A method of equi-valued surface construction from volume data on a face-centered cubic lattice

Author(s):  
Tomokazu Takahashi ◽  
Tatsuhiro Yonekura ◽  
Yoshiki Kishi
2020 ◽  
Vol 44 (1) ◽  
pp. 32-38
Author(s):  
Hani Shaker ◽  
Muhammad Imran ◽  
Wasim Sajjad

Abstract Chemical graph theory has become a prime gadget for mathematical chemistry due to its wide range of graph theoretical applications for solving molecular problems. A numerical quantity is named as topological index which explains the topological characteristics of a chemical graph. Recently face centered cubic lattice FCC(n) attracted large attention due to its prominent and distinguished properties. Mujahed and Nagy (2016, 2018) calculated the precise expression for Wiener index and hyper-Wiener index on rows of unit cells of FCC(n). In this paper, we present the ECI (eccentric-connectivity index), TCI (total-eccentricity index), CEI (connective eccentric index), and first eccentric Zagreb index of face centered cubic lattice.


2009 ◽  
Vol 18 (08) ◽  
pp. 1159-1173 ◽  
Author(s):  
CASEY MANN ◽  
JENNIFER MCLOUD-MANN ◽  
RAMONA RANALLI ◽  
NATHAN SMITH ◽  
BENJAMIN MCCARTY

This article concerns the minimal knotting number for several types of lattices, including the face-centered cubic lattice (fcc), two variations of the body-centered cubic lattice (bcc-14 and bcc-8), and simple-hexagonal lattices (sh). We find, through the use of a computer algorithm, that the minimal knotting number in sh is 20, in fcc is 15, in bcc-14 is 13, and bcc-8 is 18.


2017 ◽  
Vol 50 (3) ◽  
pp. 830-839 ◽  
Author(s):  
S. M. Suturin ◽  
V. V. Fedorov ◽  
A. M. Korovin ◽  
N. S. Sokolov ◽  
A. V. Nashchekin ◽  
...  

The development of growth techniques aimed at the fabrication of nanoscale heterostructures with layers of ferroic 3dmetals on semiconductor substrates is very important for their potential usage in magnetic media recording applications. A structural study is presented of single-crystal nickel island ensembles grown epitaxially on top of CaF2/Si insulator-on-semiconductor heteroepitaxial substrates with (111), (110) and (001) fluorite surface orientations. The CaF2buffer layer in the studied multilayer system prevents the formation of nickel silicide, guides the nucleation of nickel islands and serves as an insulating layer in a potential tunneling spin injection device. The present study, employing both direct-space and reciprocal-space techniques, is a continuation of earlier research on ferromagnetic 3dtransition metals grown epitaxially on non-magnetic and magnetically ordered fluorides. It is demonstrated that arrays of stand-alone faceted nickel islands with a face-centered cubic lattice can be grown controllably on CaF2surfaces of (111), (110) and (001) orientations. The proposed two-stage nickel growth technique employs deposition of a thin seeding layer at low temperature followed by formation of the islands at high temperature. The application of an advanced three-dimensional mapping technique exploiting reflection high-energy electron diffraction (RHEED) has proved that the nickel islands tend to inherit the lattice orientation of the underlying fluorite layer, though they exhibit a certain amount of {111} twinning. As shown by scanning electron microscopy, grazing-incidence X-ray diffraction (GIXD) and grazing-incidence small-angle X-ray scattering (GISAXS), the islands are of similar shape, being faceted with {111} and {100} planes. The results obtained are compared with those from earlier studies of Co/CaF2epitaxial nanoparticles, with special attention paid to the peculiarities related to the differences in lattice structure of the deposited metals: the dual-phase hexagonal close-packed/face-centered cubic lattice structure of cobalt as opposed to the single-phase face-centered cubic lattice structure of nickel.


1959 ◽  
Vol 26 (2) ◽  
pp. 251-258
Author(s):  
C. W. Thurston ◽  
H. Deresiewicz

Abstract A granular medium is idealized here by a model composed of contiguous like spheres arranged in a face-centered cubic lattice. Total stress-strain relations for this model are derived by integrating incremental relations, given previously by Duffy and Mindlin, for a loading program which consists of a uniaxial compression applied concurrently with a related isotropic pressure. Further, the failure stress in uniaxial compression is determined as a function of initial pressure. Results of experimental work are reported which agree with predictions of the theory.


1997 ◽  
Vol 46 (12) ◽  
pp. 2325
Author(s):  
JIN CHONG-JUN ◽  
QIN BAI ◽  
YANG MIAO ◽  
QIN RU-HU

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