text:
University of Florida/Egm4313/s12.teamboss/R7

Statement
Determine orthogonality of:
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$$ \langle \phi_i, \phi_j \rangle = 0 \ \text{ for } \ i \ne j $$ $$ \langle \phi_j, \phi_j \rangle = \frac{L}{2} \ \text{ for } \ i=j $$     (1.0)
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Where: $$\displaystyle \phi_i (x) = \sin(\omega_i x)$$, $$\displaystyle \phi_j (x) = \sin(\omega_j x)$$, $$\displaystyle \omega_i = \frac{i \pi}{L}$$, and $$\displaystyle \omega_j = \frac{j \pi}{L}$$.

Solution
The definition of a scalar product is:
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$$ \langle \bar f, \bar g \rangle := \int_0^L \bar f(x) \ \bar g(x) \, dx $$ (1.1)
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So, substituting the problem statement values into Eq. (1.0):
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$$ \langle \phi_i, \phi_j \rangle := \int_0^L \sin(\omega_i x) \ \sin(\omega_j x) \, dx $$ (1.2) and:
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$$ \langle \phi_j, \phi_j \rangle := \int_0^L \sin(\omega_j x) \ \sin(\omega_j x) \, dx $$ (1.3)
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Solving Eq. 1.2 first:
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$$ \langle \phi_i, \phi_j \rangle = \int_0^L \sin(\omega_i x) \ \sin(\omega_j x) \, dx $$ $$ = \frac {1}{2} \int_0^L \cos((\omega_i - \omega_j)x)-\cos((\omega_i+\omega_j)x) \, dx $$ $$ = \frac {1}{2(\omega_i - \omega_j)}[\sin((\omega_i - \omega_j)L)-\sin(0)]-\frac {1}{2(\omega_i + \omega_j)}[\sin((\omega_i + \omega_j)L)-\sin(0)] $$ $$ = \frac {1}{2L(i \pi - j \pi)}\sin(i \pi - j \pi)-\frac {1}{2L(i \pi + j \pi)}\sin(i \pi + j \pi) $$ Because $$\displaystyle i$$ and $$\displaystyle j$$ are both integers, the sin function will always be a periodic integer varying by $$\displaystyle \pi$$, meaning that $$\sin(i \pi - j \pi)=0$$ and $$\sin(i \pi + j \pi)=0$$. Thus proving:
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$$ \langle \phi_i, \phi_j \rangle = 0 \ \text{ for } \ i \ne j $$ (1.0.a) Now solving for Eq. 1.3:
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$$ \langle \phi_j, \phi_j \rangle = \int_0^L \sin(\omega_j x) \ \sin(\omega_j x) \, dx $$ $$ = \frac {1}{2} \int_0^L \cos((\omega_j - \omega_j)x)-\cos((\omega_j+\omega_j)x) \, dx $$ $$ = \frac {1}{2} \int_0^L \cos((j \pi - j \pi)\frac{x}{L})-\cos((j \pi+j \pi)\frac {x}{L}) \, dx $$ $$ = \frac {1}{2} \int_0^L \cos(0)-\cos(\frac {2jx \pi}{L}) \, dx $$ $$ = \frac {1}{2} \int_0^L 1-\cos(\frac {2jx \pi}{L}) \, dx $$ $$ = \frac {L}{2}-\frac {L}{2j \pi}\sin(2j \pi) $$
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Again, because $$\displaystyle j$$ is an integer, the sin function will always be a periodic integer varying by $$\displaystyle 2j \pi$$, meaning that $$\sin(2j \pi)=0$$. Thus proving:
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$$ \langle \phi_j, \phi_j \rangle = \frac{L}{2} \ \text{ for } \ i=j $$     (1.0.b)
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Author
Solved and Typed By ---Egm4313.s12.team1.durrance (talk) 16:49, 24 April 2012 (UTC) Reviewed By - Egm4313.s12.team1.armanious (talk) 23:48, 24 April 2012 (UTC)

Statement
Plot the truncated-series (3) p19-12 with n=5, and for:
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t=\alpha p_1 = \alpha \frac{2\pi}{c \omega_1} = \alpha \frac {2L}{c} $$     (2.0)
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\alpha = .5, 1, 1.5, 2 $$     (2.1)
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Solution
Let it be stated first that (3) p.19-12 is equal to:
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u(x,t) = \sum{j=1}{n} a_j cos(c \omega _j t) sin(\omega _j x) $$ (2.2)
 * $$\displaystyle
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And in this series representation, c=3, L=2, and $$ a_j $$. is equaled to this:
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a_j=\left\{\begin{matrix} 0 for j=2m (even)\\ -4/( \pi^3j^3)for j=2m+1 (odd) \end{matrix}\right. $$     (2.3)
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With this in mind, we are prepared to create these truncated-series. For $$ \alpha =.5$$
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u(x,t) = [a_1 cos(c \omega _1 \alpha \frac{2L}{c})sin(\omega _1 x)] $$      (2.4)
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+[a_2 cos(c \omega _2 \alpha \frac{2L}{c})sin(\omega _2 x)] $$
 * $$\displaystyle
 * $$\displaystyle
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+[a_3 cos(c \omega _3 \alpha \frac{2L}{c})sin(\omega _3 x)] $$
 * $$\displaystyle
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+ [a_4 cos(c \omega _4 \alpha \frac{2L}{c})sin(\omega _4 x)] $$
 * $$\displaystyle
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+[a_5 cos(c \omega _5 \alpha \frac{2L}{c})sin(\omega _5 x)] $$ These simplify below as shown, after plugging in 3 for c, 10, for L, .5 for alpha, and the value of $$ a_j $$ as determined from (2.2).
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u(x,t) = [\frac{-4}{\pi ^3} cos(\omega _1 (.5) (2*10))sin(\omega _1 x)] $$      (2.5)
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+[\frac{-4}{\pi ^3 * 3^3}cos(\omega _3 (.5)(2*10))sin(\omega _3 x)] $$
 * $$\displaystyle
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+[\frac{-4}{\pi ^3 * 5^3}cos(\omega _5 (.5)(2*10))sin(\omega _5 x)] $$
 * $$\displaystyle
 * $$\displaystyle
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Making $$ \omega $$ equal to $$ 2 \pi $$, the graph appears as shown below.

Alpha = .5 For $$ \alpha =1$$

These simplify below as shown, after plugging in 3 for c, 10, for L, 1 for alpha, and the value of $$ a_j $$ as determined from (2.2).
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u(x,t) = [\frac{-4}{\pi ^3} cos(\omega _1 (1) (2*10))sin(\omega _1 x)] $$      (2.6)
 * $$\displaystyle
 * $$\displaystyle
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+[\frac{-4}{\pi ^3 * 3^3}cos(\omega _3 (1)(2*10))sin(\omega _3 x)] $$
 * $$\displaystyle
 * $$\displaystyle
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+[\frac{-4}{\pi ^3 * 5^3}cos(\omega _5 (1)(2*10))sin(\omega _5 x)] $$
 * $$\displaystyle
 * $$\displaystyle
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Making $$ \omega $$ equal to $$ 2 \pi $$, the graph appears as shown below.

Alpha = 1

For $$ \alpha =1.5$$

These simplify below as shown, after plugging in 3 for c, 10, for L, 1.5 for alpha, and the value of $$ a_j $$ as determined from (2.2).
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u(x,t) = [\frac{-4}{\pi ^3} cos(\omega _1 (1.5) (2*10))sin(\omega _1 x)] $$      (2.7)
 * $$\displaystyle
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+[\frac{-4}{\pi ^3 * 3^3}cos(\omega _3 (1.5)(2*10))sin(\omega _3 x)] $$
 * $$\displaystyle
 * $$\displaystyle
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+[\frac{-4}{\pi ^3 * 5^3}cos(\omega _5 (1.5)(2*10))sin(\omega _5 x)] $$
 * $$\displaystyle
 * $$\displaystyle
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Making $$ \omega $$ equal to $$ 2 \pi $$, the graph appears as shown below. Alpha = 1.5 For $$ \alpha =2$$

These simplify below as shown, after plugging in 3 for c, 10, for L, 2 for alpha, and the value of $$ a_j $$ as determined from (2.2).
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u(x,t) = [\frac{-4}{\pi ^3} cos(\omega _1 (2) (2*10))sin(\omega _1 x)] $$      (2.8)
 * $$\displaystyle
 * $$\displaystyle
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+[\frac{-4}{\pi ^3 * 3^3}cos(\omega _3 (2)(2*10))sin(\omega _3 x)] $$
 * $$\displaystyle
 * $$\displaystyle
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+[\frac{-4}{\pi ^3 * 5^3}cos(\omega _5 (2)(2*10))sin(\omega _5 x)] $$
 * $$\displaystyle
 * $$\displaystyle
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Making $$ \omega $$ equal to $$ 2 \pi $$, the graph appears as shown below.

Alpha = 2

Author
Solved and Typed By - Egm4313.s12.team1.silvestri (talk) 19:01, 23 April 2012 (UTC)

Reviewed By - Egm4313.s12.team1.armanious (talk) 19:40, 25 April 2012 (UTC)

Statement
Find the scalar product <f,g>, the magnitude of f and g, and the angle between f and g for (see R7.3 Lect. 11-1 pg. 8):

1) $$f(x)=\cos x, g(x)=x, \text{for} -2\leq x \leq 10\!$$ 2) $$f(x)=\frac12(3x^2-1), g(x)=\frac12(5x^3-3x), \text{for} -1\leq x \leq +1\!$$

