Crab Nebula

Japanese and Chinese astronomers recorded this violent event nearly 1,000 years ago in 1054.

The Crab Nebula derived its name from its appearance in a drawing made by Irish astronomer Lord Rosse in 1844, using a 36-inch telescope.
The colors in the image indicate the different elements that were expelled during the explosion. Blue in the filaments in the outer part of the nebula represents neutral oxygen, green is singly-ionized sulfur, and red indicates doubly-ionized oxygen.

The meaning of process gain [1st order model]

First-order model: (tao)*(dx/dt) + x = (Kp)*u

dx/dt = derivative of state variable, x
u = input
tao = time-constant of the system
Kp = process gain

The above equation is used to represent the process or system which you considering. It can describe the behaviour of the system, so by using the model you can predict what will happen to your process in case of un- or expected incident. The parameters such, tao and Kp are very important. For time constant (tao), it describes how fast of the process dynamic to reach its new steady state after perturbed by the input as i described in the article 'The meaning of time-constant'. Now in this article, i will describe the meaning of process gain (Kp).

Time constant (tao) describes how fast to reach the new steady-state value, while process gain (Kp) describes the value of the new steady-state that process output can be changed with respect to process input. The following example, the process model has same time-constant (tao = 1) with different process gain (Kp = 1, 1.5, 2). You can see from the output profile, time to reach new steady-state is very close for all cases but new steady values of the output are different in each case.

Before i will describe how to obtain the values of process gain based gradient concept, I will show you the solution of the 1st order equation in time domain. The solution is as

following: x(t) = (Kp)*u(t)*[1-exp(-t/tao)]. This example time constant and input change are set to be 1 then the equation will be reduced to x(tao) = 0.623*(Kp). Then if Kp = 1 and you change input value from 0 to 1, the process output (x) will be reach new steady at 0.623. Thus at time = 1 (at time-constant), process output will reach 62.3% of total change (new steady-state).

Process gain	New-steady	Output	Time	Time-constant estimate
1 1.5 2	1 1.5 2	0.6247 0.93701 1.2494	1.98 1.98 1.98	0.98 0.98 0.98

Estimate of time-constant from the output data is close to real time-constant of the process, the truncation error is occurred because of the software (MATLAB) precisiton. This example just used to illustrate the concept of process gain. If process gain is large then small change of input has large effect to the output.

Process gain of the process describes sensitivity of process output [or new steady-state] with respect to input change.

The meaning of time constant [1st order model]

First-order process with different time-constant.

Transfer function: G = K/(tao.s+1) [K = 1 in this case]
and unit step input = 1/s at time t = 1

For time domain, the solution of 1^st order process is as follow:
output(t) = K.input(t).[1-exp(-t/tao)]

If t = tao (at time-constant), then output(tao) = K.input(tao).[1-exp(-1)] = 0.623.K.input(tao). That means at time-constant output have been changed 62.3% of the total change which it is going to make [K.input(infinite)].

In this example, total change is equal to 1 [K = 1 and input step-size = 1] then time-constant is time at output is equal to 0.623.

Time-constant	Output	Time	Time-constant estimate
1 2 5	0.6247 0.62283 0.62318	1.98 2.95 5.88	0.98 1.95 4.88

Estimate of time-constant from the output data is close to real time-constant of the process, the truncation error is occurred because of the software (MATLAB). Then this example just used to illustrate the concept of time-constant. If time-constant is large then process dynamic will slow (over-damped).

Time-constant of the process describes how fast of process dynamic to reach new steady-state with respect to input change.

City of Dreams by Talking Heads

Here where you are standing
The dinosaurs did a dance
The indians told a story
Now it has come to pass

The Indians had a legend
The Spaniards lived for gold
The white man came and killed them
But they haven't really gone

We live in the city of dreams
We drive on the highway of fire
Should we awake
And find it gone
Remember this, our favorite town

From germany and Europe
And Southern U.S.A.
They made this little town here
That we live in to this day

The children of the white man
Saw Indians on TV
And heard about the legend
How their city was a dream

We live in the city of dreams
We drive on the highway of fire
Should we awake
And find it gone
Remember this, our favorite town

The Civil War is over
And World War One and Two
If we can live together
The dream it might come true

Underneath the concrete
The dream is still alive
A hundred million lifetimes
A world that never dies

We live in the city of dreams
We drive on the highway of fire
Should we awake
And find it gone
Remember this, our favorite town

Who Knew - PINK

You took my hand
You showed me how
You promised me you'd be around
Uh huh
That's right
I took your words
And I believed
In everything
You said to me
Yeah huh
That's right

If someone said three years from now
You'd be long gone
I'd stand up and punch them out
Cause they're all wrong
I know better
Cause you said forever
And ever
Who knew

Remember when we were such fools
And so convinced and just too cool
Oh no
No no
I wish I could touch you again
I wish I could still call you friend
I'd give anything

When someone said count your blessings now
For they're long gone
I guess I just didn't know how
I was all wrong
They knew better
Still you said forever
And ever
Who knew

Yeah yeah
I'll keep you locked in my head
Until we meet again
Until we
Until we meet again
And I won't forget you my friend
What happened

If someone said three years from now
You'd be long gone
I'd stand up and punch them out
Cause they're all wrong and
That last kiss
I'll cherish
Until we meet again
And time makes
It harder
I wish I could remember
But I keep
Your memory
You visit me in my sleep
My darling
Who knew
My darling
My darling
Who knew
My darling
I miss you
My darling
Who knew
Who knew

Smile by Lily Allen

when you first left me
I was wanting more
but you were fucking that girl next door
what did you do that for

when you first left me
I didnt know what to say
I'd never been on my own that way
just sat by myself all day

I was so lost back then
but with a little help from my friends
I found the light in the tunnel at the end

now you're calling me up on the phone
so you can have a little whine and a moan
and it's only because you're feeling alone

at first when I see you cry
it makes me smile
yeah it makes me smile
at worst I feel bad for a while
but then I just smile
I go ahead and smile

whenever you see me
you say that you want me back
and I tell you it dont mean jack
no it dont mean jack

I couldnt stop laughing
no I just couldnt help myself
see you messed up my mental health
i was quite unwell

I was so lost back then
but with a little help from my friends
I found the light in the tunnel at the end

now you're calling me up on the phone
so you can have a little whine and a moan
and it's only because you're feeling alone

at first when I see you cry
it makes me smile
yeah it makes me smile
at worst I feel bad for a while
but then I just smile
I go ahead and smile

lalala (x26)

at first when I see you cry
it makes me smile
yeah it makes me smile
at worst I feel bad for a while
but then I just smile
I go ahead and smile

lalala (x7)

at first when I see you cry
it makes me smile
yeah it makes me smile
at worst I feel bad for a while
but then I just smile
I go ahead and smile

MY PRINCESS

My lovely princess, her name is POCKIE. She is YORKSHIRE TERRIER. I miss her sooooo much, she is not with me now. Because i have work to do then i have to leave her with my friend. She is really cute, now she is one and half years old.

MISS YOU MY LOVELY PRINCESS.