Lie sphere geometry in lattice cosmology

It is still problematic to define a direct relationship between specific properties of a nanostructured surface (e.g., wettability) and its morphology. Not surprisingly, scientists continue to explore en masse the cut‐and‐try method. In this work, new insights are presented into the correlation of functional properties of the complex nanocomposites with their morphological characteristics. Using polyethylene‐terephthalate (PET) as a model material due to its importance and wide use in experiments, super‐hydrophilic nanocomposites amenable to be used in a variety of industrial applications are first developed, by exposing PET samples to oxygen plasma under controlled conditions. The morphology of the surfaces is confirmed using AFM and SEM techniques, and wettability in air and its oleophobic properties in water using contact angle and roll‐off measurements. Next, different analytical tools such as Minkowski connectivity (Euler‐Poincaré characteristic), Hough distributions and 2D FFT are applied to study ordering, connectivity, and fractal characteristics of the samples. It is concluded that fractal dimension, along with ordering and connectivity, are among the major characteristics of the nanocomposite that determine many important physical and chemical properties of the functional nanomaterials, and the fractal dimension could be a target morphological feature to inform the design of fabrication technology.

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Section: Discussionmentioning

confidence: 99%

“…The images of Menger sponge and Von Koch objects are reprinted under conditions of Creative Commons licenses. The image of Apollonoan sphere: Reproduced under the terms of the CC-BY 3.0 license [63]. Copyright 2020, The Authors, published by IOP Publishing.…”

mentioning

confidence: 99%

Hydrophilicity and Hydrophobicity Control of Plasma‐Treated Surfaces via Fractal Parameters

Piferi

Bazaka

D'Aversa

et al. 2021

Adv Materials Inter

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“…Remark: In this context, a sustained attempt on investigations of black hole lattices is followed by Clifton and collaborators, see the review [13] and references therein and [12], as well as Fennen and Giulini [56] who investigate black hole packings. Such approaches provide constructions of exact initial conditions of spacetimes with black holes allowing to numerically explore the effect of black holes on large scales.…”

Section: Topology and Black Holes Inmentioning

confidence: 99%

Gauss–Bonnet–Chern approach to the averaged Universe

Brunswic

Buchert

2020

Class. Quantum Grav.

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The standard model of cosmology with postulated dark energy and dark matter sources may be considered as a fairly successful fitting model to observational data. However, this model leaves the question of the physical origin of these dark components open. Fully relativistic contributions that act like dark energy on large scales and like dark matter on smaller scales can be found through generalization of the standard model by spatially averaging the inhomogeneous Universe within general relativity. The spatially averaged 3 + 1 Einstein equations are effective balance equations that need a closure condition. Heading for closure we here explore topological constraints. Results are straightforwardly obtained for averaged 2 + 1 model universes. For the relevant 3 + 1 case, we employ a method based on the Gauss–Bonnet–Chern theorem generalized to Lorentzian spacetimes and implement a sandwich approach to obtain spatial average properties. The 3 + 1 topological approach supplies us with a new equation linking evolution of scalar invariants of the expansion tensor to the norm of the Weyl tensor. From this we derive general evolution equations for averaged scalar curvature and kinematical backreaction, and we discuss related evolution equations on this level of the hierarchy of averaged equations. We also discuss the relation between topological properties of cosmological manifolds and dynamical topology change, e.g. as resulting from the formation of black holes.

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Section: Plasma‐based Methods For Biowaste‐nanomaterials Conversionmentioning

confidence: 99%

Functional Nanomaterials from Waste and Low‐Value Natural Products: A Technological Approach Level

Levchenko

Mandhakini

Prasad

et al. 2022

Adv Materials Technologies

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Low‐ and negative‐value (waste) products represent a valuable resource. Its use as a source for the fabrication of high value materials represents a lucrative pathway to increasing sustainability and decreasing the economic cost of various industries. Thermochemical methods for the valorization of biowaste and low‐value natural products are simple and cheap yet sufficiently efficient to deliver significant economic benefits. Plasma‐based methods represent another family of technologies for waste‐to‐value conversion. The nanostructure nucleation and growth in plasmas involve a complex set of physical and chemical processes that occur in bulk plasma and on surfaces. The choice between these two types of technology assumes a complex optimization that takes into account several factors including the cost of precursors; initial outlay and operating cost of equipment; the cost of labor; the cost of production engineering including the research and development efforts for designing the industrial technology, which is typically higher for the plasma‐based systems, and so on. In this article a technology level comparison of thermochemical and plasma‐based techniques for the valorization of raw and waste biomass, where the intent is to use the resulting products for environmental remediation, energy storage, optoelectronics, and biomedical applications, is presented.

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Lie sphere geometry in lattice cosmology

Cited by 4 publications

References 44 publications

Hydrophilicity and Hydrophobicity Control of Plasma‐Treated Surfaces via Fractal Parameters

Hydrophilicity and Hydrophobicity Control of Plasma‐Treated Surfaces via Fractal Parameters

Gauss–Bonnet–Chern approach to the averaged Universe

Functional Nanomaterials from Waste and Low‐Value Natural Products: A Technological Approach Level

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