Solution
The scalar product, the function equivalent of the vector dot product, of two functions can be found in the following way:
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$$  \displaystyle <f,g>:=\int^b_af(x)g(x)dx $$     (3.0) The magnitude of a function is defined as the square root of the scalar product between the function and itself:
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$$  \displaystyle ||f||:=<f,f>^{1/2}=\left [\int^b_af^2(x)dx \right ]^{1/2} $$     (3.1) The cosine of the angle between two functions can be found in the following way:
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$$  \displaystyle \cos \theta = \frac{<f,g>}{||f||||g||} $$     (3.2) Note that these equations are very similar to their vector counterparts. Part 1
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$$  \displaystyle f(x)=\cos x, g(x)=x, \text{for} -2\leq x \leq 10 $$     (3.3) The scalar product of f and g can be found using (3.0):
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$$  \displaystyle <f,g>=\int_{-2}^{10}x\cos (x) dx=\left [ x\sin(x)+cos(x) \right ]_{-2}^{10} $$     (3.4) Solving this yields the scalar product:
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$$  \displaystyle (10\sin10+\cos10)-(-2\sin(-2)+\cos(-2))=-7.68 $$     (3.5) To find the magnitude of f, the scalar product of f with itself must first be found:
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$$  \displaystyle <f,f>=\int_{-2}^{10}\cos^{2}(x)dx=\int_{-2}^{10}\left (\frac12\cos(2x)+\frac12 \right )dx=\left [ \frac14\sin(2x)+\frac12x \right ]_{-2}^{10} $$     (3.6) Solving this yields:
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$$  \displaystyle \left [ \frac14\sin(2x)+\frac12x \right ]_{-2}^{10}=\left ( \frac14\sin(20)+5 \right )-\left ( \frac14\sin(-4)-1 \right )=6.04 $$     (3.7) Therefore the magnitude of f is found to be:
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$$  \displaystyle $$     (3.8) A similar approach can be taken for the magnitude of g:
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$$  \displaystyle <g,g>=\int_{-2}^{10}x^2dx=\left [ \frac{x^3}{3} \right ]_{-2}^{10} $$     (3.9)
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$$  \displaystyle \left [ \frac{x^3}{3} \right ]_{-2}^{10}=\frac{1000}3-\frac{-8}{3}=\frac{1008}{3}=336 $$     (3.10)
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$$  \displaystyle $$     (3.11) Using the above information with (3.2), the cosine of the angle between f and g is found to be
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 * g||=<g,g>^{1/2}=\sqrt{336}=18.33
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$$  \displaystyle \cos \theta = \frac{<f,g>}{||f||||g||}=\frac{-7.68}{(2.46)(18.33)}=-0.1705 $$     (3.12) Therefore, the angle between the functions f and g is
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$$  \displaystyle \theta =\cos^{-1}(-0.1705)=1.74rad=99.8^{\circ} $$     (3.13) Part 2
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$$  \displaystyle f(x)=\frac12(3x^2-1), g(x)=\frac12(5x^3-3x), \text{for} -1\leq x \leq +1 $$     (3.14) The scalar product of f and g can be found using (3.0):
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$$  \displaystyle <f,g>=\int_{-1}^{1}\frac14\left ( 3x^2-1 \right )\left ( 5x^3-3x \right ) dx=\frac14\int_{-1}^{1}\left ( 15x^5-14x^3+3x \right ) dx=\frac14\left [ \frac{15}{6}x^6-\frac{14}{4}x^4+\frac32x^2 \right ]_{-1}^{1} $$     (3.15) Solving this yields the scalar product:
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$$  \displaystyle \frac14\left [ \frac52x^6-\frac72x^4+\frac32x^2 \right ]_{-1}^{1}=\frac14\left ( \frac12-\frac12 \right )=0 $$     (3.16) To find the magnitude of f, the scalar product of f with itself must first be found:
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$$  \displaystyle <f,f>=\int_{-1}^{1}\left (\frac12\left (3x^2-1 \right )\right)^2 dx=\frac14\int_{-1}^{1}\left (9x^4-6x^2+1  \right )dx=\frac14\left [ \frac95x^5-2x^3+x \right ]_{-1}^{1} $$     (3.17) Solving this yields:
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$$  \displaystyle \frac14\left [ \left( \frac95-2+1\right )-\left (-\frac95+2-1 \right ) \right ] =\frac14\left ( \frac45+\frac45 \right )=\frac25 $$     (3.18) Therefore the magnitude of f is found to be:
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$$  \displaystyle $$     (3.19) A similar approach can be taken for the magnitude of g:
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 * f||=<f,f>^{1/2}=\sqrt{0.4}=0.632
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$$  \displaystyle <g,g>=\int_{-1}^{1}\left (\frac12\left (5x^3-3x \right )\right)^2 dx=\frac14\int_{-1}^{1}\left (25x^6-15x^4+9x^2  \right )dx=\frac14\left [ \frac{25}{7}x^7-3x^5+3x^3 \right ]_{-1}^{1} $$     (3.20)
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$$  \displaystyle \frac12 \left (\frac{25}{7}-3+3 \right ) =\frac{25}{14} $$     (3.21)
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$$  \displaystyle $$     (3.22) Using the above information with (3.2), the cosine of the angle between f and g is found to be
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 * g||=<g,g>^{1/2}=\sqrt{\frac{25}{14}}=1.336
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$$  \displaystyle \cos \theta = \frac{<f,g>}{||f||||g||}=\frac{0}{(0.632)(1.336)}=0 $$     (3.23) '''Because the scalar product of the two functions is zero, the two functions are orthogonal. That is:'''
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$$  \displaystyle \theta =\frac{\pi}{2}rad=90^{\circ} $$     (3.24)
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Author
Solved and Typed By - Egm4313.s12.team1.armanious (talk) 23:48, 21 April 2012 (UTC)

Reviewed By - --Egm4313.s12.team1.stewart (talk) 02:22, 25 April 2012 (UTC)

Statement
From Lecture 11 Pg. 8 Do K 2011 p.482 pb.6,9,12,13. Problems 6 and 12 ask to graph the function and the Fourier series of the function below (4.1).
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$$  \displaystyle f(x)=\left | x \right | $$     (4.1) Problems 9 and 13 ask to graph the function and Fourier series of the function below (4.2).
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$$  \displaystyle f(x)=\begin{Bmatrix} x\;\; if \; -\pi <x<0\\ \pi -x\;\; if \; 0<x<\pi \end{Bmatrix} $$     (4.2)
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Solution
For Question number 6, plotted using Wolfram Alpha. The Function 4.1 For Question number 9, plotted using Matlab. The Function 4.2

Question 12 asks for the Fourier series of equation 4.1, $$f(x)=\left | x \right |\!$$ which is an even function because $$f(-x)=+f(x)\!$$, and because it is even $$b_{n}=0\!$$. So the Fourier looks like this:
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$$  \displaystyle f(x)=a_0+\sum_{n=1}^{\infty}a_ncos\frac{n\pi x}{L} $$     (4.3) In which $$L= \pi \!$$ and:
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$$  \displaystyle a_0=\frac{1}{2\pi}\int_{-\pi}^{0}-xdx+\frac{1}{2\pi}\int_{0}^{\pi}xdx $$     (4.4)
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$$  \displaystyle a_{n}=\frac{1}{\pi }\int_{-\pi}^{\pi}f(x)cos(nx)dx $$     (4.5)
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$$  \displaystyle b_{n}=\frac{1}{\pi }\int_{-\pi}^{\pi}f(x)sin(nx)dx=0 $$     (4.6)
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These simplify to:

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$$  \displaystyle a_0=\frac{1}{2\pi}\frac{\pi^{2}}{2}+\frac{1}{2\pi}\frac{\pi^{2}}{2}=\frac{\pi}{2} $$     (4.7)
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$$  \displaystyle a_n=\frac{1}{\pi}\int_{-\pi}^{0}-xcos(nx)dx+\frac{1}{\pi}\int_{-\pi}^{0}xcos(nx)dx $$     (4.8)
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$$  \displaystyle a_n=\frac{-4}{n^{2}\pi} $$     (4.9)
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$$  \displaystyle f(x)=\frac{\pi}{2}+\sum_{n-1}^{\infty }\frac{4}{n^{2}\pi}cos\frac{n\pi x}{L} $$     (4.10)
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The final answer:
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$$  \displaystyle f(x)=\frac{\pi}{2}-\frac{4}{\pi}(cosx+\frac{cos3x}{9}+\frac{cos5x}{25}+...) $$     (4.11) Plotted with Wolfram Aplpha Fourier Series of Function 4.1
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Now the Fourier series of equation 4.2, we need to divide the function into two parts. First let's evaluate $$f(x)=x\; if\; - \pi <x<0 \!$$, which is an odd function because $$f(-x)=-f(x)\!$$. For an odd function $$a_{0}=a_{n}=0\!$$ so:
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$$\displaystyle f(x)=\sum\limits_{n=1}^{\infty }{\left[ {{b}_{n}}\sin (\frac{n \pi x}{L}) \right]}=\sum\limits_{n=1}^{\infty }{\left[ {{b}_{n}}\sin (nx) \right]} $$     (4.12)
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$$\displaystyle b_{n}=\frac{1}{\pi}\int_{-\pi}^{0}xsin(nx)=\frac{1}{\pi}[\frac{sin(nx)-nxcos(nx)}{n^{2}}]=\frac{-cos(-\pi n)}{n}$$ (4.13) Which simplifies to:
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$$\displaystyle b_{n}=[1,\frac{-1}{2},\frac{1}{3},\frac{-1}{4},\frac{1}{5},\frac{-1}{6}...] $$     (4.14)
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The Fourier Series for just the top part of equation 4.2
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$$\displaystyle f(x)=sinx-\frac{sin2x}{2}+\frac{sin3x}{3}-\frac{sin4x}{4}+\frac{sin5x}{5}... $$     (4.15)
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Now the bottom part of equation 4.2 is neither even nor odd so we must add all the components and at the end combine the solution with the Fourier series for the top part of equation 4.2
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$$  \displaystyle f(x)=a_{0}+\sum_{n=1}^{\infty }a_ncos(\frac{n \pi x}{L})+\sum_{n=1}^{\infty }b_nsin(\frac{n \pi x}{L})=a_{0}+\sum_{n=1}^{\infty }a_{n}cos(nx)+\sum_{n=1}^{\infty }b_{n}sin(nx) $$     (4.16)
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$$  \displaystyle a_{0}=\frac{1}{2 \pi}\int_{0}^{\pi}(\pi-x)dx=\frac{1}{2 \pi }[\pi x-\frac{x^2}{2}]=\frac{\pi}{4} $$     (4.17)
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$$  \displaystyle a_{n}=\frac{1}{ \pi}\int_{0}^{\pi}(\pi-x)cos(nx)dx=\frac{1}{ \pi }[\frac{n(\pi-x)sin(nx)-cos(nx)}{n^2}]=\frac{1-cos(\pi n)}{\pi n^2} $$     (4.18)
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$$  \displaystyle a_{n}=[\frac{2}{\pi},0,\frac{2}{6\pi},0,\frac{2}{25\pi},0,\frac{2}{49 \pi}...] $$     (4.19)
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$$  \displaystyle b_{n}=\frac{1}{\pi}\int_{0}^{\pi}(\pi-x)sin(nx)dx=\frac{1}{\pi}[\frac{sin(nx)+n(\pi-x)cos(nx)}{n^2}]=\frac{1}{n} $$     (4.20)
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$$  \displaystyle b_{n}=[1,\frac{1}{2},\frac{1}{3},\frac{1}{4},\frac{1}{5},\frac{1}{6}...] $$     (4.21)
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The Fourier Series of $$f(x)= \pi -x\; if\;  0<x< \pi \!$$.
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$$  \displaystyle f(x)=a_{0}+\sum_{n=1}^{\infty }a_{n}cos(nx)+\sum_{n=1}^{\infty }b_{n}sin(nx)=\frac{\pi}{4}+[\frac{2cosx}{\pi}+\frac{2cos3x}{6\pi}+\frac{2cos5x}{25\pi}...]+[1+\frac{sinx}{2}+\frac{sin2x}{3}+\frac{sin3x}{4}+\frac{sin4x}{5}+\frac{sin5x}{6}...] $$     (4.22)
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Combining with the Fourier Series of $$f(x)= x\; if\; -\pi <x<0 \!$$:
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$$  \displaystyle f(x)=\frac{\pi}{4}+[\frac{2cosx}{\pi}+\frac{2cos3x}{6\pi}+\frac{2cos5x}{25\pi}...]+[sinx+\frac{sin2x}{2}+\frac{sin3x}{3}+\frac{sin4x}{4}+\frac{sin5x}{5}+...]+[sinx-\frac{sin2x}{2}+\frac{sin3x}{3}-\frac{sin4x}{4}+\frac{sin5x}{5}...] $$     (4.23)
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The total series and final answer:
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$$  \displaystyle f(x)=\frac{\pi}{4}+[\frac{2cosx}{\pi}+\frac{2cos3x}{6\pi}+\frac{2cos5x}{25\pi}...]+[2sinx+\frac{2sin3x}{3}+\frac{2sin5x}{5}...] $$     (4.24) Plotted with Wolfram Alpha Fourier Series of Function 4.2
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Author
Solved and Typed By - --Egm4313.s12.team1.stewart (talk) 02:22, 25 April 2012 (UTC)

Reviewed By - Egm4313.s12.team1.essenwein (talk) 16:50, 25 April 2012 (UTC)

Statement
Consider equation (5.0) below:
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$$  \displaystyle <\phi_{2j-1},\phi_{2k-1}> = \int_{0}^{P}\sin{j\omega x}\cdot \sin{k\omega x}dx = 0 $$     (5.0)
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1) Find the exact integration of equation (5.0) with $$ P = 2\pi\!$$, $$ j = 2\!$$, $$ k = 3\!$$. 2) Confirm the result with Matlab's trapz command for the trapezoidal rule.

