What is Steady state: Definition and 175 Discussions
In systems theory, a system or a process is in a steady state if the variables (called state variables) which define the behavior of the system or the process are unchanging in time. In continuous time, this means that for those properties p of the system, the partial derivative with respect to time is zero and remains so:
∂
p
∂
t
=
0
for all present and future
t
.
{\displaystyle {\frac {\partial p}{\partial t}}=0\quad {\text{for all present and future }}t.}
In discrete time, it means that the first difference of each property is zero and remains so:
p
t
−
p
t
−
1
=
0
for all present and future
t
.
{\displaystyle p_{t}-p_{t-1}=0\quad {\text{for all present and future }}t.}
The concept of a steady state has relevance in many fields, in particular thermodynamics, economics, and engineering. If a system is in a steady state, then the recently observed behavior of the system will continue into the future. In stochastic systems, the probabilities that various states will be repeated will remain constant. See for example Linear difference equation#Conversion to homogeneous form for the derivation of the steady state.
In many systems, a steady state is not achieved until some time after the system is started or initiated. This initial situation is often identified as a transient state, start-up or warm-up period. For example, while the flow of fluid through a tube or electricity through a network could be in a steady state because there is a constant flow of fluid or electricity, a tank or capacitor being drained or filled with fluid is a system in transient state, because its volume of fluid changes with time.
Often, a steady state is approached asymptotically. An unstable system is one that diverges from the steady state. See for example Linear difference equation#Stability.
In chemistry, a steady state is a more general situation than dynamic equilibrium. While a dynamic equilibrium occurs when two or more reversible processes occur at the same rate, and such a system can be said to be in a steady state, a system that is in a steady state may not necessarily be in a state of dynamic equilibrium, because some of the processes involved are not reversible.
If this should be in the cosmological section, then i don't mind to see it moved, but since it appears to be an abandoned theory, I'm posting this in the classic physics section.
I was talking to a religious person, and he was claiming that the big bang theory was... wrong, that it had been...
Homework Statement
Question: 18. Show that every 2 x 2 stochastic matrix has at least one steady-state vector. Any such matrix can be written as
P = |1-a b |
| a 1-b |
where a and b are constants between 0 and 1. (There are two linearly independent steady-state...
Can someone tell me what Steady State (Operating) Torque is and how to calculate it?
I'm guessing that it is the troque at operating speed.
Any help would be appreciated.
Thanks,
Homework Statement
The one dimensional steady-state heat conduction equation in a medium with constant conductivity (k) with a constant volumetric heat generation in three different coordinate systems (fuel rods in a nuclear power plant) is given as:
\frac{d^2 T}{dx^2}=-\frac{\dot{q}}{k}...
Hi all!
I am asking about a question about Fourier transform.
I can only roughly remember things about Fourier transform.
I am told that Fourier transform gives the steady state solution, is it?
I can hardly relate these two concepts.
Can someone try to explain?
Many thanks.
air enters an adaibatic nozzle steadily at 300 kPa, 200 degree celcius and 30m/s and leaves at 100 kPa and 180 m/s.
find the exit temperature?
when m using energy balance equation: h1 + [ (v1)^2 / 2 ] = h2 + [(v2)^2 / 2 ]
i get the answer 184 degree celcius.
but when i use the other...
I have to solve a problem regarding "2D steady state heat conduction problem with an internal heat generation source". For boundary value, dirichlet is applied at 3 sides and neumann is at one side.
I can solve this problem when no internal heat source exists and only dirichlet is applied...
Recently the expansion of the Universe has been found to accelerate. When studying Hoyle, Gold and Bondi's Steady State Cosmology, it clearly predicts an acceleration like this. I realize that this theory has been 'put to bed', and abolished, and all the other colorful language people like to...
Homework Statement
In order to prodice a more balanced, sustainable long term mix of flower Skwhere the percentage of the offspring of red flowers are p pink and 1-p redSk= A SoSk= [r p w]Twhere A=[1-p* 1/4* 0p***** 1/2* 1/20***** 1/4* 1/2]determine the stady state eigenvectors(you do not have...
