Polymer crystallization in quasi-two dimensions. II. Kinetic models and computer simulations

In a recent commentary, J. M. Kosterlitz described how D. Thouless and he got motivated to investigate melting and suprafluidity in two dimensions [Kosterlitz JM (2016)J Phys Condens Matter28:481001]. It was due to the lack of broken translational symmetry in two dimensions—doubting the existence of 2D crystals—and the first computer simulations foretelling 2D crystals (at least in tiny systems). The lack of broken symmetries proposed by D. Mermin and H. Wagner is caused by long wavelength density fluctuations. Those fluctuations do not only have structural impact, but additionally a dynamical one: They cause the Lindemann criterion to fail in 2D in the sense that the mean squared displacement of atoms is not limited. Comparing experimental data from 3D and 2D amorphous solids with 2D crystals, we disentangle Mermin–Wagner fluctuations from glassy structural relaxations. Furthermore, we demonstrate with computer simulations the logarithmic increase of displacements with system size: Periodicity is not a requirement for Mermin–Wagner fluctuations, which conserve the homogeneity of space on long scales.

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Computer simulations of cell-target encounter including biased cell motion toward targets: Single and multiple cell-target simulations in two dimensions

Bulletin of Mathematical Biology ◽

10.1007/bf02458631 ◽

1991 ◽

Vol 53 (4) ◽

pp. 591-621 ◽

Cited By ~ 4

Author(s):

S. B. Charnick ◽

E. S. Fisher ◽

D. A. Lauffenburger

Keyword(s):

Computer Simulations ◽

Two Dimensions ◽

Cell Target ◽

Multiple Cell ◽

Cell Motion

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Computer simulations of cardiac action potentials in two dimensions

Brain Research Bulletin ◽

10.1016/0361-9230(88)90120-7 ◽

1988 ◽

Vol 21 (1) ◽

pp. 55-60 ◽

Cited By ~ 4

Author(s):

John Paul Barach

Keyword(s):

Computer Simulations ◽

Action Potentials ◽

Two Dimensions ◽

Cardiac Action

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Kinetic models of ordering in two dimensions

Journal of Materials Processing Technology ◽

10.1016/s0924-0136(03)00333-9 ◽

2003 ◽

Vol 143-144 ◽

pp. 122-125

Author(s):

C. Morón ◽

M. Mora

Keyword(s):

Kinetic Models ◽

Two Dimensions

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Aggregation kinetics in two dimensions: Real experiments and computer simulations

The Journal of Chemical Physics ◽

10.1063/1.1329344 ◽

2001 ◽

Vol 114 (1) ◽

pp. 520 ◽

Cited By ~ 6

Author(s):

Attila Vincze ◽

Attila Agod ◽

János Kertész ◽

Miklós Zrı́nyi ◽

Zoltán Hórvölgyi

Keyword(s):

Computer Simulations ◽

Two Dimensions ◽

Aggregation Kinetics

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On the Validation of the Monte Carlo Technique in Simulation of Grain Growth in Small, Two-Dimensional Systems

Materials Science Forum ◽

10.4028/www.scientific.net/msf.558-559.1087 ◽

2007 ◽

Vol 558-559 ◽

pp. 1087-1092

Author(s):

Ola Hunderi ◽

Knut Marthinsen ◽

Nils Ryum

Keyword(s):

Monte Carlo ◽

Grain Boundary ◽

Grain Growth ◽

Computer Simulations ◽

Two Dimensions ◽

Theoretical Treatment ◽

Two Dimensional ◽

Simulation Techniques ◽

Boundary Curvature ◽

Kinetics Of

The kinetics of grain growth in real systems is influenced by several unknown factors, making a theoretical treatment very difficult. Idealized grain growth, assuming all grain boundaries to have the same energy and mobility (mobility M = k/ρ, where k is a constant and ρ is grain boundary curvature) can be treated theoretically, but the results obtained can only be compared to numerical grain growth simulations, as ideal grain growth scarcely exists in nature. The validity of the simulation techniques thus becomes of great importance. In the present investigation computer simulations of grain growth in two dimensions using Monte Carlo simulations and the grain boundary tracking technique have been investigated and compared in small grain systems, making it possible to follow the evolution of each grain in the system.

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