One-dimensional crystal growth model on a square lattice substrate

2016 ◽  
Vol 380 (37) ◽  
pp. 2989-2992 ◽  
Author(s):  
Yi Cheng ◽  
Chenxi Lu ◽  
Bo Yang ◽  
Xiangming Tao ◽  
Jianfeng Wang ◽  
...  
Keyword(s):  
Crystal Growth ◽  
Growth Model ◽  
Square Lattice ◽  
One Dimensional ◽  
Dimensional Crystal

A low-dimensional crystal growth model on an isotropic and quasi-free sustained substrate

2020 ◽  
Vol 29 (3) ◽  
pp. 038101
Author(s):  
Chenxi Lu ◽  
Senjiang Yu ◽  
Lingwei Li ◽  
Bo Yang ◽  
Xiangming Tao ◽  
...  
Keyword(s):  
Crystal Growth ◽  
Growth Model ◽  
Low Dimensional ◽  
Dimensional Crystal

New exact results for the defective square lattice

1976 ◽  
Vol 80 (2) ◽  
pp. 365-381 ◽  
Author(s):  
G. Ronca
Keyword(s):  
Closed Form Solution ◽  
Exact Result ◽  
Form Solution ◽  
Square Lattice ◽  
Zero Temperature ◽  
Real Crystal ◽  
One Dimensional ◽  
Resonance Modes ◽  
The One ◽  
Dimensional Crystal

Since the publication of the fundamental papers by Lifshitz (1, 2) and Montroll and Potts (3, 4) many authors have investigated the effect of an isotopic impurity on the lattice vibrations of a harmonic crystal at zero temperature. A fairly broad knowledge is now available on scattering amplitudes, localized modes and resonance modes (6, 7). Nevertheless, as pointed out by Maradudin and Montroll (see (7), p. 430), a closed form solution to the problem has been found only for the one-dimensional crystal, the work done on two and three-dimensional crystals being predominantly numerical. Unfortunately the one-dimensional crystal, as an approximation for a real crystal is an oversimplified model, incapable as it is of exhibiting resonance modes. To the author's knowledge the most significant exact result concerning the classical behaviour at zero temperature of crystals having a dimensionality higher than one is the connexion, calculated by Mahanty et al. (5) between localized mode frequency and impurity mass for the case of a square lattice undergoing planar vibrations.

scholarly journals Viscosity solutions for a polymer crystal growth model

2011 ◽  
Vol 60 (3) ◽  
pp. 895-936
Author(s):  
Pierre Cardaliaguet ◽  
Olivier Ley ◽  
Aurelien Monteillet
Keyword(s):  
Crystal Growth ◽  
Growth Model ◽  
Viscosity Solutions ◽  
Polymer Crystal
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