termRip: Simulate termination ripples

Description

Function to simulate termination ripples in the PDF calculated as the Fourier transform of the total scattering function that arise due to the finite value of the upper integration limit Qmax.

Usage

termRip(pdf, Qmax, dr, maxR, maxRTermRip)

Arguments

Value

numeric vector of function values.

Rdversion

1.1

Examples

Run this code

## simulate a particle 
Cu <- createAtom("Cu")
part <- simPart(atoms=list(Cu), atomsShell=list(Cu), r=12, 
    rcore=10, latticep=4.08, latticepShell=3.89)

## calculate the PDF  
gr1 <- calcPDF(part, maxR=24, scatterLength=c(4.87, 7.97))
gr1 <- broadPDF(gr1, sigma=c(.01, .01), nAtomTypes=2) 
## normalization
gr1$gr <- 4*pi*gr1$r*gr1$gr

## calculate and substract the baseline term
gQSAS <- calcTotalScatt(part, type="neutron",  minQ=0.001, 
    maxQ=0.771, dQ=0.005, scatterLength=c(4.87, 7.97), 
    sigma=c(.01, .01))
gammaR <- calcQDepPDF(minR=0.01, maxR=24, dr=0.01, maxQ=.771, 
    minQ=0.001, verbose=50, 
    preTotalScat=list(Q=gQSAS$Q, gQ=gQSAS$gQ))
gr1$gr <- gr1$gr - gammaR$gr

plot(gr1$r, gr1$gr, type="l", xlim=c(0,10))
## simulate termination ripples
rvector <- gr1$r
gr1 <- termRip(gr1$gr, Qmax=11.881, dr=0.01, maxR=24, maxRTermRip=16)
## plot the PDF with simulated termination ripples:
lines(rvector, gr1, col=2)

#### compare with ripples due to finite value of Qmax:
## calculate scattering function
gQ <- calcTotalScatt(part, type="neutron", 
    scatterLength=c(4.87, 7.97),  sigma=c(.01, .01))
## set Qmax to a value between 11 and 13 at which scattering function reaches 
##  minimum:
t1 <- which(gQ$Q > 11)[1]
t2 <- which(gQ$Q > 13)[1]
cut <- gQ$Q[t1:t2][which(abs(gQ$gQ[t1:t2])
    ==min(abs(gQ$gQ[t1:t2]) ))[1]]
## calculate Q-dependent PDF
gr3 <- calcQDepPDF(minR=0.01, maxR=24, dr=0.01, minQ=.771, 
    maxQ=cut, verbose=50, preTotalScat=list(Q=gQ$Q, gQ=gQ$gQ))

## add Q-dependent PDF to plot:
lines(gr3$r, gr3$gr, col=4)
legend(5,7,c("PDF as returned by calcPDF", "PDF with simulated 
    termination ripples", "PDF as Fourier transform"), lty=1, 
    col=c(1,2,4))