Solution
1) Substituting the given values, we get equation (5.1) below:
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$$  \displaystyle <\phi_{3},\phi_{5}> = \int_{0}^{2\pi}\sin{2\omega x}\cdot \sin{3\omega x}dx = 0 $$     (5.1)
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Using the product and sum trigonometry identities, we can evaluate the definite integral:
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$$  \displaystyle \int_{0}^{2\pi}\sin{2\omega x}\cdot \sin{3\omega x}dx = \frac{1}{2}\int_{0}^{2\pi}(\cos{\omega x}-\cos{5\omega x})dx = 0 $$     (5.2)
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$$  \displaystyle \rightarrow [\frac{1}{2\omega}{\sin{\omega x} - \frac{1}{5}\sin{5\omega x}}]_0^{2\pi} = 0 $$     (5.3)
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Also, $$ \omega = \frac{2\pi}{P} = 1\!$$, and substituting this into equation (5.3) allows the definite integral to be solved:
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$$  \displaystyle [\frac{1}{2}{\sin{x} - \frac{1}{5}\sin{5x}}]_0^{2\pi} = 0 $$     (5.4)
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2) The following is the code for evaluating the definite integral in equation (5.1) in Matlab:

EDU>> X = 0:pi/100:2*pi; EDU>> Y = sin(2*X).*sin(3*X); EDU>> Z = trapz(X,Y)

Z =

-2.2633e-17

EDU>> plot(X,Y)

The returned value of the evaluated integral in Matlab is essentially equal to zero, and it can be seen in the graph that the areas under the curve cancel each other out.

Author
Solved and Typed By - Egm4313.s12.team1.wyattling

Reviewed By - Egm4313.s12.team1.rosenberg


text:
Talk:Euclidean geometry/Proofs

Is a Wordpress or Blogspot a better place to host your blog?

program PITy
How do you get menus and modules to change language when using the Joom!Fish Joomla extension?

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Talk:Euclidean geometry/Proofs


title: File:CORDIC.fixedc.1.A.20120224.pdf


text:
Talk:TAO/Creating Personas and Working with Them/unit 1

the questions are a good help to create personas Marquard Markus (talk) 15:46, 24 February 2012 (UTC)


text:
User talk:Garcia123

Martin is very attentive and looks for work even when there isn't any to do, which is a very good quality to have. This week he rented out the OBD to see how it worked with his car first and is also researching programs other people used to hack their ECU. David Ross

Martin is a great person to work with, he is very optimistic and is always willing to help everyone out. He is always trying to find new things to do which for our group is great since we need a lot of creativity for this project Kdelvill4474

title: User talk:Garcia123


text:
User talk:Kdelvill4474/enes100

Kim is the backbone of this group and stays in communication with everyone. She helped find mostly everything we used in our first week presentation and researched the OBD we're going to use in our project. Right now she is researching programs other people used to hack their ECU.

Kim brings the group together and is great with cummunicating with us. She found alot of stuff for the first presentation and alot of info about the OBD. Great person to work with. Garcia123 (talk) 02:17, 27 February 2012 (UTC)

Kim is a great person to work with. Shes friendly and gets the material fast. Just give her a brief summary in what we are planning to do and she will get it. --Garcia123 (talk) 21:01, 11 March 2012 (UTC)

http://www.youtube.com/watch?v=j3s4JwQp9_E

title: User talk:Kdelvill4474/enes100


text:
User talk:Shaun9876

Hello

title: User talk:Shaun9876


text:
Point-biserial correlation coefficient

A point-biserial correlation coefficient is a type of correlation which indicates the relationship between a dichotomous variable and a continuous variable.

title: Point-biserial correlation coefficient


text:
User talk:Robinson7

No spamming, please
Please refrain from adding promotional content or spam to Wikiversity and its sister projects. Thanks, Mathonius (talk) 21:23, 24 February 2012 (UTC)

title: User talk:Robinson7


text:
User:Marshallsumter/Keynote lectures (draft)/Mercury

"A large part of Mercury could be covered in dried lava. The planet's northern plains appear smooth because lava may have poured over the surface, smoothing it out as it moved. Although scientists don't see volcanic activity on Mercury's surface now, many think it could be a good explanation for the way the planet looks today. The two crater rings in this image might have been smoothed by volcanic material, according to NASA."

Intercrater plains
"Mercury's oldest surface is its intercrater plains [1,3], which are present (but much less extensive) on the Moon. The intercrater plains are level to gently rolling terrain that occur between and around large craters. The plains predate the heavily cratered terrain, and have obliterated many of the early craters and basins of Mercury [1,4]; they probably formed by widespread volcanism early in mercurian history."

In the image on the right are abundant shallow elongate craters and crater chains are present on the plains. This image, taken during the first mission of Mariner 10, shows a large tract of inter-crater plains centered at 3° N, 20° W. The scarp running down the middle of the image, Santa Maria Rupes cuts through both the plains and large craters. The scene is 200 km across; north is the top.

Caloris basins

The largest known crater is Caloris Basin, with a diameter of 1,550 km. The impact that created the Caloris Basin was so powerful that it caused lava eruptions and left a concentric ring over 2 km tall surrounding the impact crater. At the antipode of the Caloris Basin is a large region of unusual, hilly terrain known as the "Weird Terrain".

"Scientists think that a huge asteroid slammed into Mercury about 4 billion years ago, creating a giant crater about 960 miles (1,545 km) across. Called the Caloris Basin, the crater could fit the whole state of Texas inside it. Researchers have calculated that the asteroid that created the basin had to have been about 60 miles (100 km) wide."

"Analysis of radio tracking data have enabled maps of the gravity field of Mercury to be derived. In this image [second down on the right], overlain on a mosaic obtained by MESSENGER's Mercury Dual Imaging System and illuminated with a shape model determined from stereo-photoclinometry, Mercury's gravity anomalies are depicted in colors. Red tones indicate mass concentrations, centered on the Caloris basin (center) and the Sobkou region (right limb). Such large-scale gravitational anomalies are signatures of subsurface structure and evolution. The north pole is near the top of the sunlit area in this view."

"Color differences on Mercury are subtle, but they reveal important information about the nature of the planet's surface material. A number of bright spots with a bluish tinge are visible in this image. These are relatively recent impact craters. Some of the bright craters have bright streaks (called "rays" by planetary scientists) emanating from them. Bright features such as these are caused by the presence of freshly crushed rock material that was excavated and deposited during the highly energetic collision of a meteoroid with Mercury to form an impact crater. The large circular light-colored area in the upper right of the image [on the left] is the interior of the Caloris basin. Mariner 10 viewed only the eastern (right) portion of this enormous impact basin, under lighting conditions that emphasized shadows and elevation differences rather than brightness and color differences. MESSENGER has revealed that Caloris is filled with smooth plains that are brighter than the surrounding terrain, hinting at a compositional contrast between these geologic units. The interior of Caloris also harbors several unusual dark-rimmed craters, which are visible in this image. The MESSENGER science team is working with the 11-color images in order to gain a better understanding of what minerals are present in these rocks of Mercury's crust."

Planetary astronomy
On the right is a computer program result for the orbit of Mercury. View is from above the ecliptic (North Pole). Mercury is in yellow. A circular orbit with the same semi-major axis is in grey for reference. The orbit is plotted in brighter colours above the ecliptic and darker below. Major axis is drawn showing perihelion (q) and aphelion (Q). Positions show every 5 days before and after the perihelion on May 20, 2006. For illustration the size of the sphere is inversely proportional to the distance from the Sun. The Sun is in the center. Yellow segment points toward the vernal point. Data for the plot is from the Jet Propulsion Laboratory.

The second image on the right down from the top is an animation of the revolutions of Mercury, Venus and Earth around the Sun. Mercury takes 88 days to complete an orbit, thus the animation shows it revolving around the Sun approximately 4.14 times (yellow trail) compared to Earth's 365 days (blue trail).

The third lower diagram on the right shows how Mercury's orbital period and rotational period are locked in a 3:2 resonance.

After one orbit, Mercury has rotated 1.5 times, so after two complete orbits the same hemisphere is again illuminated.

Minerals
"The [Mercury Atmosphere and Surface Composition Spectrometer] MASCS instrument was designed to study both the exosphere and surface of Mercury. To learn more about the minerals and surface processes on Mercury, the Visual and Infrared Spectrometer (VIRS) [VIRS Color Composite Wavelengths: 575 nm as red, 415 nm/750 nm as green, 310 nm/390 nm as blue] portion of MASCS has been diligently collecting single tracks of spectral surface measurements since MESSENGER entered orbit. The track coverage is now extensive enough that the spectral properties of both broad terrains and small, distinct features such as pyroclastic vents and fresh craters can be studied. To accentuate the geological context of the spectral measurements, the MASCS data have been overlain on the MDIS monochrome mosaic."

Astrognosy
A theory for the internal structure of Mercury is shown on the right, where
 * 1) Crust - 100-200 km thick,
 * 2) Mantle - 600 km thick, and
 * 3) Nucleus - 1,800 km radius.

"Mercury's iron core takes up about 75 percent of the planet's radius. The huge core has more iron in it than any other planet's in the solar system."

Astrogony
"Scientists aren't exactly sure how Mercury's giant iron core formed, but researchers think it has something to do with its formation. If the planet formed quickly, it could have left a thin shell of crust over the relatively large core."

Hominins “lived without town or laws, speaking one tongue under the rule of Jove. But after Mercury explained the languages of men (whence he is called hermeneutes, ‘interpreter,’ for Mercury in Greek is called Hermes; he, too, divided the nations) then discord arose among mortals.”

“The meaning is clearly that Hermes invented one language for one people, another for another. The whole account reminds one of the Biblical Tower of Babel.”

"In my understanding Mercury was once a satellite of Jupiter, or possibly of Saturn. In the course of the events which followed Saturn’s interaction with Jupiter and its subsequent disruption, Mercury was pushed from its orbit and was directed to the sun by Jupiter. It could, however, have been a comet and the entwined snakes of the caduceus may memorialize the appearance it had when seen by the inhabitants of the Earth."

Electromagnetics
Despite its small size and slow 59-day-long rotation, Mercury has a significant, and apparently global, magnetic field. According to measurements taken by Mariner 10, it is about 1.1% as strong as the Earth's. The magnetic field strength at the Mercurian equator is about 300 nT. Like that of Earth, Mercury's magnetic field is dipolar. Unlike Earth, Mercury's poles are nearly aligned with the planet's spin axis. Measurements from both the Mariner 10 and MESSENGER space probes have indicated that the strength and shape of the magnetic field are stable.

During its second flyby of the planet on October 6, 2008, MESSENGER discovered that Mercury's magnetic field can be extremely "leaky." The spacecraft encountered magnetic "tornadoes" – twisted bundles of magnetic fields connecting the planetary magnetic field to interplanetary space – that were up to 800 km wide or a third of the radius of the planet. These 'tornadoes' form when magnetic fields carried by the solar wind connect to Mercury's magnetic field. As the solar wind blows past Mercury's field, these joined magnetic fields are carried with it and twist up into vortex-like structures. These twisted magnetic flux tubes, technically known as flux transfer events, form open windows in the planet's magnetic shield through which the solar wind may enter and directly impact Mercury's surface.

