byeong-joo lee calphad byeong-joo lee dept. of mse pohang university of science and technology...
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Byeong-Joo Lee www.postech.ac.kr/~calphad
Byeong-Joo LeeByeong-Joo Lee
Dept. of MSEDept. of MSE
Pohang University Pohang University
of Science and Technologyof Science and Technology
(POSTECH)(POSTECH)
[email protected]@postech.ac.kr
Atomistic SimulationsAtomistic Simulations
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Byeong-Joo Lee www.postech.ac.kr/~calphad
More about Molecular Dynamics More about Molecular Dynamics - Lecture Note of Prof. V. Vitek, 2002- Lecture Note of Prof. V. Vitek, 2002
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Byeong-Joo Lee www.postech.ac.kr/~calphad
Physical Interpretation of MD using the concept of Statistical Mechanics Physical Interpretation of MD using the concept of Statistical Mechanics
Fluctuations
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Byeong-Joo Lee www.postech.ac.kr/~calphad
Physical Interpretation of MD using the concept of Statistical Mechanics Physical Interpretation of MD using the concept of Statistical Mechanics
![Page 5: Byeong-Joo Lee calphad Byeong-Joo Lee Dept. of MSE Pohang University of Science and Technology (POSTECH)calphad@postech.ac.kr Atomistic](https://reader035.vdocuments.net/reader035/viewer/2022062720/56649f165503460f94c2cf4c/html5/thumbnails/5.jpg)
Byeong-Joo Lee www.postech.ac.kr/~calphad
Physical Interpretation of MD using the concept of Statistical Mechanics Physical Interpretation of MD using the concept of Statistical Mechanics
![Page 6: Byeong-Joo Lee calphad Byeong-Joo Lee Dept. of MSE Pohang University of Science and Technology (POSTECH)calphad@postech.ac.kr Atomistic](https://reader035.vdocuments.net/reader035/viewer/2022062720/56649f165503460f94c2cf4c/html5/thumbnails/6.jpg)
Byeong-Joo Lee www.postech.ac.kr/~calphad
Physical Interpretation of MD using the concept of Statistical Mechanics Physical Interpretation of MD using the concept of Statistical Mechanics
J. S. Rowlinson: Liquids and liquid mixtures, Butterworth: London, 1969
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Byeong-Joo Lee www.postech.ac.kr/~calphad
Physical Interpretation of MD using the concept of Statistical Mechanics Physical Interpretation of MD using the concept of Statistical Mechanics
![Page 8: Byeong-Joo Lee calphad Byeong-Joo Lee Dept. of MSE Pohang University of Science and Technology (POSTECH)calphad@postech.ac.kr Atomistic](https://reader035.vdocuments.net/reader035/viewer/2022062720/56649f165503460f94c2cf4c/html5/thumbnails/8.jpg)
Byeong-Joo Lee www.postech.ac.kr/~calphad
Physical Interpretation of MD using the concept of Statistical Mechanics Physical Interpretation of MD using the concept of Statistical Mechanics
![Page 9: Byeong-Joo Lee calphad Byeong-Joo Lee Dept. of MSE Pohang University of Science and Technology (POSTECH)calphad@postech.ac.kr Atomistic](https://reader035.vdocuments.net/reader035/viewer/2022062720/56649f165503460f94c2cf4c/html5/thumbnails/9.jpg)
Byeong-Joo Lee www.postech.ac.kr/~calphad
Physical Interpretation of MD Physical Interpretation of MD - Generalized Einstein Relations- Generalized Einstein Relations
dxtxNxN
xtx ),(1
)]0()([ 2
0
2
x
NDxN
Dt
x
Dt
NtxN
4exp
2),(
20
Consider One dimensional Diffusion
If N0 atoms were concentrated at the origin x=0 at time t=0
Mean-square displacement of atoms
Dtxtx 2)]0()([ 2
Dt
rtrt
6
)]0()([lim
2
![Page 10: Byeong-Joo Lee calphad Byeong-Joo Lee Dept. of MSE Pohang University of Science and Technology (POSTECH)calphad@postech.ac.kr Atomistic](https://reader035.vdocuments.net/reader035/viewer/2022062720/56649f165503460f94c2cf4c/html5/thumbnails/10.jpg)
Byeong-Joo Lee www.postech.ac.kr/~calphad
Physical Interpretation of MD Physical Interpretation of MD - Green-Kubo Relations- Green-Kubo Relations
)"()'('"2)"()'('")]0()(["
0000
2 tAtAdtdttAtAdtdtAtAmsdtttt
dt
dAtA )(
)0()(2
)]0()([lim
0
2
AAdt
AtAt
Shifting the time origin to t’ :
)'(')0()(0
tAdtAtAt
)0()'"()"()'( AttAtAtA
t
AAdtdtAAdAAddtmsdttttt
1)0()(2")0()(2)0()("2
00
"
00
t
AAdt
AtA t 1)0()(2
)]0()([
0
2
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Byeong-Joo Lee www.postech.ac.kr/~calphad
Physical Interpretation of MD Physical Interpretation of MD - Autocorrelations- Autocorrelations
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Byeong-Joo Lee www.postech.ac.kr/~calphad
Physical Interpretation of MD Physical Interpretation of MD - Autocorrelations- Autocorrelations
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Byeong-Joo Lee www.postech.ac.kr/~calphad
Physical Interpretation of MD Physical Interpretation of MD - Autocorrelations- Autocorrelations
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Byeong-Joo Lee www.postech.ac.kr/~calphad
More about MDMore about MD
Additional literature
D. Chandler: Introduction to Modern Statistical Mechanics, 1987, Oxford: Oxford University Press.
M. P. Allen and D. J. Tildesley: Computer Simulation of Liquids, 1987, Oxford: Oxford University Press.
J. P. Boon and S. Yip: Molecular Hydrodynamics, 1980, New York: McGraw-Hill; also Dover Publications, 1991.
J.M. Haile: Molecular Dynamics Simulation Elementary Method, 1992, John Wiley & Sons,
D. Frenkel and B. Smit: Understanding Molecular Simulations, 1996, New York, Academic Press.