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A Sourcebook for the Worldwide Discovery of a Creative Organic Universe
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III. Ecosmos: A Revolutionary Fertile, Habitable, Solar-Bioplanet Incubator Lifescape

E. Systems Cosmology: Fractal SpaceTimeMatter

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 self-similar, iterative essence can be traced even to molecular and atomic forms and sub-structures.

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 cut-out substructures show self-similarity to the parent structures. Such a series shows self-similarity 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)

During our work on repetitive molecular features we realized that every molecular substructure displays self-similarity to its parent structure. Self-similarity means that an object is similar to a part of itself. Let us derive the concept of self-similarity for organic molecules at the example of n-hexane, a linear alkane. A linear alkane consists of a chain of carbon atoms saturated with hydrogen atoms. Removing one of the two outmost carbon-atoms and the connecting bond creates a new chain with one bond less. To the chain carbon-atom from where the bond was removed, a hydrogen atom has to be added for completing the saturation of the chain. (2)

Vrobel, Susie, et al, eds. Simultaneity: Temporal Structures and Observer Perspectives. Hackensack, NJ: World Scientific, 2008. With co-editors Otto Rossler and Terry Marks-Tarlow, 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. Self-Similarity 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 \alpha-element abundances for stars in the solar neighborhood to that of local, early-type 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 early-type 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 large-structure” 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 (1795-1873) 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. Scale-Invariant 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 scale-invariant spectrum of perturbations during an early phase which asymptotes in the far past to Minkowski space-time. 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 non-scale-invariant and highly non-Gaussian. We show that if higher dimensional operators are considered, a linear coupling between background and spectator field fluctuations is induced which leads to scale-invariant and Gaussian curvature fluctuations. (Wang, Brandenberger)

We propose a novel cosmological scenario, in which standard inflation is replaced by an expanding phase with a drastic violation of the Null Energy Condition (NEC). The model is based on the recently introduced Galileon theories, which allow NEC violating solutions without instabilities. The unperturbed solution describes a Universe that is asymptotically Minkowski in the past, expands with increasing energy density until it exits the regime of validity of the effective field theory and reheats. This solution is a dynamical attractor and the Universe is driven to it, even if it is initially contracting. The study of perturbations of the Galileon field reveals some subtleties, related to the gross violation of the NEC and it shows that adiabatic perturbations are cosmologically irrelevant. The model, however, suggests a new way to produce a scale invariant spectrum of isocurvature perturbations, which can later be converted to adiabatic: the Galileon is forced by symmetry to couple to the other fields as a dilaton; the effective metric it yields on the NEC violating solution is that of de Sitter space, so that all light scalars will automatically acquire a nearly scale-invariant spectrum of perturbations. (Creminelli, et al)

Watkins, Nicholas, et al. 25 Years of Self-Organized Criticality. Space Science Reviews. Online Summer, 2015. The document is also at arXiv:1504.04991. It is a consummate paper to be published in a special retrospective issue along with Marcus Aschwanden, et al, 25 Years of SOC: Space and Laboratory Plasmas (search), James McAteer, et al, 25 Years of SOC: Numerical Detection, and other articles. As the Aschwanden posting explains, the once and future review stems from a series of International Space Science Institute workshops. In accord with a 2015 emergent synthesis of constant work and progress since the 1980s, across these widest natural domains is affirmed a robust “ubiquity, universality, generality” (26). See also a commentary on the work SOC Revisited by Mark Buchanan in Nature Physics for June 2015.

Introduced by the late Per Bak and his colleagues, self-organized criticality (SOC) has been one of the most stimulating concepts to come out of statistical mechanics and condensed matter theory in the last few decades, and has played a significant role in the development of complexity science. SOC, and more generally fractals and power laws, have attracted much comment, ranging from the very positive to the polemical. The other papers in this special issue showcase the considerable body of observations in solar, magnetospheric and fusion plasma inspired by the SOC idea, and expose the fertile role the new paradigm has played in approaches to modeling and understanding multiscale plasma instabilities. This very broad impact, and the necessary process of adapting a scientific hypothesis to the conditions of a given physical system, has meant that SOC as studied in these fields has sometimes differed significantly from the definition originally given by its creators. One aim of the present review is to address the dichotomy between the great reception SOC has received in some areas, and its shortcomings, as they became manifest in the controversies it triggered. Our article tries to clear up what we think are misunderstandings of SOC in fields more remote from its origins in statistical mechanics, condensed matter and dynamical systems by revisiting Bak, Tang and Wiesenfeld's original papers. (Abstract)

Wei, Zong-Wen, et al. Renormalization and Small-World Model of Fractal Quantum Repeater Networks. Nature Scientific Reports. 3/1222, 2013. Hangzhou Normal University, and University of Science and Technology of China, system physicists achieve a number of syntheses in this innovative paper. Traditional statistical mechanics is melded with nonlinear science to join renormalization theories with dynamic scale-free networks. By this approach, even quantum depths can be found to contain and express the same complex, self-similar system phenomena as everywhere else in nature and society. Such a novel, holistic vista can even more reveal and implicate, albeit in arcane terms than beg translation, an independent, creative, universal source.

