Geometry and Topology of Nanotubes and Nanotori

Koorepazan-Moftakhar, Fatemeh; Ашрафи, Али Реза; Ori, Ottorino; Putz, Mihai V.

doi:10.1007/978-94-017-9567-8_6

Cited by 7 publications

(3 citation statements)

References 32 publications

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“…Tiling the surface of a torus with hexagons can be realized by cutting a parallelogram out of an infinite plane tiled with regular hexagons. The corners of the parallelogram lie at centers of hexagons, and the mapping onto the surface of the torus is done in such a way that all four corners are mapped onto the same point. − We here limit the graph-theoretical discussion to the construction of TCNTs that consist of only hexagons, which are called polyhexes. When constructing TCNTs with an equal number of pentagons and heptagons, their positions have to be carefully chosen to obtain regular structures as those studied in this work.…”

Section: Methodsmentioning

confidence: 99%

Magnetically Induced Current Densities in Toroidal Carbon Nanotubes

et al. 2019

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Molecular structures of toroidal carbon nanotubes (TCNTs) have been constructed and optimized at the density functional theory (DFT) level. The TCNT structures have been constrained by using point groups with high symmetry. TCNTs consisting of only hexagons (polyhex) with armchair, chiral, and zigzag structures as well as TCNTs with pentagons and heptagons have been studied. The employed method for constructing general polyhex TCNTs is discussed. Magnetically induced current densities have been calculated using the gauge-including magnetically induced currents (GIMIC) method. The strength of the magnetically induced ring currents has been obtained by integrating the current density passing a plane cutting the ring of the TCNT. The main pathways of the current density have been identified by visualizing the current density. The calculations show that the strength of the diatropic ring current of polyhex TCNTs with an armchair structure generally increases with the size of the TCNT, whereas TCNTs with a zigzag structure sustain very weak diatropic ring currents. Some of the TCNTs with pentagons and heptagons sustain a strong diatropic ring current, whereas other TCNT structures with pentagons and heptagons sustain paratropic ring currents that are, in most cases, relatively weak. We discuss the reasons for the different behaviors of the current density of the seemingly similar TCNTs.

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Section: Methodsmentioning

confidence: 99%

Magnetically Induced Current Densities in Toroidal Carbon Nanotubes

et al. 2019

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“…Very recently, the Graovac-Pisanski index of some molecular graphs and nanostructures was extensively studied 1,3,[7][8][9]13 . Moreover, the closed formulas for the Graovac-Pisanski index of zigzag nanotubes were computed 14 .…”

Section: Introductionmentioning

confidence: 99%

Predicting melting points of hydrocarbons by the Graovac-Pisanski index

Črepnjak

Tratnik

Pleteršek

2018

Fullerenes, Nanotubes and Carbon Nanostructures

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Theoretical molecular descriptors alias topological indices are a convenient means for expressing in a numerical form the chemical structure encoded in a molecular graph. The structure descriptors derived from molecular graphs are widely used in Quantitative Structure-Property Relationship (QSPR) and Quantitative Structure-Activity Relationship (QSAR).In this paper, we are interested in the Graovac-Pisanski index (also called modified Wiener index) introduced in 1991 by Graovac and Pisanski, which encounters beside the distances in a molecular graph also its symmetries. In the QSPR analysis we first calculate the Graovac-Pisanski index for different families of hydrocarbon molecules using a simple program and then we show a correlation with the melting points of considered molecules. We show that the melting points of the alkane series can be very effectively predicted by the Graovac-Pisanski index and for the rest of considered molecules (PAH's and octane isomers) the regression models are different, but we establish some correlation with the melting points for them as well.

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“…(Gazzaniga, 2009), mind wandering (Andrews-Hanna et al, 2014) and so on. In order to build a versatile network able to simulate the brain function at micro-levels of observation, we introduce a cortical model borrowed from fullerene's geometry, e.g., a method able to evaluate symmetry constraints and topological indices for micro-structures (Koorepazan-Moftakhar et al, 2015). Although its primary application concerns the description of carbon-networks in chemical compounds, this method provides a mathematical treatment that can be used in order to rank topological invariants in the description of neural networks.…”

mentioning

confidence: 99%

Cracking the barcode of fullerene-like cortical microcolumns

Tozzi

Peters

Ori³

2017

Neuroscience Letters

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Artificial neural systems and nervous graph theoretical analysis rely upon the stance that the neural code is embodied in logic circuits, e.g., spatio-temporal sequences of ON/OFF spiking neurons. Nevertheless, this assumption does not fully explain complex brain functions. Here we show how nervous activity, other than logic circuits, could instead depend on topological transformations and symmetry constraints occurring at the micro-level of the cortical microcolumn, i.e., the embryological, anatomical and functional basic unit of the brain. Tubular microcolumns can be flattened in fullerene-like two-dimensional lattices, equipped with about 80 nodes standing for pyramidal neurons where neural computations take place. We show how the countless possible combinations of activated neurons embedded in the lattice resemble a barcode. Despite the fact that further experimental verification is required in order to validate our claim, different assemblies of firing neurons might have the appearance of diverse codes, each one responsible for a single mental activity. A two-dimensional fullerene-like lattice, grounded on simple topological changes standing for pyramidal neurons' activation, not just displays analogies with the real microcolumn's microcircuitry and the neural connectome, but also the potential for the manufacture of plastic, robust and fast artificial networks in robotic forms of full-fledged neural systems.

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Geometry and Topology of Nanotubes and Nanotori

Cited by 7 publications

References 32 publications

Magnetically Induced Current Densities in Toroidal Carbon Nanotubes

Magnetically Induced Current Densities in Toroidal Carbon Nanotubes

Predicting melting points of hydrocarbons by the Graovac-Pisanski index

Cracking the barcode of fullerene-like cortical microcolumns

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