Questions tagged [steady-state]
The steady-state tag has no usage guidance.
50 questions
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Physical Significance of power density of a point source of heat
What does the power density of a point source of heat signify?
I'll illustrate this with the help of an example
Consider a sphere of radius R and thermal conductivity k with a point source kept at ...
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How to Numerically Solve the Steady State of a Lindblad Equation with Parity Symmetry?
I am trying to reproduce some figures from this paper. like below:
The effective Hamiltonian of the system is
\begin{align}
H_{\text{eff}} = \frac{3g_x^2}{\omega} |e\rangle \langle e| + \frac{2g_x^...
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Steady-state wave equation
I know that for the heat equation $u_t=\nabla^2u$, the steady-state condition $u_t=0$ suggests we need to solve $\nabla^2u=0$ (i.e. Laplace's equation), which yields the equilibrium temperature ...
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Helmholtz decomposition of flow at non-equilibrium steady state
I'm trying to work through Karl Friston's mathematical derivation of the Free Energy Principle from Langevin Dynamics (see this paper). I'm confused about the part at the end of page 8 where he uses ...
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Quantum systems with steady states: does a system always approach the steady state as it evolves?
Say we have a quantum system whose dynamics results in there being a steady state. For example, it may be described by a Linblad master equation with several opposing dissipators. It is obvious that ...
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Numerically determining steady state in oscillating systems
As the title says, I'm trying to determine numerically when an n-DOF oscillating system (linear or nonlinear) subjected to forced base oscillation reaches the steady state solution.
Is there an energy ...
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Rigorously showing that steady state will be reached in simple DC circuits [closed]
Consider a simple DC circuit in which we have a source of emf connected to some resistance $R$.
Now all the books I have consulted give me heuristic arguments as to why a steady state will soon be ...
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Is thermodynamic steady state unique?
As an introduction to my question imagine a homogeneous 3D heat conducting body (under constant pressure) subject to Fourier's law. In steady state it satisfies
$$\nabla (\kappa \nabla T) = 0 \tag{1}\...
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Why are the Navier-Stokes equations inconsistent in this case?
Consider the case of a one-dimensional incompressible, non-viscous fluid flowing down a vertical pipe under the influence of gravity. Since we assume the flow is constant along the cross section of ...
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Do the Euler equations always converge to a steady solution if the boundary conditions are steady?
I'm considering the compressible euler equations without any heat addition, body forces, energy addition, etc. In other words, i'm using the following equations with the assumption of an ideal gas.
$$
...
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Is there a "4th law of Energetics"? How is energy conserved in a stationary flow through a pair of semi-permeable membranes?
I asked this question but got no replies there.
The below longish quote is from Rosenberg's Some Aspects on Brønsted's Energetic Theory. It concerns two chemical species, $A$ and $B$, in a stationary ...
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Freezing lake at a depth [duplicate]
The above image depicts the freezing of lake at depth y, on which I have this doubt...
I understand that at t=0, lake starts to freeze from top layer due to anomalous density variations of water. ...
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Is heat transfer, for a fixed time step, constant in transient problems?
So to further explain question in the title, this is my thinking process behind it. I recently been doing some steady state heat transfer problems, most of them I solved with the same algorithm. I was ...
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Which is uniform at steady state: flux or flow rate?
Background
My initial focus was on heat transport, but I tried to gain insight by working with the analogous mass transport equations and I realized my confusion isn't necessary specific to heat ...
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Is the gradient of temperature zero in case of steady state and no source of heat?
$$ k \frac{dT^2}{d^2 x} +heat generation =\rho c \frac{dT} {dt} $$
In steady state and in the absence of heat source, the equation becomes:
$$ k \frac{dT^2}{d^2 x} =\ 0 $$
If the laplacian of ...
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How does one get this steady-state solution?
I am studying the concept of a "gain medium" inside a laser cavity. The active atoms are taken to have the two levels $a$ and $b$, separated by energy $\hbar \omega$ and represented by a ...
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Calculate steady state temperature of an object heated by electromagnetic radiation
I would like to calculate the steady state temperature of a small cube of any material heated by electromagnetic radiation.
Suppose the cube floats in air and doesn't touch anything. The air is at 20 °...
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Is the steady-state velocity same as wind speed?
'The Blackbird problem' has been doing the rounds on the internet ever since Derek Muller uploaded a video of the Blackbird (a propeller-attached car that can travel faster than wind downwind) in the ...
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Fokker-Planck equation with time-dependent potential
Consider a Fokker-Planck (FP) equation where the advection term is a function of time, i.e.
\begin{align}
\frac{\partial P ( x , t )}{\partial t}
=
-\nabla \cdot \left[ -\mu \, P \, \nabla U (x,t) ...
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Conceptual question on heat transfer at steady state after a heated body is immersed in a fluid medium at low temperature
Recently during a discussion with a colleague we got into an argument. The discussion involved imagining a heated solid body at some temperature $T$ which is immersed in a large fluid medium ...
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About the steady state in Stokes flows
Note: I have read similar questions, but since it is not totally what I want, and they are old, I prefered to write a new one.
So, if one aims to work with Navier-Stokes at microscales, the equation ...
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Steady current Vs DC and AC
Steady current is the continuous and constant flow of free electrons in a circuit due to constant potential difference. My question is how steady current differs from DC and AC?
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Energy balance paradox
Consider a closed system consisting of a room surrounded by walls at temperature $T$ (infinitely big, so $T$ remains fixed). In this room, we place a power source with a wire of a particular material, ...
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Does density vary with time in a steady flow?
Steady flow is defined as the type of flow where density, pressure and velocity don't change with time, as far as my understanding goes. However, in the video below, they say that the density in a ...
user238352
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The Zero Energy Hypothesis and its consequences for particle creation and dualist interactionism
Most attacks on the possibility of dualist interaction cite the conservation of energy as a definitive objection. I have attempted to investigate the validity of this objection, and have found a ...
