1 Experimental Approximation of Mercury Drop Velocity Using Uniform Random Probability in Jet Geometry
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1
Experimental Approximation of Mercury Drop VelocityUsing Uniform Random Probability in Jet Geometry
2
Input Parameters & Geometry of Viewing of Drops
Case : Ellipse jet shape, b = 0.00875 ± 0.0013 m a = 0.0029 ± 0.0013 m y_m = 0.0171 ± 0.004 m t = 25*14 ± 1 microsec to = 78.6 ± 62 microsec D = 0.0915 m θ = ± π/2
Case : Circle jet shape, b = 0.00875 ± 0.0013 m a = 0.00875 ± 0.0013 m All of the rest settings are same with ellipse case.
b
a
y_m
D Focal point
Drop
θ
Chosen Example : 0T, 24GeV, 10Tp
3
CASE I : Elliptic Jet Shape
4
Probability Density of Angle θ
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-1
-0.5
0
0.5
1
1.5
theta (radian)
Pro
babi
lity
dens
ity
Uniform in theta
-2 -1.5 -1 -0.5 0 0.5 1 1.5 20.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
theta (radian)
Pro
babi
lity
dens
ity
Uniform in phi
-2 -1.5 -1 -0.5 0 0.5 1 1.5 20.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
theta (radian)
Pro
babi
lity
dens
ity
Uniform in position around circumference
Uniform in θUniform in Φ
Uniform in s
5
Random Smapled Angle θ
-2 -1.5 -1 -0.5 0 0.5 1 1.5 20
20
40
60
80
100
120
140
theta (radian)
Num
ber
of r
ando
m s
ampl
e
Uniform in theta
-2 -1.5 -1 -0.5 0 0.5 1 1.5 20
20
40
60
80
100
120
140
160
theta (radian)
Num
ber
of
random
sam
ple
Uniform in position around circumference
-2 -1.5 -1 -0.5 0 0.5 1 1.5 20
50
100
150
200
250
300
350
theta (radian)
Num
ber
of r
ando
m s
ampl
e
Uniform in phi
Uniform in θ
Uniform in Φ
Uniform in s
6
Histogram of Drop Velocity
-100 0 100 200 300 400 5000
50
100
150
200
250
300
350
400
drop velocity (m/s)
Num
ber
of
events
Uniform in theta
-100 0 100 200 300 400 5000
50
100
150
200
250
300
350
400
drop velocity (m/s)
Num
ber
of e
vent
s
Uniform in phi
-100 0 100 200 300 400 5000
50
100
150
200
250
300
350
400
drop velocity (m/s)
Num
ber
of e
vent
s
Uniform in position around the circumference
Uniform in θ
Uniform in Φ
Uniform in s
7
0 50 100 150 200 250 3000
50
100
150
200
250
300
350
400
Drop velocity (m/s)
Num
ber
of e
vent
s
Uniform in theta
Histogram data
Gaussian-fitted curve
0 50 100 150 200 250 3000
100
200
300
400
500
600
Drop velocity (m/s)
Num
ber
of e
vent
s
Uniform in position around the circumference
Histogram data
Gaussian-fitted curve
0 50 100 150 200 2500
50
100
150
200
250
300
Drop velocity (m/s)
Num
ber
of e
vent
s
Uniform in phi
Histogram data
Gaussian-fitted curveGaussian Fitting of Histogram of Drop Velocity
Uniform in θUniform in Φ
Uniform in s
8
CASE II : Circular Jet Shape
9
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
0.3183
0.3183
0.3183
0.3183
0.3183
0.3183
0.3183
0.3183
0.3183
theta (radian)
Pro
babi
lity
dens
ity
Uniform in phi
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-1
-0.5
0
0.5
1
1.5
theta (radian)
Pro
babi
lity
dens
ity
Uniform in theta
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
0.3183
0.3183
0.3183
0.3183
0.3183
0.3183
0.3183
0.3183
0.3183
theta (radian)
Pro
babi
lity
dens
ity
Uniform in position around circumference
Uniform in θUniform in Φ
Uniform in s
Probability Density of Angle θ
10
-2 -1.5 -1 -0.5 0 0.5 1 1.5 20
20
40
60
80
100
120
140
theta (radian)
Num
ber
of r
ando
m s
ampl
e
Uniform in theta
-2 -1.5 -1 -0.5 0 0.5 1 1.5 20
20
40
60
80
100
120
140
theta (radian)
Num
ber
of r
ando
m s
ampl
e
Uniform in phi
-2 -1.5 -1 -0.5 0 0.5 1 1.5 20
20
40
60
80
100
120
140
theta (radian)
Num
ber
of r
ando
m s
ampl
e
Uniform in position around circumference
Random Smapled Angle θ
Uniform in θ
Uniform in Φ
Uniform in s
11
-100 0 100 200 300 400 5000
50
100
150
200
250
300
350
400
drop velocity (m/s)
Num
ber
of e
vent
s
Uniform in theta
-100 0 100 200 300 400 5000
50
100
150
200
250
300
350
400
drop velocity (m/s)
Num
ber
of e
vent
s
Uniform in phi
-100 0 100 200 300 400 5000
50
100
150
200
250
300
350
400
drop velocity (m/s)
Num
ber
of e
vent
s
Uniform in position around the circumference
Histogram of Drop Velocity
Uniform in θ
Uniform in Φ
Uniform in s
12
0 50 100 150 200 250 3000
100
200
300
400
500
600
Drop velocity (m/s)
Num
ber
of e
vent
s
Uniform in theta
Histogram data
Gaussian-fitted curve
0 50 100 150 200 2500
100
200
300
400
500
600
Drop velocity (m/s)
Num
ber
of e
vent
s
Uniform in phi
Histogram data
Gaussian-fitted curve
-50 0 50 100 150 200 2500
100
200
300
400
500
600
Drop velocity (m/s)
Num
ber
of e
vent
s
Uniform in position around the circumference
Histogram data
Gaussian-fitted curve
Gaussian Fitting of Histogram of Drop Velocity
Uniform in θUniform in Φ
Uniform in s
13
Comparison
Jet shape P(θ)
Velocity (m/s)
Mean Sigma
Ellipse
Uniform in theta 38.1 19.2
Uniform in phi 48.1 26.4
Uniform in position s 44.0 22.2
Circle
Uniform in theta 37.7 20.3
Uniform in phi 38.8 21.0
Uniform in position s 37.2 19.4
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