Homework Statement
Prove that for any initial state vector
S0=
[r0
p0
w0]
as long as you begin with legitamite proportions (so that r0+p0+w0=1), after a long run you get the same result as
Sk=
[1/4
1/2
1/4]
Homework Equations
Sk= b1(Lambda1)^k [X1] +...
Hi
I was reading BC Kuo's Automatic Control Systems where I came across a solved problem (page 369 of 7th edition) regarding velocity control. I have a problem understanding how the steady state error has been computed. The original problem and its solution as given in the book are quoted...
I went for a run and measured time and distance. I wanted to estimate how many calories I used.
Suppose a ran a distance x in an amount of t time.
if my mass is m, then my stead state average energy would be
E=\frac{1}{2}m\frac{\Delta{x}^2}{\Delta{t}^2}
But what is the rate at which...
[SOLVED] Steady state solution
I was wondering if I did this question correctly, solving for y(t) and putting t = infinity to get a steady state solution. Or is this wrong or is there an alternative way that is much quicker (as solving for y(t) would take a page of working, where the working...
Homework Statement
Obtain the temperature distribution T(x,y) of the triangular cross section, assuming constant thermal conductivity, k.
The triangle is a right-isosceles triangle with the right angle at (0,0). The triangle goes "up" to a, and to the right to a, then diagonally across...
Homework Statement
What is the steady state solution to the equation
4y''+4y'+17y=202cos3t (*) ?
2. The attempt at a solution
The steady state solution is, if I've got it right, only the particular solution. It's got to be on the form
Kcos3x+Msin3x.
I calculate the...
In the steady state heat conduction through a solid rod the theoretical
derivation tells that
heat in-heat out-heat accumulated =0.
What is a practical steady state heat conduction problem? what is
transient heat conduction
Considering the response of a single degree of freedom system to harmonic excitation with viscous damping , following conclusions can be drawn:
Now,
The response of a single degree of freedom system to harmonic excitation can be split into:
a) Steady Sate response (or vibration) which...
When a refrigerator has been turned on for some time, steady state refrigeration occurs. This is the normal refrigerator operative state. But what exactly happens?
These things are really hard to do research on, since Internet searches, regardless of search query detailing, result in a lot...
I have some first order differential equations. I have found the steady state response for each equation. However, now I need to estimate how long it will take to reach steady state.
Can anyone tell me the formula for that or get me started on how i go about doing this. I'm not finding...
Hello everyone, confused. the directions to this problem are the following:
Find the steay-steat vector, and assuming the chain starts at 1, find the probablity that it is in state 2, after 3 transitions.
well i got the problem and i got the S0 to S3, because it said after 3 transitions, is...
I have a problem that goes as followed: http://www.webassign.net/pse/p32-19.gif
Consider the circuit in Figure P32.17, taking = 6 V, L = 4.00 mH, and R = 6.00
(a) What is the inductive time constant of the circuit?
I found this to be .6667 ms
(b) Calculate the current in the circuit 250...
Can someone help me out with the following question?
Q. The position x(t) at time t of a mass attached to a spring hanging from a moving support satisifies the differential equation:
\frac{{d^2 x}}{{dt^2 }} + 2p\frac{{dx}}{{dt}} + \omega _0 ^2 x = 2\sin \left( t \right)
a) Find the...
In my data management class we are studying matricies, we have broken the whole unit up into sections and then in small groups we have to teach the rest of the class a section or the matrix unit. Well, our section is markov chains. I understand it myself but I don't know if I'll be able to...
I need to find the initial conditions such than an underdamped harmonic oscillator will immediately begin steady-state motion under the time dependent force F = m f cosωt.
For the underdamped case:
x(t) = ae^{-\gamma t}cos(\Omega t+\alpha)+\frac{f}{r}cos(\omega t-\theta)
and if it matter...
Can anyone explain the difference between a system at equilibrium and a system at steady-state water flow?
I know that equilibrium occurs at equal rates, no net change is produced. But I don't understand steady state system...Please explain it to me... Thanks
also the difference between...