다중규모 모사
Multiscale simulation for process development
[Ch. 2]
in Computational multiscale modeling of fluids and solids by M.O. Steinhauser
Major: Interdisciplinary program of the integrated biotechnology
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+Time and space
+Four-dimensional space-time
+Isaac Newton’s Principia (1687): physical
modeling of the world (calculus: differential equation with time and space)
+Max Planck’s Quantum theory (1900):
+Einstein’s Principle of general relativity (1916)
Ch. 2. Multiscale computational material science
Ch. 2.2 Material science in the scale
Earth D
atom 1 Å
Atom Galaxy
D
earth=13,000 km =1.3 10
17Å
D
galaxy=100, 000 light years
1.0 10
31Å
Ch. 2.2 Material science on multiscale
Fig. 2.1 (p32, Steinhauser, 2007).
Reducing Degree of Freedom
Instruments:
+ TEM (Transmission Electron Microscope) - resolution = 0.2nm
+ SEM (Scanning Electron Microscope) - resolution = 10nm
Length: 12 orders of magnitude (100 ~ 1012 )
Ch. 2.3 Modeling
Fig. 2.6 (p38, Steinhauser, 2007).
Fig. 2.6. Galilei’s method (1638) of using experiments to test idealizations of theories which in turn are based on abstract mathematical principles
Model equation:
+ Newton’s classical mechanics (continuum-based modeling) - macroscopic state variables = T, P, V, S, F, G, , ij
- state variables are expressed as functions of x, y, z, and t.
+ Quantum theory (discrete atom modeling):
- position (r), momentum of molecules
Ch. 2.4.2 Structure property paradigm
Microscopic structure determines macroscopic properties
Table 2.1 (p47, Steinhauser, 2007).
Ch. 2.4.4 Numerical modeling and simulation
Fig. 2.9 (p56, Steinhauser, 2007).
Microscopic structure
determines macroscopic properties
Ch. 2.4.5 Unification of physical theories
Fig. 2.10 (p57, Steinhauser, 2007).
Einstein (1916)
Newton (1687)
Reductionism in physics
Dirac (1931)
Plank (1900)
4 fundamental forces:
- weak interaction on quarks
- strong interaction on atomic nuclei
- electron-magnetic interaction on charged particles - gravitational interaction between astronomic objects
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