The process of linking interplanetary and planetary magnetic fields, called magnetic reconnection, is common throughout the cosmos. It occurs in Earth's magnetic field, where it generates magnetic tornadoes as well. The MESSENGER observations show the reconnection rate is ten times higher at Mercury. Mercury's proximity to the Sun only accounts for about a third of the reconnection rate observed by MESSENGER.

There are "observed MHD fluctuations in the magnetosphere" of Mercury.

"The Mariner 10 spacecraft had revealed that Mercury possessed a magnetic field similar to Earth's, albeit one that is about 100 times weaker."

"This means Mercury's core has to be at least partially liquid. This was a surprise at first, because Mercury is very small, so you would expect it to cool quickly after it formed and be completely solid. [But,] if there was a little bit of nonmetallic stuff in Mercury's core, that'd lower its freezing point and make it hard to be completely solid."

In "the fall of 2014 and 2015, when the spacecraft flew incredibly close to the planet's surface, at altitudes as low as 9 miles (15 kilometers)."

"The signals we detected are really small, and very, very hard to measure. We'd never have been able to measure them if not for these really risky low-altitude observations in the last few months of the MESSENGER mission."

"The scientists detected magnetized rocks in a part of Mercury's crust that, due to the presence of many craters from cosmic impacts, appears to be quite ancient. [Shown in the second image down on the right.] The researchers suggest the rocks were once magnetized by the planet's magnetic field, and based on the age and amount of the magnetized rocks, as well as how strongly they were magnetized, the investigators deduced that Mercury's magnetic field has persisted for 3.8 billion years."

"The strength of Mercury's magnetic field may have ranged anywhere from its strength today to something about 100 times stronger, comparable to the strength of Earth's magnetic field at Earth's surface today."

"Being able to pin down how long Mercury has had a magnetic field helps us narrow down scenarios for the early history of Mercury and how it has changed over time. This in turn helps us understand more about planetary evolution in general."

Cosmic rays
From the Mariner 10 observations in electron astronomy, it is concluded that "[d]ue to the limited shielding provided by its relatively weak magnetic dipole moment, the surface of Mercury is everywhere subject to bombardment by cosmic rays and solar energetic particles with energies greater than 1 MeV/nucleon."

"Galactic cosmic rays should have very similar fluxes on Mercury and the Moon." "Solar Cosmic Rays which result in the formation of particle tracks also increase by a factor of up to 10 when compared to the Moon. However, surface temperatures reach 700 K, which can result over millions of years in the annealing of irradiation effects."

Protons
"During the Mercury flyby of Mariner 10, observations of large fluxes of energetic ... protons (0.53 < E < 1.9 MeV) have been reported" but these may be due to "the pileup of low-energy electrons rather than the presence of protons in the vicinity of Mercury."

The Energetic Particles Experiment aboard Mariner 10 "was designed to measure energetic ... protons ... in the interplanetary medium and in the vicinities of Venus and Mercury. The instrumentation consisted of a main telescope and a low-energy telescope. The main telescope consisted of six co-linear sensors (five silicon detectors and one CsI scintillator) surrounded by a plastic scintillator anti-coincidence cup. One pulse height analysis was performed every 0.33 s, and counts accumulated in each coincidence/anti-coincidence mode were measured every 0.6 s. Particles stopping in the first sensor were protons ... in the range 0.62--10.3 MeV/nucleon ... . The aperture half angle for this mode was 47 degrees, and the geometric [factor was] 7.4 sq cm-sr for protons ... . The telescope aperture half-angle decreased to 32 degrees for coincident counts in the first and third sensors. The low-energy telescope, a two-element (plus anti-coincidence) detector with a 38 degree half angle aperture and a 0.49 sq cm sr geometrical factor, was designed to measure 0.53--1.9 MeV and 1.9--8.9 MeV protons without responding to electrons over a wide range of electron energies and intensities."

"The ... solar proton flare on 20 April 1998 at W 90° and S 43° (9:38 UT) was measured by the GOES-9-satellite (Solar Geophysical Data 1998), as well as by other experiments on WIND ... and GEOTAIL. Protons were accelerated up to energies > 110 MeV and are therefore able to hit the surface of Mercury."

Neutrons
The neutron spectrometer on the MESSENGER spacecraft determines the hydrogen mineral composition to a depth of 40 cm by detecting low-energy neutrons that result from the collision of cosmic rays and the minerals.

"During large solar flares, the region near Mercury may be strongly illuminated with solar neutrons."

"The Messenger spacecraft, which swung into orbit around Mercury in March 2011 and has completed its primary mission, took a closer look by counting particles known as neutrons that are flying off the planet. High-energy cosmic rays break apart atoms, and the debris includes neutrons."

"But when a speeding neutron hits a hydrogen atom, which is almost the same weight, it comes to almost a complete stop, just as the cue ball in billiards transfers its momentum when it hits another ball. Water molecules contain two hydrogen atoms, and thus when Messenger passed over ice-rich areas, the number of neutrons dropped."

“Water ice is the only candidate we’ve got that fits all those observations.”

"The ice is almost pure water, which indicates that it arrived within the last few tens of millions of years, possibly from a comet that smacked into Mercury."

"Several young craters on the surface of Mercury could be candidates for such an impact."

"Not all of the icy regions were bright. In slightly warmer regions, where temperatures exceed minus 280, the ice was covered by a dark layer about half a foot thick."

"Between the scorched equator and the frozen poles, temperatures on Mercury can be temperate, especially a few feet below the surface, where the soil insulates against the temperature swings between day and night — an ideal location to build a colony."

Electrons
Mariner 10 has aboard "one backward facing electron spectrometer (BESA). ... An electron spectrum [is] obtained every 6 s, ... within the energy range 13.4-690 eV. ... [B]y taking into account [the angular] distortion [caused by the solar wind passing the spacecraft] and the spacecraft sheath characteristics ... some of the solar wind plasma parameters such as ion bulk speed, electron temperature, and electron density [are derived]."

Mariner 10 had three encounters with Mercury on March 29, 1974, September 21, 1974, and on March 16, 1975.

The BESA measurements "show that the planet interacts with the solar wind to form a bow shock and a permanent magnetosphere. ... The magnetosphere of Mercury appears to be similar in shape to that of the earth but much smaller in relation to the size of the planet. The average distance from the center of Mercury to the subsolar point of the magnetopause is ∼ 1.4 planetary radii. Electron populations similar to those found in the earth’s magnetotail, within the plasma sheet and adjacent regions, were observed at Mercury; both their spatial location and the electron energy spectra within them bear qualitative and quantitative resemblance to corresponding observations at the earth."

"[T]he Mercury encounter (M I) by Mariner 10 on 29 March 1974 occurred during the height of a Jovian electron increase in the interplanetary medium."

X-rays
The MESSENGER X-ray spectrometer (XRS) maps mineral composition within the top millimeter of the surface on Mercury by detecting X-ray spectral lines from magnesium, aluminum, sulphur, calcium, titanium, and iron, in the 1-10 keV range.

"Now, 205 measurements of Mercury's surface composition, made by the X-ray spectrometer onboard Messenger, reveal how much Mercury's surface differs from those of other planets in the solar system."

"The surface is dominated by minerals high in magnesium and enriched in sulfur, making it similar to partially melted versions of an enstatite chondrite, a rare type of meteorite that formed at high temperatures in low-oxygen conditions in the inner solar system."

""The similarity between the constituents of these meteorites and Mercury's surface leads us to believe that either Mercury formed via the accretion of materials somewhat like the enstatite chondrites, or that both enstatite chondrites and the Mercury precursors were built from common ancestors," [Shoshana] Weider [a planetary geologist at the Carnegie Institution of Washington] said."

Opticals
"Optical reflectance studies of Mercury provide evidence for Mg silicates."

"Solar heating at ‘‘noontime’’ at Mercury’s equator causes surface temperatures of ~700 K, while the side of Mercury away from the Sun cools to ~100 K (due to radiation losses) during the long night."

"Mercury [has a] tenuous ballistic [atmosphere]."

"The Tolstoj basin (355 km in diameter) can be seen at the bottom edge of the frame [on the right], its center filled with smooth plains and surrounded by a large region of low-reflectance ejecta. The fresh, bright-rayed crater Nureyev is visible near the limb."

Ultraviolets
"[U]ltraviolet observations by Mariner 10 provided evidence for the presence of H and He in the atmosphere (~1011 and 1012 atoms cm-2 respectively3".

Aboard Mariner 10, "[t]he extreme ultraviolet spectrometer consisted of two instruments: an occultation spectrometer that was body-fixed to the spacecraft and an airglow spectrometer that was mounted on the scan platform. When the sun was obscured by the limbs of the planet, the occultation spectrometer measured the extinction properties of the atmosphere. The occultation spectrometer had a plane grating which operated at grazing incidence. The fluxes were measured at 47.0, 74.0, 81.0, and 89.0 nm using channel electron multipliers. Pinholes defined the effective field of view of the instrument which was 0.15 degree full width at half maximum (FWHM). Isolated spectral bands at approximately 75 nm (FWHM) were also measured. The objective grating airglow spectrometer was flown to measure airglow radiation from Venus and Mercury in the spectral range from 20.0--170.0 nm. With a spectral resolution of 2.0 nm, the instrument measured radiation at the following wavelengths: 30.4, 43.0, 58.4, 74.0, 86.9, 104.8, 121.6, 130.4, 148.0, and 165.7 nm. In addition, to provide a check on the total incident extreme UV flux to the spectrometer, two zero-order channels were flown. The effective field of view of the instrument was 0.13 by 3.6 degree. Data also include the interplanetary region."

Visuals
"Mercury, the closest planet to the Sun, possesses a lot of ice — 100 billion to one trillion tons [...] near Mercury’s poles, deep within craters where the Sun never shines, temperatures dip to as cold as minus 370."

Blues
"MESSENGER's Wide Angle Camera (WAC), part of the Mercury Dual Imaging System (MDIS), is equipped with 11 narrow-band color filters. As the spacecraft receded from Mercury after making its closest approach on January 14, 2008, the WAC recorded a 3x3 mosaic covering part of the planet not previously seen by spacecraft. The color image shown here was generated by combining the mosaics taken through the WAC filters that transmit light at wavelengths of 1000 nanometers (infrared), 700 nanometers (far red), and 430 nanometers (violet). These three images were placed in the red, green, and blue channels, respectively, to create the visualization presented here. The human eye is sensitive only across the wavelength range from about 400 to 700 nanometers. Creating a false-color image in this way accentuates color differences on Mercury's surface that cannot be seen in black-and-white (single-color) images."

Yellows
"[H]igh-resolution spectral measurements of Mercury show emission in sodium D lines (Potter and Morgan 1985a). This suggests a substantial sodium population in Mercury's atmosphere ... possibly due to photo-sputtering of the planetary surface".

Reds
"A higher-reflectance, relatively red material occurs as a distinct class of smooth plains that were likely emplaced volcanically; a lower-reflectance material with a lesser spectral slope may represent a distinct crustal component enriched in opaque minerals, possibly more common at depth."

"The distinctively red smooth plains (HRP) appear to be large-scale volcanic deposits stratigraphically equivalent to the lunar maria (20), and their spectral properties (steeper spectral slope) are consistent with magma depleted in opaque materials. The large areal extent (>106 km2) of the Caloris HRP is inconsistent with the hypothesis that volcanism was probably shallow and local (10); rather, such volcanism was likely a product of extensive partial melting of the upper mantle."

