scholarly journals Topological Symmetry Transition between Toroidal and Klein Bottle Graphenic Systems

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1233
Author(s):  
Mihai V. Putz ◽  
Ottorino Ori
Keyword(s):  
Klein Bottle ◽  
Translation Invariance ◽  
Lattice Stability ◽  
Cubic Graphs ◽  
Many Worlds ◽  
Constant Length ◽  
Threshold Size ◽  
Nano Structures ◽  
Wiener Number ◽  
Original Argument

In the current study, distance-based topological invariants, namely the Wiener number and the topological roundness index, were computed for graphenic tori and Klein bottles (named toroidal and Klein bottle fullerenes or polyhexes in the pre-graphene literature) described as closed graphs with N vertices and 3N/2 edges, with N depending on the variable length of the cylindrical edge LC of these nano-structures, which have a constant length LM of the Möbius zigzag edge. The presented results show that Klein bottle cubic graphs are topologically indistinguishable from toroidal lattices with the same size (N, LC, LM) over a certain threshold size LC. Both nano-structures share the same values of the topological indices that measure graph compactness and roundness, two key topological properties that largely influence lattice stability. Moreover, this newly conjectured topological similarity between the two kinds of graphs transfers the translation invariance typical of the graphenic tori to the Klein bottle polyhexes with size LC ≥ LC, making these graphs vertex transitive. This means that a traveler jumping on the nodes of these Klein bottle fullerenes is no longer able to distinguish among them by only measuring the chemical distances. This size-induced symmetry transition for Klein bottle cubic graphs represents a relevant topological effect influencing the electronic properties and the theoretical chemical stability of these two families of graphenic nano-systems. The present finding, nonetheless, provides an original argument, with potential future applications, that physical unification theory is possible, starting surprisingly from the nano-chemical topological graphenic space; thus, speculative hypotheses may be drawn, particularly relating to the computational topological unification (that is, complexification) of the quantum many-worlds picture (according to Everett’s theory) with the space-curvature sphericity/roundness of general relativity, as is also currently advocated by Wolfram’s language unification of matter-physical phenomenology.

Introductory Remarks

1980 ◽  
Vol 38 ◽  
pp. 598-599
Author(s):  
H. Mohri
Keyword(s):  
Muscle Contraction ◽  
Experimental Evidence ◽  
Sea Urchin ◽  
Constant Length ◽  
Thin Filaments ◽  
Bridge Formation ◽  
Thick Filaments ◽  
Sliding Mechanism ◽  
Radial Spokes ◽  
Cilia And Flagella

In 1959, Afzelius observed the presence of two rows of arms projecting from each outer doublet microtubule of the so-called 9 + 2 pattern of cilia and flagella, and suggested a possibility that the outer doublet microtubules slide with respect to each other with the aid of these arms during ciliary and flagellar movement. The identification of the arms as an ATPase, dynein, by Gibbons (1963)strengthened this hypothesis, since the ATPase-bearing heads of myosin molecules projecting from the thick filaments pull the thin filaments by cross-bridge formation during muscle contraction. The first experimental evidence for the sliding mechanism in cilia and flagella was obtained by examining the tip patterns of molluscan gill cilia by Satir (1965) who observed constant length of the microtubules during ciliary bending. Further evidence for the sliding-tubule mechanism was given by Summers and Gibbons (1971), using trypsin-treated axonemal fragments of sea urchin spermatozoa. Upon the addition of ATP, the outer doublets telescoped out from these fragments and the total length reached up to seven or more times that of the original fragment. Thus, the arms on a certain doublet microtubule can walk along the adjacent doublet when the doublet microtubules are disconnected by digestion of the interdoublet links which connect them with each other, or the radial spokes which connect them with the central pair-central sheath complex as illustrated in Fig. 1. On the basis of these pioneer works, the sliding-tubule mechanism has been established as one of the basic mechanisms for ciliary and flagellar movement.

War in Social Thought

2012 ◽  
Author(s):  
Hans Joas ◽  
Wolfgang Knöbl
Keyword(s):  
Twentieth Century ◽  
Intellectual History ◽  
Large Scale ◽  
Theoretical Work ◽  
German Idealism ◽  
Social Thought ◽  
Social Progress ◽  
Modern World ◽  
Critical History ◽  
Original Argument

This book provides a sweeping critical history of social theories about war and peace from Thomas Hobbes to the present. It presents both a broad intellectual history and an original argument as it traces the development of thinking about war over more than 350 years—from the premodern era to the period of German idealism and the Scottish and French enlightenments, and then from the birth of sociology in the nineteenth century through the twentieth century. While focusing on social thought, the book draws on many disciplines, including philosophy, anthropology, and political science. It demonstrate the profound difficulties most social thinkers—including liberals, socialists, and those intellectuals who could be regarded as the first sociologists—had in coming to terms with the phenomenon of war, the most obvious form of large-scale social violence. With only a few exceptions, these thinkers, who believed deeply in social progress, were unable to account for war because they regarded it as marginal or archaic, and on the verge of disappearing. This overly optimistic picture of the modern world persisted in social theory even in the twentieth century, as most sociologists and social theorists either ignored war and violence in their theoretical work or tried to explain it away. The failure of the social sciences and especially sociology to understand war, the book argues, must be seen as one of the greatest weaknesses of disciplines that claim to give a convincing diagnosis of our times.

Galileo Unbound

2018 ◽  
Author(s):  
David D. Nolte
Keyword(s):  
Free Fall ◽  
The Sun ◽  
Quantum Field ◽  
Many Worlds ◽  
Quantum Particles ◽  
Light Rays ◽  
History Of ◽  
And Control ◽  
The Universe ◽  
Insight Into

Galileo Unbound: A Path Across Life, The Universe and Everything traces the journey that brought us from Galileo’s law of free fall to today’s geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman’s dilemma of quantum particles taking all paths at once—setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.

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