scholarly journals Probing the shear modulus of two-dimensional multiplanar nanostructures and heterostructures

Nanoscale ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 5280-5294 ◽  
Author(s):  
T. Mukhopadhyay ◽  
A. Mahata ◽  
S. Adhikari ◽  
M. Asle Zaeem
Keyword(s):  
Shear Modulus ◽  
Closed Form ◽  
Analytical Approach ◽  
High Fidelity ◽  
Two Dimensional

Generalized high-fidelity closed-form formulae have been developed to predict the shear modulus of hexagonal graphene-like monolayer nanostructures and nano-heterostructures based on a physically insightful analytical approach.

scholarly journals Colored HOMFLY-PT for hybrid weaving knot $$ {\hat{\mathrm{W}}}_3 $$(m, n)

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Vivek Kumar Singh ◽  
Rama Mishra ◽  
P. Ramadevi
Keyword(s):  
Closed Form ◽  
Topological Strings ◽  
Chebyshev Polynomials ◽  
Fibonacci Numbers ◽  
Infinite Family ◽  
Closed Form Expression ◽  
Two Dimensional ◽  
Laurent Polynomials ◽  
Form Expression ◽  
Torus Knots

Abstract Weaving knots W(p, n) of type (p, n) denote an infinite family of hyperbolic knots which have not been addressed by the knot theorists as yet. Unlike the well known (p, n) torus knots, we do not have a closed-form expression for HOMFLY-PT and the colored HOMFLY-PT for W(p, n). In this paper, we confine to a hybrid generalization of W(3, n) which we denote as $$ {\hat{W}}_3 $$ W ̂ 3 (m, n) and obtain closed form expression for HOMFLY-PT using the Reshitikhin and Turaev method involving $$ \mathrm{\mathcal{R}} $$ ℛ -matrices. Further, we also compute [r]-colored HOMFLY-PT for W(3, n). Surprisingly, we observe that trace of the product of two dimensional $$ \hat{\mathrm{\mathcal{R}}} $$ ℛ ̂ -matrices can be written in terms of infinite family of Laurent polynomials $$ {\mathcal{V}}_{n,t}\left[q\right] $$ V n , t q whose absolute coefficients has interesting relation to the Fibonacci numbers $$ {\mathrm{\mathcal{F}}}_n $$ ℱ n . We also computed reformulated invariants and the BPS integers in the context of topological strings. From our analysis, we propose that certain refined BPS integers for weaving knot W(3, n) can be explicitly derived from the coefficients of Chebyshev polynomials of first kind.

Fluctuations and Shear Modulus of a Classical Two-Dimensional Electron Solid: Experiment

1982 ◽  
Vol 49 (3) ◽  
pp. 212-215 ◽  
Author(s):  
F. Gallet ◽  
G. Deville ◽  
A. Valdès ◽  
F. I. B. Williams
Keyword(s):  
Shear Modulus ◽  
Two Dimensional ◽  
Dimensional Electron

scholarly journals Thermos Array: Two-Dimensional Sparse Array with Reduced Mutual Coupling

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Lei Sun ◽  
Minglei Yang ◽  
Baixiao Chen
Keyword(s):  
Closed Form ◽  
Degrees Of Freedom ◽  
Mutual Coupling ◽  
Doa Estimation ◽  
Two Dimensional ◽  
Spatial Smoothing ◽  
Planar Arrays ◽  
Half Wavelength ◽  
Planar Array ◽  
Small Spacing

Sparse planar arrays, such as the billboard array, the open box array, and the two-dimensional nested array, have drawn lots of interest owing to their ability of two-dimensional angle estimation. Unfortunately, these arrays often suffer from mutual-coupling problems due to the large number of sensor pairs with small spacing d (usually equal to a half wavelength), which will degrade the performance of direction of arrival (DOA) estimation. Recently, the two-dimensional half-open box array and the hourglass array are proposed to reduce the mutual coupling. But both of them still have many sensor pairs with small spacing d, which implies that the reduction of mutual coupling is still limited. In this paper, we propose a new sparse planar array which has fewer number of sensor pairs with small spacing d. It is named as the thermos array because its shape seems like a thermos. Although the resulting difference coarray (DCA) of the thermos array is not hole-free, a large filled rectangular part in the DCA can be facilitated to perform spatial-smoothing-based DOA estimation. Moreover, it enjoys closed-form expressions for the sensor locations and the number of available degrees of freedom. Simulations show that the thermos array can achieve better DOA estimation performance than the hourglass array in the presence of mutual coupling, which indicates that our thermos array is more robust to the mutual-coupling array.

scholarly journals Shear modulus of two-dimensional colloidal crystals

2002 ◽  
Vol 57 (2) ◽  
pp. 219-225 ◽  
Author(s):  
A Wille ◽  
F Valmont ◽  
K Zahn ◽  
G Maret
Keyword(s):  
Shear Modulus ◽  
Colloidal Crystals ◽  
Two Dimensional

scholarly journals Buckling of regular, chiral and hierarchical honeycombs under a general macroscopic stress state

