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- 검색키워드
- 저자 : Ziatdinov, M. (검색결과 3 건)
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Ziatdinov, R.,Yoshida, N.,Kim, T.w. North-Holland 2017 Computer aided geometric design Vol.56 No.-
In biangular coordinates, a G<SUP>1</SUP> Hermite interpolation reduces to the problem of choosing appropriate functions interpolating the coordinates of the curve at its endpoints. The simplest linear equations in biangular coordinates correspond to a sectrix of Maclaurin, which can be extended by introducing two shape parameters that stretch the curve toward the sides of its triangular envelope. However, these additional degrees of freedom complicate the possibility of obtaining analytical conditions for curvature monotonicity. Therefore, we determine the regions of monotonic curvature experimentally, for different values of the interpolant's shape parameters. We show that the parameter space of curves based on a sectrix of Maclaurin contain larger regions of monotonic curvature than those of a quadratic Bezier curve and its rational form. This suggests that our approach provides more flexibility in designing applications requiring curvature monotonicity. Finally, we classify curves with monotonic curvature based on their regions of monotonic curvature.
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Chemically induced topological zero mode at graphene armchair edges
Ziatdinov, M.,Lim, H.,Fujii, S.,Kusakabe, K.,Kiguchi, M.,Enoki, T.,Kim, Y. Royal Society of Chemistry 2017 Physical chemistry chemical physics Vol.19 No.7
<P>The electronic and magnetic properties of chemically modified graphene armchair edges are studied using a combination of tight-binding calculations, first-principles modelling, and low temperature scanning tunneling microscopy (STM) experiments. The atomically resolved STM images of the hydrogen etched graphitic edges suggest the presence of localized states at the Fermi level for certain armchair edges. We demonstrate theoretically that the topological zero-energy edge mode may emerge at armchair boundaries with asymmetrical chemical termination of the two outermost atoms in the unit cell. We particularly focus our attention on armchair edges terminated by various combinations of the hydrogen (H, H-2) and methylene (CH2) groups. The inclusion of the spin component in our calculations reveals the appearance of pi-electron-based magnetism at the armchair edges under consideration.</P>
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Two-point <sup> G 1 </sup> Hermite interpolation in biangular coordinates
Ziatdinov, Rushan,Kim, Tae-wan,Nabiyev, Rifkat I. Koninklijke Vlaamse Ingenieursvereniging 2015 Journal of computational and applied mathematics Vol.287 No.-
<P><B>Abstract</B></P> <P>We construct <SUP> G 1 </SUP> Hermite interpolating curves in biangular coordinates, and provide sufficient conditions for their convexity. In a biangular coordinate system, the problem reduces to that of choosing suitable functions interpolating the biangular coordinates of the curve at its end points. The simplest linear equations, γ = ( ( 1 − t ) α , t β ) , in biangular coordinates correspond to a sectrix of Maclaurin, which we extend by introducing two shape parameters that pull the curve towards the sides of its triangular envelope. In addition, we consider a class of curves whose biangular coordinates have a constant sum, and we analyze their shape and curvature.</P> <P><B>Highlights</B></P> <P> <UL> <LI> The equations of most curves in biangular coordinate system are not yet known. </LI> <LI> We construct <SUP> G 1 </SUP> Hermite interpolating curves in biangular coordinates. </LI> <LI> Interpolation problem reduces to choosing suitable functions in biangular coordinates. </LI> <LI> The simplest linear equations correspond to the sectrix of Maclaurin. </LI> <LI> Proposed interpolation method may reduce the computational cost in some cases. </LI> </UL> </P> <P><B>Graphical abstract</B></P> <P>[DISPLAY OMISSION]</P>
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