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Mathematical analysis of molecular d...

Li, Dong.

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Mathematical analysis of molecular dynamics and related problems .

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Mathematical analysis of molecular dynamics and related problems ./
Author:	Li, Dong.
Description:	158 p.
Notes:	Adviser: E. Weinan.
Contained By:	Dissertation Abstracts International67-09B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3236183
ISBN:	9780542894459

Mathematical analysis of molecular dynamics and related problems .
Li, Dong.

Mathematical analysis of molecular dynamics and related problems . - 158 p.

Adviser: E. Weinan.

Thesis (Ph.D.)--Princeton University, 2006.

This thesis consists of three parts. In the first part we carry out a mathematical analysis of some most commonly used molecular dynamics algorithms. A complete analysis is done for the Andersen thermostat which is a frequently used tool in molecular dynamics. After reformulating the continuous and discrete time Andersen dynamics, we prove that in both cases the Andersen dynamics is uniformly ergodic. A detailed numerical analysis is presented, establishing the rate of convergence of most commonly used numerical algorithms for the Andersen thermostat. Transport properties such as the diffusion constant are also investigated. It is proved for the Lorentz gas model where there is intrinsic diffusion, the diffusion coefficient calculated using the Andersen thermostat converges to the true diffusion coefficient in the limit of vanishing collision frequency in the Andersen thermostat.

ISBN: 9780542894459Subjects--Topical Terms:

515831
Mathematics.

Mathematical analysis of molecular dynamics and related problems .
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020 $a 9780542894459
035 $a (UnM)AAI3236183
035 $a AAI3236183
040 $a UnM $c UnM
100 1 $a Li, Dong. $3 1287283
245 1 0 $a Mathematical analysis of molecular dynamics and related problems .
300 $a 158 p.
500 $a Adviser: E. Weinan.
500 $a Source: Dissertation Abstracts International, Volume: 67-09, Section: B, page: 5112.
502 $a Thesis (Ph.D.)--Princeton University, 2006.
520 $a This thesis consists of three parts. In the first part we carry out a mathematical analysis of some most commonly used molecular dynamics algorithms. A complete analysis is done for the Andersen thermostat which is a frequently used tool in molecular dynamics. After reformulating the continuous and discrete time Andersen dynamics, we prove that in both cases the Andersen dynamics is uniformly ergodic. A detailed numerical analysis is presented, establishing the rate of convergence of most commonly used numerical algorithms for the Andersen thermostat. Transport properties such as the diffusion constant are also investigated. It is proved for the Lorentz gas model where there is intrinsic diffusion, the diffusion coefficient calculated using the Andersen thermostat converges to the true diffusion coefficient in the limit of vanishing collision frequency in the Andersen thermostat.
520 $a The second part of this thesis consists of proofs of crystallization of the 3D diamond lattice at the zero temperature. Recently Florian Theil showed that in 2D under natural assumptions on the potential function V the ground state energy per particle converges to a explicit constant in the thermodynamic limit. Furthermore, if suitable Dirichlet or periodic boundary conditions are used, then the minimizers form a triangular lattice. In this work we generalize Florian Theil's technique to the diamond lattice. For a class of atomic potentials we show that the corresponding lattice is the global minimizer at zero temperature.
520 $a In the third part (joint work with Prof. Yakov Sinai) we prove the blow ups of complex solutions of 3D Navier-Stokes systems. We consider complex-valued solutions of the three-dimensional Navier-Stokes system without external forcing on R3. We show that there exists an open set in the space of 10-parameter families of initial conditions such that for each family from this set there are values of parameters for which the solution develops blow up in finite time.
590 $a School code: 0181.
650 4 $a Mathematics. $3 515831
690 $a 0405
710 2 0 $a Princeton University. $3 645579
773 0 $t Dissertation Abstracts International $g 67-09B.
790 $a 0181
790 1 0 $a Weinan, E., $e advisor
791 $a Ph.D.
792 $a 2006
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3236183