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Byeong-Joo Lee Byeong-Joo Lee Dept. of MSE Pohang University of Science and Technology Atomistic.

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Presentation on theme: "Byeong-Joo Lee Byeong-Joo Lee Dept. of MSE Pohang University of Science and Technology Atomistic."— Presentation transcript:

1 Byeong-Joo Lee www.postech.ac.kr/~calphad Byeong-Joo Lee Dept. of MSE Pohang University of Science and Technology (POSTECH)calphad@postech.ac.kr Atomistic Simulations

2 Byeong-Joo Lee www.postech.ac.kr/~calphad More about Molecular Dynamics - Lecture Note of Prof. V. Vitek, 2002

3 Byeong-Joo Lee www.postech.ac.kr/~calphad Physical Interpretation of MD using the concept of Statistical Mechanics Fluctuations

4 Byeong-Joo Lee www.postech.ac.kr/~calphad Physical Interpretation of MD using the concept of Statistical Mechanics

5 Byeong-Joo Lee www.postech.ac.kr/~calphad Physical Interpretation of MD using the concept of Statistical Mechanics

6 Byeong-Joo Lee www.postech.ac.kr/~calphad Physical Interpretation of MD using the concept of Statistical Mechanics J. S. Rowlinson: Liquids and liquid mixtures, Butterworth: London, 1969

7 Byeong-Joo Lee www.postech.ac.kr/~calphad Physical Interpretation of MD using the concept of Statistical Mechanics

8 Byeong-Joo Lee www.postech.ac.kr/~calphad Physical Interpretation of MD using the concept of Statistical Mechanics

9 Byeong-Joo Lee www.postech.ac.kr/~calphad Physical Interpretation of MD - Generalized Einstein Relations Consider One dimensional Diffusion If N 0 atoms were concentrated at the origin x=0 at time t=0 Mean-square displacement of atoms

10 Byeong-Joo Lee www.postech.ac.kr/~calphad Physical Interpretation of MD - Green-Kubo Relations Shifting the time origin to t’ :

11 Byeong-Joo Lee www.postech.ac.kr/~calphad Physical Interpretation of MD - Autocorrelations

12 Byeong-Joo Lee www.postech.ac.kr/~calphad Physical Interpretation of MD - Autocorrelations

13 Byeong-Joo Lee www.postech.ac.kr/~calphad Physical Interpretation of MD - Autocorrelations

14 Byeong-Joo Lee www.postech.ac.kr/~calphad More 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.

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