"Despite the dearth of ferrous iron in silicates, Mercury's surface nonetheless darkens and reddens with time like that of the Moon. This darkening and reddening has been interpreted to be the result of production of nanophase iron (e.g., Pieters et al., 2000; Hapke, 2001), which could be derived from an opaque phase in the crustal material or from delivery by micrometeorite impacts (Noble and Pieters, 2003). On the Moon, deposits that are brighter and redder than the average Moon spectrum appear to be lower in iron (e.g., highland material); deposits that are darker and redder than average are higher in iron (e.g., low-Ti mare material) (Lucey et al., 1995)."

Radars
Water ice strongly reflects radar, and observations by the 70 m [Goldstone Deep Space Communications Complex] Goldstone telescope and the [Very Large Array] VLA in the early 1990s revealed that there are patches of very high radar reflection near the poles. While ice is not the only possible cause of these reflective regions, astronomers believe it is the most likely.

Radar astronomy of Mercury improved the value for the distance from the earth including rotational period, libration, and surface mapping, especially of the polar regions.

Craters
Mercury's surface is heavily cratered and similar in appearance to Earth's Moon. For example, an unusual crater with radiating troughs has been discovered which scientists called "the spider." Craters on Mercury range in diameter from small bowl-shaped cavities to multi-ringed impact basins hundreds of kilometers across. They appear in all states of degradation, from relatively fresh rayed craters to highly degraded crater remnants. Mercurian craters differ subtly from lunar craters in that the area blanketed by their ejecta is much smaller, a consequence of Mercury's stronger surface gravity.

Overall, about 15 impact basins have been identified on the imaged part of Mercury. A notable basin is the 400 km wide, multi-ring Tolstoj Basin which has an ejecta blanket extending up to 500 km from its rim and a floor that has been filled by smooth plains materials. Beethoven Basin has a similar-sized ejecta blanket and a 625 km diameter rim. Like the Moon, the surface of Mercury has likely incurred the effects of space weathering processes, including Solar wind and micrometeorite impacts.

On November 29, 2012, NASA confirmed that images from the space probe Mercury Messenger had detected that craters at the north pole contained water ice. Sean C. Solomon was quoted in the New York Times as estimating the volume of the ice as large enough to "encase Washington, D.C., in a frozen block two and a half miles deep."

A small crater named Hun Kal provides the reference point for measuring longitude. The center of Hun Kal is 20° west longitude.

Mariner 10 provided the first close-up images of Mercury's surface, which immediately showed its heavily cratered nature.

"This spectacular view of the crater Degas [lower image on the right] was obtained as a high-resolution targeted observation (90 m/pixel). Impact melt coats its floor, and as the melt cooled and shrank, it formed the cracks observed across the crater. For context, Mariner 10’s view of Degas is shown at left. Degas is 52 km in diameter and is centered at 37.1° N, 232.8° E."

The Scarlatti crater on Mercury has its center located at 40.71°N latitude, 101.09°W longitude.

Scarlatti crater is a pit crater.

"Pit craters are rimless steep-sided depressions that are inferred to have formed by non-impact processes."

Pit "craters on Mercury formed through collapse into an underlying drained magma chamber. Pit-floor craters thus provide evidence for near-surface magmatic activity on Mercury and extend the range of evidence for magmatism beyond such surface expressions as smooth plains and pyroclastic deposits."

Atmospheres
"As the MESSENGER spacecraft approached Mercury, the UVVS field of view was scanned across the planet's exospheric "tail," which is produced by the solar wind pushing Mercury's exosphere (the planet's extremely thin atmosphere) outward. This figure [on the right] shows a map of the distribution of sodium atoms as they stream away from the planet (see PIA10396); red and yellow colors represent a higher abundance of sodium than darker shades of blue and purple, as shown in the colored scale bar, which gives the brightness intensity in units of kiloRayleighs. The escaping atoms eventually form a comet-like tail that extends in the direction opposite that of the Sun for many planetary radii. The small squares outlined in black correspond to individual measurements that were used to create the full map. These measurements are the highest-spatial-resolution observations ever made of Mercury's tail. In less than six weeks, on October 6, 2008, similar measurements will be made during MESSENGER's second flyby of Mercury. Comparing the measurements from the two flybys will provide an unprecedented look at how Mercury's dynamic exosphere and tail vary with time."

"These figures [on the lower right] show observations of calcium and magnesium in Mercury's neutral tail during the third MESSENGER Mercury flyby. The distribution of neutral calcium in the tail appears to be centered near the equatorial plane and the emission rapidly decreases to the north and south as well as in the anti-sunward direction. In contrast, the distribution of magnesium in the tail exhibits several strong peaks in emission and a slower decrease in the north, south, and anti-sunward directions. These distributions are similar to those seen during the second flyby, but the densities were higher during the third flyby, a different "seasonal" variation than for sodium. Studying the changes of the "seasons" for a range of species during MESSENGER's orbital mission phase will be key to quantifying the processes that generate and maintain the exosphere and transport volatile material within the Mercury environment."

Meteorites
"NWA 7325 is actually a group of 35 meteorite samples discovered in 2012 in Morocco. They are ancient, [...] an age of about 4.56 billion years."

"NWA 7325 has a lower magnetic intensity — the magnetism passed from a cosmic body's magnetic field into a rock — than any other rock yet found."

"Data sent back from NASA's Messenger spacecraft currently in orbit around Mercury shows that the planet's low magnetism closely resembles that found in NWA 7325."

"NWA 7325 has olivine in it that is insanely magnesium-rich. Iron and magnesium are two elements that are almost always found together in rocks; the ions they make have the same size and charge so they happily occupy the same positions in crystal lattices. It's weird to have a rock that is so dominantly magnesium-rich. Mercury's surface rocks are known (thanks to MESSENGER) to be unusually low in iron."

"NWA 7325's oxygen isotope ratios do not match any known meteorites from any other planet-size body. In fact, they're not particularly similar to much of anything that we've measured oxygen isotope ratios for."

"The ratios of Al/Si (0.224) and Mg/Si (0.332) plus the very low Fe content of NWA 7325 are consistent with the compositions of surface rocks on Mercury [6], but the Ca/Si ratio (0.582) is far too high. However, since NWA 7325 is evidently a plagioclase cumulate (and presumably excavated from depth), it may not match surface rocks on its parent body. The abundance of diopside rather than enstatite might be consistent with some earlier spectral observations of Mercury [7]."

"[I]t's about 23 times harder to get a rock from Mercury to Earth than it is from Mars to Earth. Given that we've got more than 70 known Mars meteorites in our collections, that means we ought to have found 3 (give or take a couple) Mercury meteorites by now."

Mercury
"There is also the shrinking issue. As the planet’s core cooled, it contracted, which led to the crust crumpling and fracturing into a rugged landscape. Detailed mapping of the cracks at the surface could help determine how quickly the shrinking is happening and reveal more about the underlying processes driving it."

"The [BepiColombo] spacecraft, scheduled to launch in October 2018, will investigate the existence of water ice at Mercury’s poles and its volcanoes, and attempt to explain the surprising discovery that the solar system’s smallest planet appears to be shrinking."

Astrogeology
"The crater in the lower right-hand corner of this image [on the right] has a patch of very dark material located near its center. The region of this image has been seen only with the Sun high overhead in the sky. Such lighting conditions are good for recognizing color differences of rocks but not well suited for ascertaining the topography of surface features from shadows. The shape of the surface in this area is difficult to resolve given the lighting angle, but the dark patch is not in shadow. Dark surfaces have also been seen on other regions of Mercury, including this dark halo imaged during the second Mercury flyby (PIA11357) and near such named craters as Nawahi, Atget, and Basho seen during MESSENGER's first Mercury encounter. The example here is particularly striking, however, and from this NAC image the material may appear even darker than in other example areas. The dark color is likely due to rocks that have a different mineralogical composition from that of the surrounding surface. Understanding why these patches of dark rocks are found on Mercury's surface is a question of interest to the MESSENGER Science Team. The right edge of the image here aligns with this previously released NAC image (see PIA11763), where other dark surface material, as well as patches of light-colored rocks, can be seen."

The second lower image on the right from the top shows "a double-ring impact basin, with another large impact crater on its south-south-western side. Double-ring basins are formed naturally when a large meteoroid strikes the surface of a rocky planet. Smaller, more recent impacts also formed comparatively fresh craters across the entire surface visible in this image. The floor within the inner or peak ring appears to be smoother than the floor between the peak ring and the outer rim, possibly the result of lava flows that partially flooded the basin some time after impact."

The lowest image from the top on the right is a closeup of the weird terrain of Mercury.

"Weird terrain best describes this hilly, lineated region of Mercury. Scientists note that this area is at the antipodal point to the large Caloris basin. The shock wave produced by the Caloris impact may have been reflected and focused to the antipodal point, thus jumbling the crust and breaking it into a series of complex blocks. The area covered is about 800 km (497 mi) on a side."

Sun-Mercury system
In the image on the right sunspot #923, which is just below the equator at the left-hand side, is much bigger than Mercury. Two more sunspots are on the right-hand side at the equator. Mercury is a small black dot in the lower middle of the solar disk. The picture was taken with a white filter.

The diagram in the second image from the top on the right shows that because "Mercury and Venus orbit the Sun within Earth's orbit, they stay close to the Sun in the sky as seen from Earth. At their greatest angular distance from the Sun they are said to be at elongation. Here the two planets are shown at eastern elongation; they set after the Sun and appear as evening stars."

The third down image on the right shows "five versions of observations that NASA's Curiosity made about one hour apart while Mercury was passing in front of the sun on June 3, 2014. Two sunspots, each about the diameter of Earth, also appear, moving much less than Mercury during the hour."

"This is the first transit of the sun by a planet observed from any planet other than Earth, and also the first imaging of Mercury from Mars. Mercury fills only about one-sixth of one pixel as seen from such great distance, so the darkening does not have a distinct shape, but its position follows Mercury's expected path based on orbital calculations."

"This is a nod to the relevance of planetary transits to the history of astronomy on Earth."

"Observations of Venus transits were used to measure the size of the solar system, and Mercury transits were used to measure the size of the sun."

"The observations were made on June 3, 2014, from Curiosity's position inside Gale Crater on Mars. In addition to showing the Mercury transit, the same Mastcam frames show two sunspots approximately the size of Earth. The sunspots move only at the pace of the sun's rotation, much slower than the movement of Mercury."

Astrography
The geography of the surface of Mercury (or Hermes) could be called Hermography or maybe Hermeography.

The image on the right is part of the first-ever complete map of Mercury's surface.

The image on the left is a topographic map of part of Mercury's surface.

"Measurements from MESSENGER's MLA instrument during the spacecraft's greater than four-year orbital mission have mapped the topography of Mercury's northern hemisphere in great detail. The view shown here is an interpolated shaded relief map of these data. The lowest regions are shown in purple, and the highest regions are shown in red. The difference in elevation between the lowest and highest regions shown here is roughly 10 kilometers! Among the prominent features visible here are the smooth northern volcanic plains and the enigmatic northern rise. The low-lying craters near the north pole host radar-bright materials, thought to be water ice. Linear artifacts can be seen in some areas of this map. These are due to individual MLA tracks that need minor adjustments in order to fit the rest of the data. Crossover analysis and better knowledge of the spacecraft position can be used to adjust these tracks and improve the map."

Classical planets
In antiquity the classical planets were the non-fixed objects visible in the sky, known to various ancient cultures. The classical planets were therefore the Sun and Moon and the five non-earth planets of our solar system closest to the sun (and closest to the Earth); all easily visible without a telescope. They are Mercury, Venus, Mars, Jupiter, and Saturn.

