Chapter 32 Parameters dependence on g

32.0.1 2par Kiso 1 Kcot

$$K_{df}^{iso}=\frac{P[0] M_0^2 }{E^2-M_r^2}$$

$$\frac{k}{m} \cot \delta= \frac{1}{a_0m}$$

fitting $\Gamma=g^n$

$\chi^2=$ 0.499318

$n=$ 1.731639

fitting $M_R^2=g^n$

fit <- nls(MR2~a+b*g/(1 +d*g)  ,data=df, weights=df$dMR2, start=list(a=9.2, b=-0.05 , d=1))
gg<- myggplot()
gg<- geom_error(gg=gg, x=df$g, y=df$MR2, dy=df$dMR2, width=0.7)

sp<-data.frame("g"=c(0:20))
gg<- gg+ geom_line(aes(x=sp$g, y=predict(fit,sp)), color="red")  
chi2<- sum(((residuals(fit)/weights(fit))^2)/df.residual(fit))

cat("$\\chi^2=$",chi2,"\n\n")

$\chi^2=$ 1.031278

fig<-myplotly(gg,"","g","$M_R^2$", to_print = TRUE)

32.0.2 3par Kiso 1 Kcot

$$K_{df}^{iso}=\frac{P[0] M_0^2 }{E^2-M_r^2}+P[2]$$

$$\frac{k}{m} \cot \delta= \frac{1}{a_0m}$$

fitting $\Gamma=g^n$

$\chi^2=$ 1.185918

$n=$ 1.78097

fitting $M_R^2=g^n$

fit <- nls(MR2~a+b*g/(1 +d*g)  ,data=df, weights=df$dMR2, start=list(a=9.2, b=-0.05 , d=1))
gg<- myggplot()
gg<- geom_error(gg=gg, x=df$g, y=df$MR2, dy=df$dMR2, width=0.7)

sp<-data.frame("g"=c(0:20))
gg<- gg+ geom_line(aes(x=sp$g, y=predict(fit,sp)), color="red")  
chi2<- sum(((residuals(fit)/weights(fit))^2)/df.residual(fit))

cat("$\\chi^2=$",chi2,"\n\n")

$\chi^2=$ 0.297934

fig<-myplotly(gg,"","g","$M_R^2$", to_print = TRUE)