Analysis of Domain-Size Distributions in Epitaxial Growth Using Leed Angular Profiles

1984 ◽  
Vol 41 ◽  
Author(s):  
D. Saloner ◽  
M. G. Lagally
Keyword(s):  
Epitaxial Growth ◽  
Size Effects ◽  
Finite Size ◽  
Domain Size ◽  
Growth Mode ◽  
Size Distributions ◽  
Two Dimensional ◽  
Finite Size Effects ◽  
Degree Of Order ◽  
Surface Of Crystals

AbstractAngular profiles of diffracted beams in surface-sensitive diffraction techniques can be used to establish the degree of order at the surface of crystals. Results are presented showing the sensitivity of such profiles to the growth mode of overlayer islands. A method is presented to incorporate the two-dimensional nature of the problem into the analysis and to extract finite-size effects from fundamental and superlattice beams.

Coupling-anisotropy and finite-size effects in interfacial tension of the two-dimensional Ising model

1999 ◽  
Vol 32 (26) ◽  
pp. 4897-4906 ◽  
Author(s):  
Ming-Chya Wu ◽  
Ming-Chang Huang ◽  
Yu-Pin Luo ◽  
Tsong-Ming Liaw
Keyword(s):  
Ising Model ◽  
Interfacial Tension ◽  
Size Effects ◽  
Finite Size ◽  
Two Dimensional ◽  
Finite Size Effects

SCALING AND FINITE-SIZE EFFECTS FOR THE CRITICAL BACKBONE

Fractals ◽  
2003 ◽  
Vol 11 (supp01) ◽  
pp. 19-27 ◽  
Author(s):  
M. BARTHELEMY ◽  
S. V. BULDYREV ◽  
S. HAVLIN ◽  
H. E. STANLEY
Keyword(s):  
Fractal Dimension ◽  
Probability Distribution ◽  
Size Effects ◽  
Infinite System ◽  
Finite Size ◽  
Multifractal Spectrum ◽  
System Size ◽  
Two Dimensional ◽  
High Current ◽  
Finite Size Effects

In a first part, we study the backbone connecting two given sites of a two-dimensional lattice separated by an arbitrary distance r in a system of size L. We find a scaling form for the average backbone mass and we also propose a scaling form for the probability distribution P(MB) of backbone mass for a given r. For r ≈ L, P(MB) is peaked around LdB, whereas for r ≪ L, P(MB) decreases as a power law, [Formula: see text], with τB ≃ 1.20 ± 0.03. The exponents ψ and τB satisfy the relation ψ = dB(τB - 1), and ψ is the codimension of the backbone, ψ = d - dB. In a second part, we study the multifractal spectrum of the current in the two-dimensional random resistor network at the percolation threshold. Our numerical results suggest that in the infinite system limit, the probability distribution behaves for small i as P(i) ~ 1/i where i is the current. As a consequence, the moments of i of order q ≤ qc = 0 diverge with system size, and all sets of bonds with current values below the most probable one have the fractal dimension of the backbone. Hence we hypothesize that the backbone can be described in terms of only (i) blobs of fractal dimension dB and (ii) high current carrying bonds of fractal dimension going from d red to dB, where d red is the fractal dimension of the red bonds carrying the maximal current.

scholarly journals Coulomb finite-size effects in quasi-two-dimensional systems

2004 ◽  
Vol 16 (6) ◽  
pp. 891-902 ◽  
Author(s):  
B Wood ◽  
W M C Foulkes ◽  
M D Towler ◽  
N D Drummond
Keyword(s):  
Size Effects ◽  
Finite Size ◽  
Two Dimensional ◽  
Finite Size Effects
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