Wednesday is the day of Mercury and its color varies blue/brown/black.

Ancient history
The ancient history period dates from around 8,000 to 3,000 b2k.

~ 5102 b2k, is the historical year assigned to a Hindu table of planets that does include the classical planet Mercury (or Hermes). "Hermès observait en -1660; donc les Indiens observaient en -3102, et ils observaient bien!" "Babylonian astronomy, too, had a four-planet system. In ancient prayers the planets Saturn, Jupiter, Mars, and Mercury are invoked; ... and one speaks of "the four-planet system of the ancient astronomers of Babylonia." "

~ 3300 b2k: The earliest known recorded observations of Mercury are from the Mul.Apin tablets. These observations were most likely made by an Assyrian astronomer around the 14th century BC. The cuneiform name used to designate Mercury on the Mul.Apin tablets is transcribed as Udu.Idim.Gu\u4.Ud ("the jumping planet").

~ 2900 b2k: Babylonian records of Mercury date back to the 1st millennium BC. The Babylonians called the planet Nabu after the messenger to the gods in their mythology.

~2400 b2k: The ancient Greeks of Hesiod's time knew the planet as (Stilbon), meaning "the gleaming", and (Hermaon). Later Greeks called the planet Apollo when it was visible in the morning sky, and Hermes when visible in the evening. Around the 4th century BC, Greek astronomers came to understand that the two names referred to the same body.

The Romans named the planet after the swift-footed Roman messenger god, Mercury (Latin Mercurius), which they equated with the Greek Hermes, because it moves across the sky faster than any other planet.

In ancient China, Mercury was known as Chen Xing (辰星), the Hour Star. It was associated with the direction north and the phase of water in the Wu Xing. ... Hindu mythology used the name Budha for Mercury, and this god was thought to preside over Wednesday. The god Odin (or Woden) of Germanic paganism was associated with the planet Mercury and Wednesday. The Maya may have represented Mercury as an owl (or possibly four owls; two for the morning aspect and two for the evening) that served as a messenger to the underworld.

Technology
Mariner 10, sections above, made a true color image of Mercury that shows its reddish color.

The image on the right is a mosaic of Mercury taken by the Mariner 10 spacecraft during its approach on 29 March 1974. The mosaic consists of 18 images taken at 42 s intervals during a 13 minute period when the spacecraft was 200,000 km (about 6 hours prior to closest approach) from the planet.

"The MESSENGER spacecraft [an artist's impression on the lowwer right] is the first ever to orbit the planet Mercury, and the spacecraft's seven scientific instruments and radio science investigation are unraveling the history and evolution of the Solar System's innermost planet. During the first two years of orbital operations, MESSENGER acquired over 150,000 images and extensive other data sets. MESSENGER is capable of continuing orbital operations until early 2015."

Hypotheses

 * 1) The current orbit and location of Mercury in the Solar System may have been arrived at within hominin recorded history.


title: File:BJTBias.1.A.20120225.pdf


text:
Engineering Experience 4: Design a Small Solar Vehicle/Nl/2012: Team PM7

Inleiding
Welkom op de Wikiversity-pagina van Team PM7 "SolarTronics". De komende weken zal u op deze pagina terecht kunnen voor alle informatie omtrent onze Small Solar Vehicle (SSV). Lees ook onze blog waarin je het wekelijks nieuws kunt lezen over ons project.

Opdracht
Engineering Experience 4 draait rond het thema "Make Stuff Work". Ons team wordt gezien als een ingenieursbureau dat van het Umicore Solar Team de opdracht krijgt om een miniatuur zonnewagen te ontwikkelen, een Small Solar Vehicle (SSV). Het gedrag van dit model wordt naderhand aan diverse analyses onderworpen en een rapport wordt opgesteld voor UST. Met ons model zullen we bovendien aan een race deelnemen. Het project bestaat uit twee luiken: ontwerp en kritische analyses.

Luik 1: Ontwerp
Het eerste deel van de opdracht bestaat eruit om het bestelde zonnewagentje te ontwikkelen. We krijgen daarbij een startbudget van €200, een zonnepaneel en een motor.

Luik 2: Kritische analyses
SolarTronics moet in deze fase verschillende tests uitvoeren op zowel onze SSV als de bestaande Umicar, de racewagen op zonne-energie van Groep T studenten. Aërodynamica, wiskunde, materiaalkunde, ... zullen allemaal getoetst en gerapporteerd worden. Nabij dienen we ook een volledig strategisch marketingplan uit te werken voor onze SSV.

Experiment op het zonnepaneel
Ieder zonnepaneel heeft verschillende eigenschappen in vergelijking met andere panelen. De eigenheid van ons zonnepaneel kan omschreven worden met behulp van de diodefactor. De diodefactor geeft de mate waarin een diode voldoet aan het model van de ideale diode weer. Dit model zegt dat bij een reverse bias de stroom door de diode nul is. Bij 0 volt zal deze geleiden en bij iedere andere spanning vloeit er een infinitisimaal grote stroom door de diode. Theoretisch gezien compenseert de diodefactor dus voor het niet-ideale gedrag van een diode en ligt voor degelijke niet-ideale dioden vaak tussen 1.1 of 1.5, en is gelijk aan één voor een ideale diode. De diodekarakteristiek is uiteindelijk verkregen door metingen te doen in het labo. Zoals te zien is in de grafiek, was de meting echter niet honderd procent correct. Dit komt omdat het opwarmen van het paneel door de spot gezorgd heeft voor een onnauwkeurigheid op de meting, wat duidelijk te zien is in de grafiek door de vele oneffenheden vanaf 7,5V. De temperatuur is dus een bepalende factor is in het meten van de efficiëntie. De diodefactor kunnen we uit de karakteristieke formule halen. Deze is: I=I_sc-I_s*(e^(U/(m*N*U_r ))-1) Hierbij is: Omgezet naar een formule voor m geeft dit: m=U/(N*U_r*ln((I_sc-I)/I_s +1) )
 * Isc is de kortsluitstroom, m.a.w. de stroom die gemeten wordt bij een spanning van (benaderd) 0V. Bij ons bleek dit 0.35A te bedragen.
 * Ur stelt de thermische spanning voor, te vinden in de tabel met waarde 0.0257.
 * Is is de saturatiestroom, gegeven door 1e-8 en 0.14A;
 * N stelt het aantal zonnecellen voor. In dit geval is dat 15.
 * U en I werden geregeld via de verschuifbare weerstand.

Eenmaal de diodefactor van 1,24 bepaald is, kan er een diodekarakteristiek van het zonnepaneel gevonden worden, waaruit gemakkelijk het vermogen bij een bepaalde spanning afgelezen kan worden. Om de diodekarakteristiek te vinden, moet het vermogen nog eerst berekenen worden. Stroom vermenigvuldigen met spanning resulteert in het vermogen.

Overbrengingsverhouding
De overbrengingsverhouding is de verhouding van de omwentelingen van tandwielen in de aandrijving van onze SSV. Deze verhouding wordt bepaald door het aantal tanden, omtrek of diameter van de tandwielen. Een grote verhouding wil zeggen een hoge topsnelheid en een lage verhouding wil zeggen meer trekkracht. Het doel van een overbrenging is de snelheid om zetten in kracht. Formulevorm: Met:
 * i = overbrengingsverhouding (dimensieloos)
 * w = hoeksnelheid (rad/s)
 * n = toerental (omwentelingen/min)
 * z = aantal tanden (dimensieloos)
 * T = koppel (Nm)
 * D = diameter (m)
 * r = straal (m)

Simulatie overbrenging MatLab
In MatLab werd getracht om eveneens tien overbrengingsratio’s te testen, waarbij telkens een afstand/tijd en een snelheid/tijd diagram bekomen werd. Vergelijken van deze diagrammen resulteert in een optimale gear ratio. De meest belangrijke factor zal voor ons de maximale snelheid zijn, pas dan de geschatte aankomsttijd. De volgende figuur geeft een overzicht van de maximale snelheid en aankomsttijd per gear ratio:

Het is duidelijk te zien dat een gear ratio van 14 de maximale snelheid zal opleveren. Met deze overbrengingsverhouding zal de SSV eveneens in de kortste tijd de eindmeet halen. In de volgende figuur de grafiek uit MatLab:

Beschouw eerst de linkse grafiek. Deze geeft de snelheid in functie van de tijd weer. De rode lijn geeft de maximale snelheid weer. Het is te zien dat na iets meer dan twee seconden de SSV zijn maximale snelheid van 3,4m/s zal hebben bereikt. Deze zal zich aan het einde van het dalend traject bevinden, aan het begin van het rechte stuk. Beschouw nu de oranje lijn. Na vier seconden bereikt de SSV de voet van de stijgende helling. Dit zal met een snelheid van ongeveer 3,3m/s zijn. Vervolgens begint deze te klimmen en zien we dat de snelheid afneemt. Wanneer men nu de rechtse grafiek onderzoekt, merken men dat de SSV de finish (14m) na iets meer dan vijf en een halve seconde zal bereiken. Om een vergelijking te maken: wanneer een gear ratio hoger dan 14 wordt gekozen, tonen de grafieken een verlaging van de maximale snelheid (zelfs 2,7 m/s voor een gear ratio van 24). De SSV zal er eveneens langer over doen om de finish te halen. Wanneer nu een lagere gear ratio in acht wordt genomen, zal de maximale snelheid eveneens dalen en de SSV zal er langer over doen om de finish te halen. Sterker nog, bij een gear ratio van 6 of 8 blijkt deze de finish helemaal niet te bereiken. Een overbrengingsverhouding van 14 zal dus in de SSV gebruikt worden.

Ontwerp SSV
Er zal vooral gefocust worden op gewicht en stevigheid van het ontwerp. Dit is immers een bepalende factor in de aankomsttijd en de maximale snelheid van de SSV. Om ervoor te zorgen dat deze ook licht blijft, werd er besloten om een driehoekframe te bouwen. Bovendien zal het frame gevormd worden als vakwerk, waardoor de massa zal verminderen zonder daarbij aan stevigheid te verliezen, Bovendien zal de vorm ook meer aerodynamisch worden. Het frame zal gebouwd worden uit hout, met plexiglas voor extra stevigheid. Bij de uitgevoerde materiaalanalyse bewijst het materiaal eveneens zijn nut. Voorts werd er besloten om het zonnepaneel zelf met behulp van een scharnierend systeem aan het frame vast te maken. Daarbij wel op een manier die toestaat om het paneel er gemakkelijk vanaf te halen. We dachten daarbij aan een zuignap. Op die manier kan het paneel zo optimaal mogelijk gericht worden tijdens de race en kan het bovendien losgekoppeld worden om te koelen. Het kogelgewricht is sterk genoeg om het paneel op zijn plaats te houden, zelfs na eventuele kleine schokken tijdens het rijden. De wielen zullen gemaakt worden uit plexiglas. Om het wagentje op de baan te houden, plaatsen we een begeleidingssysteem onder de SSV. Dit bestaat uit een wieltje met holle groef. Deze groef past mooi op de begeleidingsrail en zal ervoor zorgen dat de SSV niet van het parcours rijdt.

