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Nucleation in the Ising model, Lenna...

Clark University.

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Nucleation in the Ising model, Lennard-Jones liquid, and the long-range FPU model.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Nucleation in the Ising model, Lennard-Jones liquid, and the long-range FPU model./
Author:	Wang, Hui.
Description:	120 p.
Notes:	Adviser: Harvey Gould.
Contained By:	Dissertation Abstracts International68-09B.
Subject:	Physics, Condensed Matter. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3282770
ISBN:	9780549254300

Nucleation in the Ising model, Lennard-Jones liquid, and the long-range FPU model.
Wang, Hui.

Nucleation in the Ising model, Lennard-Jones liquid, and the long-range FPU model. - 120 p.

Adviser: Harvey Gould.

Thesis (Ph.D.)--Clark University, 2007.

The distribution of nucleation times for the Ising model is determined using the Metropolis algorithm. I find that the nucleation rate is suppressed at early times even after global variables such as the magnetization and energy are apparently in metastable equilibrium. I relate the observed nonequilibrium behavior of the nucleation rate to the time required for clusters of spins in the stable phase to grow to a size comparable to the size of the nucleating droplet. I also find subtle structural differences between the nucleating droplets formed before and after metastable equilibrium has been established. My results suggest that using global variables as indicators of metastable equilibrium may not be appropriate in general, and distinguishing between equilibrium and transient nucleation is important in studying the structures of nucleating droplets.

ISBN: 9780549254300Subjects--Topical Terms:

1018743
Physics, Condensed Matter.

Nucleation in the Ising model, Lennard-Jones liquid, and the long-range FPU model.
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005 20100713
008 100713s2007 ||||||||||||||||| ||eng d
020 $a 9780549254300
035 $a (UMI)AAI3282770
035 $a AAI3282770
040 $a UMI $c UMI
100 1 $a Wang, Hui. $3 836732
245 1 0 $a Nucleation in the Ising model, Lennard-Jones liquid, and the long-range FPU model.
300 $a 120 p.
500 $a Adviser: Harvey Gould.
500 $a Source: Dissertation Abstracts International, Volume: 68-09, Section: B, page: 6029.
502 $a Thesis (Ph.D.)--Clark University, 2007.
520 $a The distribution of nucleation times for the Ising model is determined using the Metropolis algorithm. I find that the nucleation rate is suppressed at early times even after global variables such as the magnetization and energy are apparently in metastable equilibrium. I relate the observed nonequilibrium behavior of the nucleation rate to the time required for clusters of spins in the stable phase to grow to a size comparable to the size of the nucleating droplet. I also find subtle structural differences between the nucleating droplets formed before and after metastable equilibrium has been established. My results suggest that using global variables as indicators of metastable equilibrium may not be appropriate in general, and distinguishing between equilibrium and transient nucleation is important in studying the structures of nucleating droplets.
520 $a The homogeneous and heterogeneous nucleation of a Lennard-Jones liquid is investigated using the umbrella sampling method. The free energy cost of forming a nucleating droplet is determined as a function of the quench depth, and the saddle point nature of the nucleating droplets is verified using an intervention technique. The structure and symmetry of the nucleating droplets is found for a range of temperatures. I find that at deep quenches the nucleating droplets become more diffuse and anisotropic with no well defined core. The environment of the nucleating droplets form randomly stacked hexagonal planes. This behavior is consistent with a spinodal nucleation interpretation. I also find that the free energy barrier for heterogeneous nucleation is a minimum when the lattice spacing of the impurity equals the lattice spacing of the equilibrium crystalline phase. If the lattice spacing of the impurity is different, the crystal grows into the bulk instead of wetting the impurity.
520 $a Some preliminary results regarding the non-ergodic behavior of the long-range FPU model are obtained. Although the system is non-ergodic for nearest-neighbor interaction, it becomes ergodic in the mean-field limit. It is possible to explain its ergodic behaviors by assuming that the system can be described by a free energy picture.
590 $a School code: 0048.
650 4 $a Physics, Condensed Matter. $3 1018743
690 $a 0611
710 2 $a Clark University. $3 1017690
773 0 $t Dissertation Abstracts International $g 68-09B.
790 $a 0048
790 1 0 $a Gould, Harvey, $e advisor
791 $a Ph.D.
792 $a 2007
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3282770