2014 ◽  
Vol 470 (2167) ◽  
pp. 20130856 ◽  
Author(s):  
Babak Haghpanah ◽  
Jim Papadopoulos ◽  
Davood Mousanezhad ◽  
Hamid Nayeb-Hashemi ◽  
Ashkan Vaziri
Keyword(s):  
Finite Element ◽  
Stress State ◽  
Closed Form ◽  
Plane Stress ◽  
Plane Stress State ◽  
Cellular Structures ◽  
Two Dimensional ◽  
Buckling Strength ◽  
Macroscopic Stress ◽  
Unit Cells

An approach to obtain analytical closed-form expressions for the macroscopic ‘buckling strength’ of various two-dimensional cellular structures is presented. The method is based on classical beam-column end-moment behaviour expressed in a matrix form. It is applied to sample honeycombs with square, triangular and hexagonal unit cells to determine their buckling strength under a general macroscopic in-plane stress state. The results were verified using finite-element Eigenvalue analysis.

Direct Coupling of a Two-Dimensional Fan Model in a Turbofan Engine Performance Simulation

2016 ◽  
Author(s):  
Ioannis Templalexis ◽  
Alexios Alexiou ◽  
Vassilios Pachidis ◽  
Ioannis Roumeliotis ◽  
Nikolaos Aretakis
Keyword(s):  
Three Dimensional ◽  
Engine Performance ◽  
System Level ◽  
Design Parameters ◽  
High Fidelity ◽  
Two Dimensional ◽  
Performance Simulation ◽  
Cfd Models ◽  
Component Design ◽  
Complex Phenomena

Coupling of high fidelity component calculations with overall engine performance simulations (zooming) can provide more accurate physics and geometry based estimates of component performance. Such a simulation strategy offers the ability to study complex phenomena and their effects on engine performance and enables component design changes to be studied at engine system level. Additionally, component interaction effects can be better captured. Overall, this approach can reduce the need for testing and the engine development time and cost. Different coupling methods and tools have been proposed and developed over the years ranging from integrating the results of the high fidelity code through conventional performance component maps to fully-integrated three-dimensional CFD models. The present paper deals with the direct integration of an in-house two-dimensional (through flow) streamline curvature code (SOCRATES) in a commercial engine performance simulation environment (PROOSIS) with the aim to establish the necessary coupling methodology that will allow future advanced studies to be performed (e.g. engine condition diagnosis, design optimization, mission analysis, distorted flow). A notional two-shaft turbofan model typical for light business jets and trainer aircraft is initially created using components with conventional map-defined performance. Next, a derivative model is produced where the fan component is replaced with one that integrates the high fidelity code. For both cases, an operating line is simulated at sea-level static take-off conditions and their performances are compared. Finally, the versatility of the approach is further demonstrated through a parametric study of various fan design parameters for a better thermodynamic matching with the driving turbine at design point operation.

Site-bond percolation in two-dimensional kagome lattices: Analytical approach and numerical simulations

2021 ◽  
Vol 104 (1) ◽  
Author(s):  
M. I. González-Flores ◽  
A. A. Torres ◽  
W. Lebrecht ◽  
A. J. Ramirez-Pastor
Keyword(s):  
Numerical Simulations ◽  
Analytical Approach ◽  
Bond Percolation ◽  
Two Dimensional

Closed-form solutions of an elliptical crack subjected to coupled phonon–phason loadings in two-dimensional hexagonal quasicrystal media

2018 ◽  
Vol 24 (6) ◽  
pp. 1821-1848 ◽  
Author(s):  
Yuan Li ◽  
CuiYing Fan ◽  
Qing-Hua Qin ◽  
MingHao Zhao
Keyword(s):  
Closed Form ◽  
Integral Equations ◽  
Analytical Solutions ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Elliptical Crack ◽  
Two Dimensional ◽  
Crack Face ◽  
Penny Shaped Crack ◽  
Crack Problems

An elliptical crack subjected to coupled phonon–phason loadings in a three-dimensional body of two-dimensional hexagonal quasicrystals is analytically investigated. Owing to the existence of the crack, the phonon and phason displacements are discontinuous along the crack face. The phonon and phason displacement discontinuities serve as the unknown variables in the generalized potential function method which are used to derive the boundary integral equations. These boundary integral equations governing Mode I, II, and III crack problems in two-dimensional hexagonal quasicrystals are expressed in integral differential form and hypersingular integral form, respectively. Closed-form exact solutions to the elliptical crack problems are first derived for two-dimensional hexagonal quasicrystals. The corresponding fracture parameters, including displacement discontinuities along the crack face and stress intensity factors, are presented considering all three crack cases of Modes I, II, and III. Analytical solutions for a penny-shaped crack, as a special case of the elliptical problem, are given. The obtained analytical solutions are graphically presented and numerically verified by the extended displacement discontinuities boundary element method.

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