Simulatie 1
In de eerste simulatie zullen we de reeds gemeten waarden voor de stroom en spanning van ons zonnepaneel laten controleren. Hiervoor gaan we het gebruikte netwerk simuleren in Simulink. Dit netwerk bestaat uit een verwisselbare weerstand, het zonnepaneel, een ampèremeter en een voltmeter. Hierbij zijn er voorlopig enkel parameters aan de verschillende componenten toegekend. Deze parameters worden hier aan toegekend in een zogenoemde m-file van Matlab. Hierbij hebben we de zonne-intensiteit gemiddeld gekozen voor 800Watt/m², maar deze is sterk afhankelijk van de weersomstandigheden. De intensiteit van de lamp bedraagt ongeveer 700 W/m². De berekende kortsluitstroom bedraagt 0.35A, de berekende openklemspanning 8.6V en de berekende diodefactor 1.22. Voor deze berekeningen verwijzen we u graag door naar case SSV. De reden waarom we de openklemspanning nog delen door 15 is omdat deze over alle zonnecellen verdeeld is. Als output krijgen we dan, zoals in de laatste twee paragraven van de m-file beschreven staat, twee figuren. Enerzijds is er de grafiek die de verhouding tussen vermogen en voltage weergeeft. Anderzijds is er de grafiek die de verhouding tussen stroom en voltage weergeeft.

Simulatie 2
In dit deel is het de bedoeling om een simulatie te maken van wanneer onze zonnewagen vanop de helling zouden laten afrollen. Dit houdt in dat er geen aandrijving is van de motor dankzij het zonnepaneel. In de figuur ziet u het door ons gebruikte Simulink model. Er zijn drie subsystemen te onderscheiden. Het eerste, grijskleurige is het zonnepaneel waarin de vijftien zonnecellen gesimuleerd zijn. Dit gedeelte is echter overbodig. We gaan er immers van uit dat de wagen van de helling rolt, dus zonder voortstuwing. Voor de volledigheid hebben we het er echter in laten staan, maar de stralingsfluxdichtheid op nul gezet. Dit houdt essentieel in dat het zonnepaneel geen licht krijgt en de motor dus niet zal werken, wat dus neerkomt op rollen. De andere twee subsystemen stellen de rolweerstand en de hellingweer-stand weer en respectievelijk in onderstaande figuur afgebeeld. Beide subsystemen hebben dezelfde opbouw, namelijk drie waarden en twee schakelaars. Dit komt omdat de baan waarop wij moeten racen bestaat uit een 4m dalende helling, een 6m vlak stuk en een 4m stijgende helling. Op ieder stuk bereiken deze twee weerstanden een andere waarden. De schakelaars zorgen ervoor dat op 4m en 10m tussen de waarden wordt geschakeld om zo de juiste weerstandswaarde te behouden. De luchtweerstand is een constante, ongeacht de hoek waaronder de wagen rijdt, vandaar dat deze niet op een dergelijke manier is opgebouwd.

Besluit
In bovenstaande figuur zien we dat de wagen ongeveer 12,25m ver zal geraken. Dit stemt volledig overeen met onze verwachtingen. Hij daalt namelijk de eerste vier meter en de snelheid neemt lineair toe, waardoor de positie parabolisch toeneemt. Hierna zal de snelheid hetzelfde blijven, met een klein verlies aan lucht- en rolweerstand, waardoor de positie quasi lineair toeneemt. Vanaf tien meter komt hij op de tweede helling, waardoor de snelheid lineair afneemt en de positie parabolisch afneemt. Tevens zal hij nooit de grens van 14m mogen halen. Dit is in overeenstem-ming met de fysica. Als er immers geen enkele weerstand was, dan zou hij exact 14m moeten halen, gezien de symmetrie van de hellingen. Hier zijn er echter wel weerstanden, waardoor hij tussen de 10m en 14m moet beginnen terugrollen. De door ons vooropgestelde statements zoals beschreven in de twee voor-gaande paragrafen kunnen we allemaal herkennen in de simulatie. De simulatie lijkt ons dus realistisch.

Week 1
Na de inleidende seminarie te hebben gekregen, zijn we er meteen in gevlogen. Eerst even algemeen kennismaken met alle teamleden en een contactenlijst opstellen. We besloten meteen om een facebookgroep en een dropboxfolder aan te maken, teneinde de communicatie ten allen tijde goed te laten verlopen. Onze eerste deadline was vrijdag al, dus haast was geboden. Mathias zou een Work Breakdown Structure (WBS) maken, Frédérick en Willem zouden beginnen aan een Plan Van Aanpak (PVA), Wouter en Alexander namen de Gantt-Chart op zich, Tom en Nick stelden het Samenwerkingscontract op en Glenn, die werd aangeduid als teamleider, zou alles verzamelen, nakijken, opsturen en de eerste stappen naar een WIKI-pagina zetten. Alle taken zijn afgerond en nagekeken. En nu alles opsturen naar de coach!
 * Dinsdag 14 februari 2012
 * Vrijdag 17 februari 2012

Week 2
Een boeiende les gekregen over de karakteristieken van zonnecellen en DC-motoren. Daarna gezamelijk een experiment uitvoeren om de karakteristieken van ons zonnepaneel te meten. Aansluitend teamvergadering om ons wat beter te oriënteren. De opdracht is onderverdeeld in Engineering, Educating en Enterprising. We besloten ons team echter op te delen in sub-teams (Marketing, Design en Energy) om efficiënter aan de opdracht en diverse cases te kunnen werken. Nadien sessie met de coach: de Gantt-chart moeten we nauwkeuriger opstellen en de PVA kan nog wat verdieping gebruiken.
 * Dinsdag 28 februari 2012

Week 3
Het team voor dat instaat voor het zonnepaneel boekt mooie vooruitgang. Verder zijn er ook vorderingen voor de ratio's van de tandwielen. Een Excel-file wordt naast Matlab gebruikt om diverse tandwielverhoudingen te berekenen en de beste eruit te selecteren. We zijn ook aan de Simulink simulatie begonnen en wordt er druk geprobeerd sponsoring binnen te krijgen.
 * Dinsdag 6 maart 2012

Week 4
Na het seminarie hebben we de handen in mekaar gestoken en heeft team Design een prototype van het autootje in K'nex gebouwd. Daarna zijn we begonnen met het ontwerpen van het autootje in SolidEdge. Een deel van het team heeft daarnaast verder gewerkt aan de Simulink, welke bijna af is.
 * Dinsdag 13 maart 2012

Week 5
Deze week werd er vooral gewerkt aan het verslag. De Simulink werd uitgebreid getest, ook de MatLab simulatie werd gerund. Die laatste bleek echter nog niet zo gemakkelijk, pas na een dik uur werken, verkregen we enigzins realistische resultaten te zien.
 * Dinsdag 20 maart 2012

Week 6
Vandaag heeft SolarTronics feedback gehad over het tussentijds rapport. Over het algemeen was het wel oke. Echter onze modellering en berekeningen van de overbrengingsverhouding was niet precies zoals het moest zijn. Hier moeten we nog een klein beetje herzien. Het ontwerp is goedgekeurd, dus nu is het de boodschap om zo snel mogelijk aan het bouwen te gaan! De Simulink simulaties waren uitstekend.
 * Dinsdag 27 maart 2012

Week 7
We zijn begonnen met de bouw! Het ontwerp in SolidEdge is volledig af, dus op naar FabLab voor de componenten. De tandwielen en kogellagers zijn eveneens besteld.
 * Dinsdag 17 april 2012

Week 8
Het bouwen gaat vlot! Aan de SSV wordt de laatste hand gelegd. Het bedrijf heeft een van de tandwielen verkeerd geleverd. We zijn dus genoodzaakt of een andere gearratio te nemen of met K'nex te werken. Volgende week ook nog even doorwerken en testen!
 * Dinsdag 24 april 2012

Week 9
Tijd om het autootje te testen! We bevestigen een 9V-batterij in plaats van het zonnepaneel. Wat blijkt, met de gear ratio die we gemaakt hebben met behulp van de tandwielen geraken we de berg niet op. Dus toch maar K'nex dan!
 * Dinsdag 1 mei 2012

Week 10
De race gaat niet door. Genoeg tijd om nog wat te testen en de laatste hand te leggen aan het verslag.
 * Dinsdag 8 mei 2012


text:
Dominant group/Mythology

"The term mythology can refer either to the study of myths ..., or to a body or collection of myths ".

As examples, comparative mythology "is the systematic comparison of myths from different cultures. " whereas "Greek mythology is the body of myths and legends belonging to the ancient Greeks"

When the patrician class is also the ruling class or an influential or dominant class, patrician class is a relative synonym for dominant group.

Dominant group
Examples from primary sources are to be used to prove or disprove each hypothesis. These can be collected per subject or in general.

 * 1) Accident hypothesis: dominant group is an accident of whatever processes are operating.
 * 2) Artifact hypothesis: dominant group may be an artifact of human endeavor or may have preceded humanity.
 * 3) Association hypothesis: dominant group is associated in some way with the original research.
 * 4) Bad group hypothesis: dominant group is the group that engages in discrimination, abuse, punishment, and additional criminal activity against other groups. It often has an unfair advantage and uses it to express monopolistic practices.
 * 5) Control group hypothesis: there is a control group that can be used to study dominant group.
 * 6) Entity hypothesis: dominant group is an entity within each field where a primary author of original research uses the term.
 * 7) Evolution hypothesis: dominant group is a product of evolutionary processes, such groups are the evolutionary process, produce evolutionary processes, or are independent of evolutionary processes.
 * 8) Identifier hypothesis: dominant group is an identifier used by primary source authors of original research to identify an observation in the process of analysis.
 * 9) Importance hypothesis: dominant group signifies original research results that usually need to be explained by theory and interpretation of experiments.
 * 10) Indicator hypothesis: dominant group may be an indicator of something as yet not understood by the primary author of original research.
 * 11) Influence hypothesis: dominant group is included in a primary source article containing original research to indicate influence or an influential phenomenon.
 * 12) Interest hypothesis: dominant group is a theoretical entity used by scholarly authors of primary sources for phenomena of interest.
 * 13) Metadefinition hypothesis: all uses of dominant group by all primary source authors of original research are included in the metadefinition for dominant group.
 * 14) Null hypothesis: there is no significant or special meaning of dominant group in any sentence or figure caption in any refereed journal article.
 * 15) Object hypothesis: dominant group is an object within each field where a primary author of original research uses the term.
 * 16) Obvious hypothesis: the only meaning of dominant group is the one found in Mosby's Medical Dictionary.
 * 17) Original research hypothesis: dominant group is included in a primary source article by the author to indicate that the article contains original research.
 * 18) Primordial hypothesis: dominant group is a primordial concept inherent to humans such that every language or other form of communication no matter how old or whether extinct, on the verge of extinction, or not, has at least a synonym for dominant group.
 * 19) Purpose hypothesis: dominant group is written into articles by authors for a purpose.
 * 20) Regional hypothesis: dominant group, when it occurs, is only a manifestation of the limitations within a region. Variation of those limitations may result in the loss of a dominant group with the eventual appearance of a new one or none at all.
 * 21) Source hypothesis: dominant group is a source within each field where a primary author of original research uses the term.
 * 22) Term hypothesis: dominant group is a significant term that may require a 'rigorous definition' or application and verification of an empirical definition.

Mythology
Def. "[t]he study of myths and the systematic collection of myths of a people, concerning the origin of the people, history, deities, ancestors and heroes" is called mythology.

Def. "[a] traditional story which embodies a belief regarding some fact or phenomenon of experience, and in which often the forces of nature and of the soul are personified; a sacred narrative regarding a god, a hero, the origin of the world or of a people, etc." is called a myth.

Folktale
Def. "[a] tale or story that is part of the oral tradition of a people or a place" is called a folktale.

"A fairy tale ... is a type of short story that typically features folkloric fantasy characters, such as fairies, goblins, elves, trolls, dwarves, giants, mermaids, or gnomes, and usually magic or enchantments. Fairy tales may be distinguished from other folk narratives such as legends (which generally involve belief in the veracity of the events described) and explicitly moral tales, including beast fables."

