Negative Gaussian curvature distribution in physical and biophysical systems—Curved nanocarbons and ion-channel membrane proteins

2012 ◽  
Vol 112 (11) ◽  
pp. 114316 ◽  
Author(s):  
Sanju Gupta ◽  
Avadh Saxena
Keyword(s):  
Membrane Proteins ◽  
Ion Channel ◽  
Gaussian Curvature ◽  
Negative Gaussian Curvature ◽  
Curvature Distribution

Negative Gaussian curvature induces significant suppression of thermal conduction in carbon crystals

Nanoscale ◽  
2017 ◽  
Vol 9 (37) ◽  
pp. 14208-14214 ◽  
Author(s):  
Zhongwei Zhang ◽  
Jie Chen ◽  
Baowen Li
Keyword(s):  
Gaussian Curvature ◽  
Thermal Conduction ◽  
Negative Curvature ◽  
Positive Curvature ◽  
Significant Suppression ◽  
Carbon Allotropes ◽  
Zero Curvature ◽  
Negative Gaussian Curvature

From the mathematic category of surface Gaussian curvature, carbon allotropes can be classified into three types: zero curvature, positive curvature, and negative curvature.

scholarly journals Chirality in curved polyaromatic systems

2017 ◽  
Vol 46 (6) ◽  
pp. 1643-1660 ◽  
Author(s):  
Michel Rickhaus ◽  
Marcel Mayor ◽  
Michal Juríček
Keyword(s):  
Gaussian Curvature ◽  
Carbon Allotrope ◽  
Carbon Allotropes ◽  
Negative Gaussian Curvature ◽  
Helical Chirality

Chiral non-planar polyaromatic systems that display zero, positive or negative Gaussian curvature are analysed and their potential to ‘encode’ chirality of larger sp2-carbon allotropes is evaluated. Shown is a hypothetical peanut-shaped carbon allotrope, where helical chirality results from the interplay of various curvature types.

scholarly journals Encoding Gaussian curvature in glassy and elastomeric liquid crystal solids

2016 ◽  
Vol 472 (2189) ◽  
pp. 20160112 ◽  
Author(s):  
Cyrus Mostajeran ◽  
Mark Warner ◽  
Taylor H. Ware ◽  
Timothy J. White
Keyword(s):  
Gaussian Curvature ◽  
Logarithmic Spiral ◽  
Geometric Constraints ◽  
Intrinsic Geometry ◽  
Constant Gaussian Curvature ◽  
Spatially Inhomogeneous ◽  
Negative Gaussian Curvature ◽  
Annular Domains ◽  
Spherical Caps ◽  
Local Deformations

We describe shape transitions of thin, solid nematic sheets with smooth, preprogrammed, in-plane director fields patterned across the surface causing spatially inhomogeneous local deformations. A metric description of the local deformations is used to study the intrinsic geometry of the resulting surfaces upon exposure to stimuli such as light and heat. We highlight specific patterns that encode constant Gaussian curvature of prescribed sign and magnitude. We present the first experimental results for such programmed solids, and they qualitatively support theory for both positive and negative Gaussian curvature morphing from flat sheets on stimulation by light or heat. We review logarithmic spiral patterns that generate cone/anti-cone surfaces, and introduce spiral director fields that encode non-localized positive and negative Gaussian curvature on punctured discs, including spherical caps and spherical spindles. Conditions are derived where these cap-like, photomechanically responsive regions can be anchored in inert substrates by designing solutions that ensure compatibility with the geometric constraints imposed by the surrounding media. This integration of such materials is a precondition for their exploitation in new devices. Finally, we consider the radial extension of such director fields to larger sheets using nematic textures defined on annular domains.

Edge Influence Coefficients for Toroidal Shells of Negative Gaussian Curvature

1960 ◽  
Vol 82 (1) ◽  
pp. 69-75 ◽  
Author(s):  
G. D. Galletly
Keyword(s):  
Gaussian Curvature ◽  
Constant Thickness ◽  
Toroidal Shell ◽  
Uniform Pressure ◽  
Simple Manner ◽  
Negative Gaussian Curvature ◽  
Influence Coefficients ◽  
Bending Loads ◽  
Edge Influence ◽  
Toroidal Shells

Continuing the work presented in reference [1], the present paper gives additional tables for the edge deformations of constant-thickness toroidal shells subject to edge bending loads and uniform pressure. The two papers together thus cover a wide variety of toroidal shell geometries and enable a designer to calculate in a simple manner the edge moments and shears at toroidal shell junctions.

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