, and Liang Fu advance deep understandings about how cosmic nature’s is actually suffused by intrinsic structural geometries. See also Haah’s 2011 original paper Local Stabilizer Codes in Three Dimensions without String Logical Operators at 1101.1962 with much set off this quest. We introduce exactly solvable models of interacting (Majorana) fermions in d≥3 spatial dimensions that realize a new kind of topological quantum order, building on a model presented in ref. [1]. These models have extensive topological groundstate degeneracy and a hierarchy of pointlike, topological excitations that are only free to move within submanifolds of the lattice. In particular, one of our models has fundamental excitations that are completely stationary. To demonstrate these results, we introduce a powerful polynomial representation of commuting Majorana Hamiltonians. Remarkably, the physical properties of the topologicallyordered state are encoded in an algebraic variety, defined by the common zeros of a set of polynomials over a finite field. This provides a "geometric" framework for the emergence of topological order. (Abstract) Von Korff, Modest and Thomas Sander. Molecular Complexity Calculated by Fractal Dimension. Nature Scientific Reports. 9/967, 2019. Scientific Computing Drug Discovery, Idorsia Pharmaceuticals, Switzerland researchers achieve another novel recognition that nature’s proclivity to adopt and display a selfsimilar, iterative essence can be traced even to molecular and atomic forms and substructures. Molecular complexity is an important characteristic of organic molecules for drug discovery. How to calculate molecular complexity has been discussed in the scientific literature for decades. It was known from early on that the numbers of substructures that can be cut out of a molecular graph are of importance. However, it was never realized that the cutout substructures show selfsimilarity to the parent structures. Such a series shows selfsimilarity similar to fractal objects. The fractal dimension of a molecule is a new matter constant that incorporates all features that are currently known to be important for describing molecular complexity.(Abstract) Vrobel, Susie, et al, eds. Simultaneity: Temporal Structures and Observer Perspectives. Hackensack, NJ: World Scientific, 2008. With coeditors Otto Rossler and Terry MarksTarlow, a volume emanating from an Institute for Fractal Research which seems to get wound up in its own vernacular claiming “the next revolution in physics” due to novel appreciations of human observership and the inherent “fractality of space and time.” An eclectic collection, with various contributions by the editors, Peter Allen on a hierarchy of evolutionary systems, Uri Fidelman on complementary brain hemispheres whereof the right side achieves its simultaneous synthesis, and on to a brush with econophysics. In any event, still another sign of coming universe change. Walcher,, C. J., et al. SelfSimilarity in the Chemical Evolution of Galaxies. arXiv:1607.00015. A ten person team from Germany and South America report signs of a universal geometric repetition across material, stellar and galactic realms that is “more than just a coincidence.” Recent improvements in the age dating of stellar populations and single stars allow us to study the ages and abundance of stars and galaxies with unprecedented accuracy. We here compare the relation between age and \alphaelement abundances for stars in the solar neighborhood to that of local, earlytype galaxies. This quantitative similarity seems surprising, given the different types of galaxies and scales involved. The data are consistent with a power law delay time distribution. We thus confirm that the delay time distribution inferred for the Milky Way from chemical evolution arguments also must apply to massive earlytype galaxies. Wang, Xin and Alex Szalay. On the Nonlinear Evolution of Cosmic Web. arXiv.1411.4117. Johns Hopkins University astrophysicists explain “cosmic morphologies of the largestructure” by way of Lagrangian dynamics, a technical finesse of statistical mechanics. We cite because by natural philosophy wonder, how fantastic is it that human folks can altogether suddenly traverse and quantify such infinite vistas. You might read Johns Hopkins (17951873) biography on Wikipedia for some context. Surely we peoples ought to grant ourselves a central significance to the course and fate of this genesis universe. Wang, Yi and Robert Brandenberger. ScaleInvariant Fluctuations from Galilean Genesis. arXiv:1007.0027. Posted June 2012, McGill University physicists take up the work of Paolo Creminelli, et al, Abdus Salam International Centre for Theoretical Physics, posted October 2010 (search arXiv) to glean further insights upon a fractal cosmos. We include both Abstracts. “Inflation on Trial” by Alexandra Witze in Science News for July 25, 2012 reports on these 21st century revisions of the 1980s and 1990s instant inflation theories. We study the spectrum of cosmological fluctuations in scenarios such as Galilean Genesis in which a spectator scalar field acquires a scaleinvariant spectrum of perturbations during an early phase which asymptotes in the far past to Minkowski spacetime. In the case of minimal coupling to gravity and standard scalar field Lagrangian, the induced curvature fluctuations depend quadratically on the spectator field and are hence nonscaleinvariant and highly nonGaussian. We show that if higher dimensional operators are considered, a linear coupling between background and spectator field fluctuations is induced which leads to scaleinvariant and Gaussian curvature fluctuations. (Wang, Brandenberger)
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