1 Disparate impact Qinglan Bai Disparate impact Qinglan Bai.
Bai Tap Nguyen Ly Bien Phan Part 2-Demo
4
Part 2: Consider an ODE form of a homogenization problem with the constitute matrix that depends on the micro information as follows: in =(0,1) 2 on D (1) where (2) The analytical form is (3) 1. Plot with 0.01, 0.001, 0.0001, 0.00001, 0.0000001 and show the properties ( in code matlab ‘b.m’ ) consider the component a 11
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Transcript of Bai Tap Nguyen Ly Bien Phan Part 2-Demo
Part 2:
Consider an ODE form of a homogenization problem with the constitute matrix that depends on the micro information as follows:
in =(0,1)2
on D
(1)
where
(2)
The analytical form is
(3)
1. Plot with 0.01, 0.001, 0.0001, 0.00001, 0.0000001 and show the properties ( in code matlab ‘b.m’ )consider the component a11
00.2
0.40.6
0.81
0
0.5
10
2
4
6
x1
(x2 + 1) (sin(200 x1) + 2) + x12 + 1/5
x20
0.20.4
0.60.8
1
0
0.5
10
2
4
6
x1
(x2 + 1) (sin(2000 x1) + 2) + x12 + 1/5
x2
00.2
0.40.6
0.81
0
0.5
10
2
4
6
x1
(x2 + 1) (sin(200000 x1) + 2) + x12 + 1/5
x20
0.20.4
0.60.8
1
0
0.5
10
2
4
6
x1
(x2 + 1) (sin(2000000 x1) + 2) + x12 + 1/5
x2
figure 2.1 properties of a11 when tends to zeros
Consider component a22
00.2
0.40.6
0.81
0
0.5
11
2
3
4
5
6
7
x1
(x1 x2 + 1) (sin(200 x2) + 2) + x22 + 1/20
x20
0.20.4
0.60.8
1
0
0.5
11
2
3
4
5
6
x1
(x1 x2 + 1) (sin(2000 x2) + 2) + x22 + 1/20
x2
00.2
0.40.6
0.81
0
0.5
11
2
3
4
5
6
7
x1
(x1 x2 + 1) (sin(200000 x2) + 2) + x22 + 1/20
x20
0.20.4
0.60.8
1
0
0.5
11
2
3
4
5
6
x1
(x1 x2 + 1) (sin(2000000 x2) + 2) + x22 + 1/20
x2
figure 2.2 properties of a22 when tends to zeros
2. when we plot the a0(x), strain are infinite. when tends to zeros, a0(x) have frequency, which tends to infinite. So, the harmonic vibrations are increase.
hence
hence,
0
0.2
0.4
0.6
0.8
1
00.20.40.60.81
0.02
0.03
0.04
0.05
0.06
0.07
x1
x2
(5 atan((5 x2 + 5)/(25 x14 + 100 x1
2 x2 + 110 x12 + 75 x2
2 + 170 x2 + 96)1/2))/( (25 x14 + 100 x1
2 x2 + 110 x12 + 75 x2
2 + 170 x2 + 96)1/2)
0
0.2
0.4
0.6
0.8
1 00.2
0.40.6
0.81
0.02
0.04
0.06
0.08
x2
(20 atan((20 x1 x2 + 20)/(1200 x12 x2
2 + 1600 x1 x23 + 2480 x1 x2 + 400 x2
4 + 1640 x22 + 1281)1/2))/( (1200 x1
2 x22 + 1600 x1 x2
3 + 2480 x1 x2 + 400 x24 + 1640 x2
2 + 1281)1/2)
x1
figure 2.3 intergal of a110 and a22
0
3. A aplication of Lax- Mil-gram theorem gives us a family of solutions which are
bounded in independently of and the variational form of (1) is to
find such that
for all , where
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