Non-interacting, sp2 carbon on a ferroelectric lead zirco-titanate: towards graphene synthesis on ferroelectrics in ultrahigh vacuum

RSC Advances ◽  
2016 ◽  
Vol 6 (72) ◽  
pp. 67883-67887 ◽  
Author(s):  
N. G. Apostol ◽  
G. A. Lungu ◽  
I. C. Bucur ◽  
C. A. Tache ◽  
L. Hrib ◽  
...  
Keyword(s):  
Surface Density ◽  
Ultrahigh Vacuum ◽  
Carbon Surface ◽  
Two Dimensional ◽  
Weakly Interact ◽  
Graphene Synthesis

Carbon layers grown on lead zirco-titanate (PZT) weakly interact with the substrate and exhibit nearly two dimensional character, up to a carbon surface density approaching that of graphene.

A two-dimensional ultrahigh vacuum positioner for scanning tunneling microscopy

1998 ◽  
Vol 69 (3) ◽  
pp. 1403-1405 ◽  
Author(s):  
K. Pond ◽  
B. Z. Nosho ◽  
H. R. Stuber ◽  
A. C. Gossard ◽  
W. H. Weinberg
Keyword(s):  
Scanning Tunneling Microscopy ◽  
Ultrahigh Vacuum ◽  
Scanning Tunneling ◽  
Two Dimensional ◽  
Tunneling Microscopy

scholarly journals Van der Waals Epitaxy of Two-Dimensional MoS2–Graphene Heterostructures in Ultrahigh Vacuum

ACS Nano ◽  
2015 ◽  
Vol 9 (6) ◽  
pp. 6502-6510 ◽  
Author(s):  
Jill A. Miwa ◽  
Maciej Dendzik ◽  
Signe S. Grønborg ◽  
Marco Bianchi ◽  
Jeppe V. Lauritsen ◽  
...  
Keyword(s):  
Van Der Waals ◽  
Ultrahigh Vacuum ◽  
Two Dimensional

On the Mathematical Reconstruction of Two Dimensional Plants

2006 ◽  
Vol 26 (2) ◽  
pp. 113-129 ◽  
Author(s):  
Zbigniew J. Grzywna ◽  
Przemysław Borys ◽  
Gabriela Dudek
Keyword(s):  
Pattern Recognition ◽  
Quantitative Analysis ◽  
Medicinal Plants ◽  
Surface Density ◽  
Iterated Function Systems ◽  
Linear Ordering ◽  
Mathematical Representation ◽  
Computer Memory ◽  
Two Dimensional ◽  
Iterated Function

A set of 10, chosen medicinal plants (some of them with a reputation as remedies for tuberculosis) has been investigated through Partitioned Iterated Function Systems-Semi Fractals with Angle (PIFS-SFA) coding, Lempel, Ziv, Welch with quantization and noise (LZW-QN) compression, and surface density statistics (f(α)-SDS) discrimination techniques. The final outcomes of this quantitative analysis were, firstly: the linear ordering of the plants in question accompanied by the hope that it reflects their medical significance, secondly: the mathematical representation of each of the plants, and thirdly: the impressive compression achieved, leading to remarkable computer memory saving, and still permitting successful pattern recognition i.e., proper identification of the plant from the compressed image.

scholarly journals DIFFUSIVE TRANSPORT OF PARTIALLY QUANTIZED PARTICLES: EXISTENCE, UNIQUENESS AND LONG-TIME BEHAVIOUR

2006 ◽  
Vol 49 (3) ◽  
pp. 513-549 ◽  
Author(s):  
N. Ben Abdallah ◽  
F. Méhats ◽  
N. Vauchelet
Keyword(s):  
Diffusion Equation ◽  
Relative Entropy ◽  
Surface Density ◽  
Particle Density ◽  
Order Approximation ◽  
Three Dimensional ◽  
Diffusive Transport ◽  
Two Dimensional ◽  
Drift Diffusion ◽  
One Dimensional

AbstractA self-consistent model for charged particles, accounting for quantum confinement, diffusive transport and electrostatic interaction is considered. The electrostatic potential is a solution of a three-dimensional Poisson equation with the particle density as the source term. This density is the product of a two-dimensional surface density and that of a one-dimensional mixed quantum state. The surface density is the solution of a drift–diffusion equation with an effective surface potential deduced from the fully three-dimensional one and which involves the diagonalization of a one-dimensional Schrödinger operator. The overall problem is viewed as a two-dimensional drift–diffusion equation coupled to a Schrödinger–Poisson system. The latter is proven to be well posed by a convex minimization technique. A relative entropy and an a priori $L^2$ estimate provide sufficient bounds to prove existence and uniqueness of a global-in-time solution. In the case of thermodynamic equilibrium boundary data, a unique stationary solution is proven to exist. The relative entropy allows us to prove the convergence of the transient solution towards it as time grows to infinity. Finally, the low-order approximation of the relative entropy is used to prove that this convergence is exponential in time.

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