"In less technical contexts, the term is also used to describe something blessed with unusual happiness, as in "fairy tale ending" (a happy ending) or "fairy tale romance" (though not all fairy tales end happily). Colloquially, a "fairy tale" or "fairy story" can also mean any farfetched story or tall tale; it's used especially of any story that not only isn't true, but couldn't possibly be true."

Folklore
"Folklore (or lore) consists of legends, music, oral history, proverbs, jokes, popular beliefs, fairy tales, stories, tall tales, and customs that are the traditions of a culture, subculture, or group. It is also the set of practices through which those expressive genres are shared."

"In usage, there is a continuum between folklore and mythology. Stith Thompson made a major attempt to index the motifs of both folklore and mythology, providing an outline into which new motifs can be placed, and scholars can keep track of all older motifs."

"Folklore can be divided into four areas of study: artifact (such as voodoo dolls), describable and transmissible entity (oral tradition), culture, and behavior (rituals). These areas do not stand alone, however, as often a particular item or element may fit into more than one of these areas. "

Legend
Def. "[a] story of unknown origin describing plausible but extraordinary past events" is called a legend.

"In cultures where demons and witches are perceived as real, fairy tales may merge into legends, where the narrative is perceived both by teller and hearers as being grounded in historical truth. However, unlike legends and epics, they usually do not contain more than superficial references to religion and actual places, people, and events; they take place once upon a time rather than in actual times. "

"A legend ... is a narrative of human actions that are perceived both by teller and listeners to take place within human history and to possess certain qualities that give the tale verisimilitude. Legend, for its active and passive participants includes no happenings that are outside the realm of "possibility", defined by a highly flexible set of parameters, which may include miracles that are perceived as actually having happened, within the specific tradition of indoctrination where the legend arises, and within which it may be transformed over time, in order to keep it fresh and vital, and realistic. A majority of legends operate within the realm of uncertainty, never being entirely believed by the participants, but also never being resolutely doubted. "

Classes of meaning
A dominant group in mythology may have at least four meanings: (1) a mythology-based entity, (2) source, (3) object, or (4) in some way associated with mythology.

The term may serve as an indicator or identifier. In Kirby's An Introduction to Entomology from 1826, a dominant group of species is determined by a regional distribution. Later, this regional distribution became relative and the term entered the field of evolution. Perhaps it is an evolutionary process.

As the field of dominant group is unknown, mythology is as likely as any other. But, mythologists study the myths and their uses by human groups.

Any dominant group may be only an accident.

Artifacts
Def. "[a]n object, such as a tool, weapon or ornament, ... structure or finding in an experiment or investigation ... made or shaped by some agent or intelligence, ... [as] a result of external action, the test arrangement, or an experimental error ... rather than an inherent element" is called an artifact, or artefact.

"Cultural artifact is a term used in the social sciences, particularly anthropology, ethnology, and sociology ... for anything created by humans which gives information about the culture of its creator and users. Usage of this term encompasses the type of archaeological artifact which is recovered at archaeological sites; however, current objects of modern or near-modern society are also cultural artifacts. For example, in an anthropological context, a 17th-century lathe, a piece of faience, or a television each provide a wealth of information about the time in which they were manufactured and used. Cultural artifacts can provide knowledge about technological processes, economy and social makeup, and a host of other subjects."

Dominant group may be only an artifact.

Patrician class
"According to Livy, the first 100 men appointed as senators by Romulus were referred to as "fathers" (patres), and the descendants of those men became the Patrician class. The patricians were distinct from the plebeians because they had wider political influence, at least in the times of the Republic."

"Until the year 445 B.C. [-2445 b2k] a regular marriage (iustae nuptiae) could be contracted only between patricians - members of the ruling class." Bold added.

"'Consequently, the ruling class accumulated all the wealth for themselves, and the slave-population filled the country, while the real Italian population decreased terribly, worn out by poverty, taxation, and military service. And when there was a respite from these things they found themselves unemployed, because the land was owned by rich men who used slaves instead of freemen on their farms.' Whatever the origin of this passage may be, it shows the necessary result of the military expansion of Rome,"

Romulus
Def. in Roman mythology, "[t]he legendary founder of Rome and the twin brother of Remus" is called Romulus.

"Ioannes the Lydian, writing in the sixth century on the usage of his native town, says: 'Our own Philadelpheia still preserves a trace of the ancient belief. On the first day of the month (sc. January) there goes in procession no less a personage than Ianus himself, dressed up in a two-faced mask, and people call him Saturnus, identifying him with Kronos2.'"

"The twins [Romulus and Remus], as in the case of Janus, attach themselves to the Universal Monarch as his two faces, looking in opposite directions."

Romulus may not have been a human, but something in the sky used by a group of humans to make themselves into a ruling class.

Entities
"A sociocultural ontology buttressed by mythology and folklore ... reinforces individual and group perceptions of the superiority of the dominant group."

Objects
"The Life Tree in a matrilineal society was evidently the dominant group in the succession, consisting of the women and the high status male priests, Page 7."

Jupiter
"At the beginning of the play Fred was just a regular man who, like Jupiter in his human form, could not convince Lizzie of anything; however, after Lizzie's inaction reinstalls the myth that maintains the superiority of his dominant group, he suddenly takes on the mythic qualities of the Senator."

"Jupiter "is the king of the gods and of the universe and, as such, the supreme master of everything including those men who sheepishly submit to his decrees, live by his laws, abide by his commands" (Debusscher 311)."

Saturn
"He further suggests that the fraternity was that of the Drapers, apparently in Chaucer's time the dominant group among crafts concerned with textiles and cloth."

"Lenormant, speaking of Rome and Olympia, remarks, "It is impossible not to note that the Capitoline was first of all the Mount of Saturn, and that the Roman archaeologists established a complete affinity between the Capitoline and Mount Cronios in Olympia, from the standpoint of their traditions and religious origin (Dionysius Halicarn., i., 34). This Mount Cronios is, as it were, the Omphalos of the sacred city of Elis, the primitive centre of its worship. It sometimes receives the name Olympos."1 Here is not only symbolism in general, but also a symbolism pointing to the Arctic Eden, already shown to be the primeval mount of Kronos, the Omphalos of the whole earth.2"

Venus
"Instead we have, appropriately to the theme, a dominant group of knights, Cambel and the three sons of Agape, set in symmetrical relationship and forming, in themselves, a unity; a unity which is emphasised by another tournament which stands over against theirs, the tournament for Florimell's girdle, a scene of pointless and chaotic strife."

America
“Of "Weasel" I have heard only one instance, here in current application by members of a political faction for the leader of the rival, dominant group, a man notorious for being somewhere else when he was wanted.”

Asia
"The Sadani literature studied for the present purpose was recorded in the area where the Uraons form the dominant group."

China
“Hence, Ma Ji, who is originally rejected by the Rakshas, appears like them by hiding his 'ugly' features under black make-up, and becomes accepted by the dominant group.”

Indo-Europe
“Finally, the previously mentioned theme of a war between representatives of the first two functions and those of the third is expressed, he asserts, in the mythical conflict between the Aesir, the dominant group of gods, to which Othinn, Tyr, and Thor belong, and the Vanir, to which Freyr, Njordr, and Freyja belong”

Korea
"Korean folk tales emphasize community values rather than individual values, reinforcing, in the process of reinventing oral tradition, the contemporary ideology of the dominant group, the male elite."

Western folklores
"Perhaps not so clearly, folk has carried with it a political and economic meaning, for in most of our employments of the term, an underclass (in analogy to a peasantry) is evoked: one fixed in a marginal socioeconomic relationship to a more centrist and dominant group."

Hypotheses

 * 1) Dominant group came before mythology.

title: Dominant group/Mythology


text:
Volcanoes, list/Asama

Asama volcano is located at the border of the Izu-Marianas and NE Japan volcanic arcs. The modern cone of Maekake-yama forms the summit of the volcano and is facing east of the horseshoe-shaped remnant of an older andesitic volcano, Kurofu-yama, which was destroyed by a late-Pleistocene landslide about 20,000 years before present (BP). Growth of a dacitic shield volcano was accompanied by pumiceous pyroclastic flows, the largest of which occurred about 14,000-11,000 years BP, and by growth of the Ko-Asama-yama lava dome on the east flank. Maekake-yama, capped by the Kama-yama pyroclastic cone that forms the present summit of the volcano, is probably only a few thousand years old and has an historical record dating back at least to the 11th century AD. Maekake-yama has had several major plinian eruptions, the last two of which occurred in 1108 (Asama's largest Holocene eruption) and 1783 AD.

1783 Volcanic Eruption
The Asama, Japan Volcanic eruption in 1783 started on 9th May 1783. The eruption produced andesitic pumice falls, pyroclastic flows, lava flows, and built a cone. The climactic eruption began on the night of 4th August and lasted for 15 hours, when there were pumice fall and pyroclastic flows. The eruption killed 1,400 people due to all the destruction.

Other Eruptions
Asama Volcano eruptions:2015,2009, 2008, 2004, 2003, 1990, 1983, 1982, 1982, 1973, 1965, 1961, 1958-59, 1953-55, 1952, 1952, 1950-51, 1949, 1947, 1946, 1944-45, 1938-42, 1935-37, 1934, 1934, 1933, 1931-32, 1930, 1929, 1929, 1927-28, 1924, 1922, 1920-21, 1919, 1918(?), 1917, 1916, 1915, 1914, 1909-14, 1908, 1908, 1907, 1907, 1906, 1905(?), 1904, 1903, 1902, 1902, 1900-01, 1899, 1899, 1894, 1889, 1879, 1878(?), 1875, 1869, 1815, 1803, 1803, 1783, 1779(?), 1777, 1776, 1769, 1762, 1755, 1754, 1733, 1732, 1731, 1729, 1729, 1728, 1723, 1723, 1722, 1721, 1720, 1719, 1718, 1717, 1711, 1710, 1708-09, 1706, 1704, 1703, 1669, 1661, 1661, 1660, 1659, 1658, 1657, 1656, 1655, 1653, 1652, 1651, 1650(?), 1649, 1648, 1648, 1647, 1645, 1644, 1609, 1605, 1604, 1600, 1598, 1597, 1596, 1596, 1595(?), 1591, 1590, 1532, 1528, 1527, 1518, 1427(?), 1281, 1108, 887, 685

Volcano Facts
Asama volcano is the most active volcano of Honshu and one of the volcanoes with the longest recorded history of documented eruptions. It is located 130 km from Tokyo in central Honshu, overlooking the resort town of Karuizawa.Asama's activity is typically explosive, including frequent strombolian to vulcanian activity. It has had several major eruptions, including 2 plinian eruptions in 1108 and 1783 AD. Plinian eruptions are known by columns of gas and volcanic ash extending high into the stratosphere, a high layer of the atmosphere. The key characteristics are ejection of large amount of pumice and very powerful continuous gas blast eruptions. It's almost like a fountain of gas spraying into the stratosphere.

Asama Japan Volcano
This volcano eruption was indeed one of the strongest.It caused so much destruction many shops,store,and hot springs nearby were quickly put to cancellation. The damage took months to repair. This is a volcano eruption many of the japanese will remember many ashes drifted as far as Tokyo, about 140 km (90 miles) to the southeast.This eruption is known for a huge eruption in 1783 that caused widespread damage and killed about 1,500 people. No one lived from the blast that were 2.5 miles away from the eruption.

title: Volcanoes, list/Asama