CP11_data - Modeling of Data 5 4 3 Interpolation 4 Y 2 1...

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1 Modeling of Data Modeling of Data 02468 1 0 0 1 2 3 4 5 Y X Interpolation Interpolation = local approximation 1 0 1 2 3 4 data points linear interpolation spline interpolation X
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2 Modeling of Data Modeling of Data Data fit Data modeling = global behavior 02468 1 0 0 1 2 3 4 5 Y X 1 0 0 1 2 3 4 5 data poits polinomial fit Y =-2.62+4.99X-1.74X 2 +0.24X 3 -0.01X 4 X
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3 Why data modeling? Why data modeling? Condense and summarize the data Using data in applications Getting deeper insight in mechanisms
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4 Example: Example: Godunov et al, Godunov et al, Physica Physica Scripta Scripta 59, 277 (1999) 59, 277 (1999) On analytical fit for electron impact ionization cross sections On analytical fit for electron impact ionization cross sections 10 100 1000 10000 Energy (eV) 0 4 8 C r o s e c t i n ( 1 0 - 7 m 2 ) Bleakney (1930) Nagy et al. (1980) Stephan et al. (1980) Wetzel et al. (1987) Krishnakumar et al. (1988) Almeida et al. (1995) Shchemelinin et al. (1975) Recommended BELI-3 Recommended BELI-5
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5 Steps in data modeling Steps in data modeling 1. Observation (experiment) Data are generally not exact (measurement errors, noise) 2. Selecting a model 1. General: a function with adjustable parameters y(x;a 1 ,a 2 ,…a n ) 2. Specific: reflecting the nature of data 3. Fitting procedure
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6 Example: Good model for data fit for p + He Example: Good model for data fit for p + He p + He p + He + + e + e - Experiment: Experiment: Bordenave Bordenave -Montesquieu et al Montesquieu et al (1996) (1996) Fitting equation derived from Fitting equation derived from theory Godunov et al 1995 theory Godunov et al 1995 (5 parameters) (5 parameters) Shore parameterization (4 parameters)
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CP11_data - Modeling of Data 5 4 3 Interpolation 4 Y 2 1...

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