Curvature distribution and autocorrelations in elliptic cylinders and cones
Abstract
Not all micro-vessels (MV) are traditionally circular and there are examples of elliptic cylindrical MVs in life sciences, particularly if projected with a slant. Similarly, certain biological structures, ferroelectric liquid crystals, aluminum oxide clusters and witherite crystallites’ crosssection appear to be elliptical cones. We studied the mean curvature (H) distribution of these elliptic morphological structures with geometric parameter such as eccentricity; e (ratio of semi-minor to semi-major axes) and a measure of how much diagonal section deviates from circularity and height (h) in case of cones. By means of topographical cues, we defined the curvature-curvature autocorrelation function (gk) and applied this notion to mean curvature (H) of circular and elliptical cylinders and cones. The Fourier transform of correlation function, i.e. “curvature factor” is analogous to “structure factor (or Patterson function)” in X-ray and neutron scattering intensity. It elucidates critically important information related to surface curvature fluctuation relevant to shape (geometry), network and phase transformation. The latter is induced by cells under mechanical stress, occurring in many soft systems (polymeric liquid crystals, foams, bubbles) and biological tissues, particularly cell walls of primary and branched vessels bed in microvasculature that distributes blood within tissue during hypertension and migraines. This perspective is usefulmore »
- Authors:
- Western Kentucky Univ., Bowling Green, KY (United States). Dept. of Physics & Astronomy,
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theoretical Division and Center for Nonlinear Studies
- Publication Date:
- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE Laboratory Directed Research and Development (LDRD) Program
- OSTI Identifier:
- 1566114
- Report Number(s):
- LA-UR-19-23839
Journal ID: ISSN 2158-3226
- Grant/Contract Number:
- 89233218CNA000001
- Resource Type:
- Accepted Manuscript
- Journal Name:
- AIP Advances
- Additional Journal Information:
- Journal Volume: 9; Journal Issue: 8; Journal ID: ISSN 2158-3226
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Material Science
Citation Formats
Gupta, Sanju, and Saxena, Avadh. Curvature distribution and autocorrelations in elliptic cylinders and cones. United States: N. p., 2019.
Web. doi:10.1063/1.5106380.
Gupta, Sanju, & Saxena, Avadh. Curvature distribution and autocorrelations in elliptic cylinders and cones. United States. doi:10.1063/1.5106380.
Gupta, Sanju, and Saxena, Avadh. Thu .
"Curvature distribution and autocorrelations in elliptic cylinders and cones". United States. doi:10.1063/1.5106380. https://www.osti.gov/servlets/purl/1566114.
@article{osti_1566114,
title = {Curvature distribution and autocorrelations in elliptic cylinders and cones},
author = {Gupta, Sanju and Saxena, Avadh},
abstractNote = {Not all micro-vessels (MV) are traditionally circular and there are examples of elliptic cylindrical MVs in life sciences, particularly if projected with a slant. Similarly, certain biological structures, ferroelectric liquid crystals, aluminum oxide clusters and witherite crystallites’ crosssection appear to be elliptical cones. We studied the mean curvature (H) distribution of these elliptic morphological structures with geometric parameter such as eccentricity; e (ratio of semi-minor to semi-major axes) and a measure of how much diagonal section deviates from circularity and height (h) in case of cones. By means of topographical cues, we defined the curvature-curvature autocorrelation function (gk) and applied this notion to mean curvature (H) of circular and elliptical cylinders and cones. The Fourier transform of correlation function, i.e. “curvature factor” is analogous to “structure factor (or Patterson function)” in X-ray and neutron scattering intensity. It elucidates critically important information related to surface curvature fluctuation relevant to shape (geometry), network and phase transformation. The latter is induced by cells under mechanical stress, occurring in many soft systems (polymeric liquid crystals, foams, bubbles) and biological tissues, particularly cell walls of primary and branched vessels bed in microvasculature that distributes blood within tissue during hypertension and migraines. This perspective is useful in a sustained release of angiogenic/vasculogenic factors and relevant for precision medicine and engineered microvessels and tissues in vitro and in vivo extended cellular processes. The quantitative analysis carried out in this work facilitates our understanding of the mechanical mechanisms associated with thrombosis during surgery that typically occur in bent or stretched MVs due to microenvironment such as localized shear stresses and biochemical factors.},
doi = {10.1063/1.5106380},
journal = {AIP Advances},
number = 8,
volume = 9,
place = {United States},
year = {2019},
month = {8}
}
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