Analytic properties for the honeycomb lattice Green function at the origin

2018 ◽  
Vol 51 (18) ◽  
pp. 185002 ◽  
Author(s):  
G S Joyce
Keyword(s):  
Green Function ◽  
Honeycomb Lattice

THE COMPENSATION BEHAVIOR AND INITIAL SUSCEPTIBILITIES OF A MIXED-SPIN HEISENBERG FERRIMAGNETIC SYSTEM IN AN EXTERNAL MAGNETIC FIELD

2007 ◽  
Vol 21 (07) ◽  
pp. 1077-1087 ◽  
Author(s):  
JUN LI ◽  
AN DU ◽  
GUOZHU WEI
Keyword(s):  
Magnetic Field ◽  
Magnetic Properties ◽  
Transition Temperature ◽  
External Magnetic Field ◽  
Green Function ◽  
Compensation Point ◽  
Function Technique ◽  
Honeycomb Lattice ◽  
Mixed Spin ◽  
Compensation Behavior

The magnetic properties of a mixed spin-2 and spin-5 / 2 Heisenberg ferrimagnetic system on a layered honeycomb lattice are investigated theoretically by a multisublattice Green-function technique which takes into account the quantum nature of Heisenberg spins. We calculate the magnetization and the compensation temperature and transition temperature of the system in an external magnetic field and in a zero external magnetic field, and find that the transition temperature of the system increases on the effect of an external magnetic field, the compensation point disappears when the single-ion anisotropy is not large and there are two compensation points when the anisotropy is large. We also calculate the initial susceptibilities of the system.

Exponentially Convergent Approximation to the Elliptic Solution Operator

2006 ◽  
Vol 6 (4) ◽  
pp. 386-404 ◽  
Author(s):  
Ivan. P. Gavrilyuk ◽  
V.L. Makarov ◽  
V.B. Vasylyk
Keyword(s):  
Green Function ◽  
Boundary Value Problem ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Solution Operator ◽  
Hyperbolic Operator ◽  
Elliptic Solution ◽  
Elliptic Boundary Value ◽  
Sine Family ◽  
The Green Function

AbstractWe develop an accurate approximation of the normalized hyperbolic operator sine family generated by a strongly positive operator A in a Banach space X which represents the solution operator for the elliptic boundary value problem. The solution of the corresponding inhomogeneous boundary value problem is found through the solution operator and the Green function. Starting with the Dunford — Cauchy representation for the normalized hyperbolic operator sine family and for the Green function, we then discretize the integrals involved by the exponentially convergent Sinc quadratures involving a short sum of resolvents of A. Our algorithm inherits a two-level parallelism with respect to both the computation of resolvents and the treatment of different values of the spatial variable x ∈ [0, 1].

2D Honeycomb Silicon: A Review on Theoretical Advances for Silicene Field-Effect Transistors

2020 ◽  
Vol 16 (4) ◽  
pp. 595-607 ◽  
Author(s):  
Mu Wen Chuan ◽  
Kien Liong Wong ◽  
Afiq Hamzah ◽  
Shahrizal Rusli ◽  
Nurul Ezaila Alias ◽  
...  
Keyword(s):  
Field Effect ◽  
Field Effect Transistors ◽  
Semiconductor Industry ◽  
Honeycomb Lattice ◽  
Theoretical Studies ◽  
Fabrication Technology ◽  
Dirac Cone ◽  
Free Standing ◽  
Silicene Nanoribbons ◽  
Effect Transistor

Catalysed by the success of mechanical exfoliated free-standing graphene, two dimensional (2D) semiconductor materials are successively an active area of research. Silicene is a monolayer of silicon (Si) atoms with a low-buckled honeycomb lattice possessing a Dirac cone and massless fermions in the band structure. Another advantage of silicene is its compatibility with the Silicon wafer fabrication technology. To effectively apply this 2D material in the semiconductor industry, it is important to carry out theoretical studies before proceeding to the next step. In this paper, an overview of silicene and silicene nanoribbons (SiNRs) is described. After that, the theoretical studies to engineer the bandgap of silicene are reviewed. Recent theoretical advancement on the applications of silicene for various field-effect transistor (FET) structures is also discussed. Theoretical studies of silicene have shown promising results for their application as FETs and the efforts to study the performance of bandgap-engineered silicene FET should continue to improve the device performance.

scholarly journals Existence of Positive Solutions for a Kind of Fractional Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Hongjie Liu ◽  
Xiao Fu ◽  
Liangping Qi
Keyword(s):  
Fixed Point ◽  
Green Function ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Existence Of Positive Solutions ◽  
Liouville Fractional Derivative ◽  
Fractional Boundary Value Problems

We are concerned with the following nonlinear three-point fractional boundary value problem:D0+αut+λatft,ut=0,0<t<1,u0=0, andu1=βuη, where1<α≤2,0<β<1,0<η<1,D0+αis the standard Riemann-Liouville fractional derivative,at>0is continuous for0≤t≤1, andf≥0is continuous on0,1×0,∞. By using Krasnoesel'skii's fixed-point theorem and the corresponding Green function, we obtain some results for the existence of positive solutions. At the end of this paper, we give an example to illustrate our main results.

Sign in / Sign up

Export Citation Format

Share Document