Quantum networks provide access to exchange of quantum information. The primary task of quantum networks is to distribute entanglement between remote nodes. Although quantum repeater protocol enables long distance entanglement distribution, it has been restricted to one-dimensional linear network. Here we develop a general framework that allows application of quantum repeater protocol to arbitrary quantum repeater networks with fractal structure. Entanglement distribution across such networks is mapped to renormalization. Furthermore, we demonstrate that logarithmical times of recursive such renormalization transformations can trigger fractal to small-world transition, where a scalable quantum small-world network is achieved. Our result provides new insight into quantum repeater theory towards realistic construction of large-scale quantum networks. (Abstract)

To summarize, we have generalized one-dimensional quantum repeaters to high fractal dimension by introducing an approach called CR (coupled renormalization), which relates entanglement distribution over arbitrary fractal QRN (quantum repeater network) to recursive renormalization transformations. We assume that QRN is fractal and scale-free, which is the case for a large number of real-world networks. In spite of the large size of QRN, there exists a relatively small critical nesting level for CR, at which small-world is obtained. Small-world seems to be a necessary element for a scalable quantum network. Our study suggests that concepts and tools from statistical physics will play an important role in the joint study. It has conceived another significant direction which may open new avenue to address the outstanding issue of complexity. That is, quantum simulation of dynamic process on complex networks or design of quantum algorithms for sophisticated questions in network science. All of these attempts may dramatically alter the landscape of both fields. (5)

Weil, Melinda and Ralph Pudritz. Cosmological Evolution of Supergiant Star-Forming Clouds. The Astrophysical Journal. 556/164, 2001. Galaxies form into hierarchical clusters due to a “robust power-law mass spectrum.”

Wen, Xiao-Gang. Zoo of Quantum-Topological Phases of Matter. arXiv:1610.03911. The MIT physicist and author has engaged this field for some years (check his publications page) and was interviewed by Natalie Wolchover for her 2018 Quanta report above which displays a “Periodic Table of Phases” that Wen conceived. This paper advances the 2010s turn in condensed matter physics from material and energetic aspects to realize that nature’s quantum realm is equally distinguished by innate geometric formations, which seem to arrange in an orderly way. We quote a full paragraph to convey its content.

What are topological phases of matter? First, they are phases of matter at zero temperature. Second, they have a non-zero energy gap for the excitations above the ground state. Third, they are disordered liquids that seem have no feature. But those disordered liquids actually can have rich patterns of many-body entanglement representing new kinds of order. This paper will give a simple introduction and a brief survey of topological phases of matter. We will first discuss topological phases that have topological order (ie with long range entanglement). Then we will cover topological phases that have no topological order. (Abstract)

New World of Condensed Matter Physics: However, through the researches in last 30 years, a different picture starts to emerge. It appears that what we have seen is just the end of beginning. There is a whole new world ahead of us waiting to be explored. A peek into the new world is offered by the discovery of fractional quantum Hall (FQH) effect. Another peek is offered by the discovery of high Tc superconductors. Both phenomena are completely beyond the paradigm of Landau’s symmetry breaking theory. Rapid and exciting developments in FQH effect and in high Tc superconductivity resulted in many new ideas and new concepts. Looking back at those new developments, it becomes more and more clear that, in last 30 years, we were actually witnessing an emergence of a new theme in condensed matter physics. The new theme is associated with new kinds of orders, new states of matter and new class of materials beyond Landau’s symmetry breaking theory. This is an exciting time for condensed matter physics. The new paradigm may even have an impact in our understanding of fundamental questions of nature – the emergence of elementary particles and the four fundamental interactions, which leads to an unification of matter and quantum information. (2)

Zhou, Yuan-Wu, et al. Multifractal and Complex Network Analyses of Protein Molecular Dynamics. arXiv:1403.4719. As the Abstract excerpts note, Xiangtan University, Hunan, and Queens University of Technology, Brisbane, researchers find nature’s universal self-similarity to be equally present in this vital class of intricate biomolecules.

Based on protein molecular dynamics, we analyze fractal properties of energy, pressure and volume time series using the multifractal detrended fluctuations analysis (MF-DFA); and investigate the topological and multifractal properties of their visibility graph (complex network) representations. The energy terms of proteins we considered are bonded potential, angle potential, dihedral potential, improper potential, kinetic energy, Van der Waals potential, electrostatic potential, total energy and potential energy. Results of MF-DFA show that these time series are multifractal. Results of complex networks analysis based on visibility graph algorithm show that these visibility graphs are exponential. Our numerical results of multifractal analysis of the visibility graphs show that multifractality exists in these networks. (Abstract)

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