BSA Flow Software Installation and User's Guide - CSI

Corrected particle
Max
d e ( Di
)
C ( Di
) =
d ( D )
e
i
where d is the effective probe volume diameter for size class D and where
e
Max
the maximum measured particle size D is the last non-em pty size bin.
d e
is calculated as for the flux and concentration algorithm:
3 2
d e(
Di
) = Li
2
where
L is the mean burst length for each size class D .
2
i
2
Li i
= Aln(
D ) + B
The corrected particle number for the size class D becomes:
cor
number n i = ni
× C(
Di
) where ni
is the measured number of particles per size.
The corrected mean diameters can be written as follow:
10 =
Ni
cor
∑ ni
Di
i=
1
Ni
cor
∑ ni
i=
1
D
,
D
Ni
cor 3
∑ ni
Di
i=
1
32 = and so forth.
Ni
cor 2
∑ ni
Di
i=
1
Note As described in chapter 7.11.2, the correction is by design implemented in
the flux and concentration algorithms.
7.12 Spectral analysis (two-time statistics)
Definition of correlation and covariance
As opposed to moment-calculation, spectral-analysis investigates the
relations between samples and the timing of events. Since all of these
calculations are based on pairs of values, this is sometimes referred to as
two-time statistics.
Consider an ideal experiment producing continuous measurements
represented as time functions u(t) and v(t):
[ ]
i
ut (), vt (), K t∈ 0 , T
(7-53)
In the context of LDA-measurements, u(t) and v(t) will normally be
velocities, but may in principle represent temperature, pressure, or something
else.
Correlation The exact definition of the correlation function Ruv(t1,t2) is:
{ }
*
( , ) ( ) ( )
R t t ≡ E u t ⋅ v t
(7-54)
uv 1 2 1 2
-where E{…} is the notation for the expectation value (mean).
BSA Flow Software:Reference guide 7-121
i
i
i