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What boundary conditions does a steady state initial temperature profile that evolves according to the heat flow equation obey?
A cylindrical rod of length $L$ is insulated over its curved surface. The end of the rod at $x = 0$ is in contact with a heat bath at temperature $\Theta_0$ and the end of the rod at $x = L$ is in ...
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Force exerted by a motor, velocity, and friction
Some motor make an object move on a surface very slowly. One can write at steady state : $F_{motor}-F_{friction}=0$. The friction is supposed to come from the surface so : $F_{motor}-\mu_s m g=0$ with ...
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Reynolds decomposition of non-linear dynamics
Can we apply the Reynolds decomposition,
$$u(x,t)=U(x)+u'(x,t),$$
to any strongly non-linear dynamics problem, where the final state is dependent on the initial condition like Lorenz's equation or ...
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Heat Equation: Newton's Law of Cooling and Steady-State Equation [closed]
So I was given this boundary value problem: A thin rod insulated along the length of $10$ cm with ends kept one at $50$ C and the other in contact with a fluid bath at $150$ C. The initial ...
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Steady state solution to density matrix
A density matrix follows the dynamics
$$
\dot{\rho} = \mathcal{L}\rho,
$$
where $\mathcal{L}$ is the Liouvillian super-operator. If put in Lindblad form, it can be written as
$$
\mathcal{L}\rho = -...
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Steady state conditions of a heat-generating annulus
Background: University heat transfer course, TA did a problem on the board involving a uniform heat-generating annular solid, cooled on the inside and outside by a coolant flow. The boundary ...
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What is a simple, effective, and physically consistent explanation of Bernoulli's principle (in the context of airfoil lift)? [duplicate]
I am not here to continue any debate about what really allows airplanes to fly. Rather, what I am looking for is an informed, thoughtful, illuminating and self-contained explanation of Bernoulli's ...
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Steady-state current and equation of continuity
I am learning EM and a bit confused when it comes to steady-state current and the equation of continuity.
Equation of continuity:
$$\nabla \cdot\textbf{J}=-\frac{\partial \rho}{\partial t}\rightarrow\...
user147507
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Reynolds transport theorem and steady flow
Consider the Reynolds Transport Theorem in the following form: $$ \frac{d}{dt}\int_V{\rho}\boldsymbol{v} \ dV = \int_V{\frac{\partial(\rho\boldsymbol{v})}{\partial t}} \ dV + \int_S{(\rho\boldsymbol{v}...
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Jim's Simple Physics Issue #i: The Big Bang Theory and Inflation [closed]
this is Jim again with another of my Simple Physics installments. This time I want to cover the much misunderstood concepts of the Big Bang theory and cosmological inflation. Like many of my other ...
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Reversibility = non-causality. Can this be right?
I read yesterday the Norton Dome's paper, which shows that some Newtonian systems can be non-causal, based on specific solutions of Newton's laws. The author justifies the solutions in very nice, ...
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In heat conduction, what does it actually mean to be in the steady state?
I have read about the method of heat conduction and I have some questions related to this topic:
If I consider a metal bar and supply heat in one end, the heat will flow through the bar and if I ...
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1-D Fick's first law - partial derivative?
I've recently been reviewing some concepts, including diffusion. Fick's 1st law:
$$J = -D\frac{\partial C(x,t)}{\partial x}$$
as I understand it, applies to the steady state.
For 1-D diffusion and ...
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A cylindrical vessel open at the top
A cylindrical vessel open at the top is 20cm high and 10cm in diameter. Circular hole whose cross-sectional area 1 cm² is cut at the centre of the bottom of the vessel water flows from a tube above it ...
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General Definition of Steady State
According to many sources (including Wikipedia, Stephani&Kluge, D.J. Acheson) a steady state ist:
In systems theory, a system in a steady state has numerous properties that are unchanging in time....
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The steady state theory, can it now be falsified on particle physics grounds, in addition to CMB data?
The steady state theory is no longer taken seriously by most physicists and the Big Bang theory is supported by an enormous amount of evidence, especially the CMB data.
But from a quick scan through ...
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Steady-state solution of Fokker-Planck DE
I have this differential equation:
$$\frac{\partial f}{\partial t} = \frac{1}{\tau_s v^2} \frac{\partial}{\partial v}(v^3+v_c^3)f + S$$
It is a Fokker-Planck equation that describes collisional ...
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Flow between two infinite plates [closed]
I recently got set this problem and I was wondering if anyone would be able to give me some hints/intuition on how to solve it. Thanks.
An incompressible thermal conducting fluid is contained between ...
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Steady State Solution for Carrier Concentration of Intrinsic Silicon in an Electric Field
I'm trying to model carrier action in intrinsic silicon under an applied electric field in one dimension.
Taking $n$ and $p$ to be the concentrations of electrons and holes respectively, I got that
$...
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Why is it valid to assume that the liquid-vapour interface is always saturated during evaporation?
For steady state evaporation, I read from two textbooks which simply states that the partial pressure of vapour of interest (say water) at the liquid-vapour interface is equal to the saturation ...
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Steady-state adiabatic nozzle, unknown exit velocity & temperature [closed]
The question is 2.10 taken from: Introductory Chemical Engineering Thermodynamics, 2E by Elliot,Lira
Air at 30ºC and 2MPa flows ata steady state in a horizontal pipeline with a velocity of 25m/s. ...
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Interpretation of decay associated difference spetrum
We measured transient absorption spectra and we got
$\Delta A(\lambda,t)=A(\lambda,t)-A(\lambda,0)$. If we use DAS (decay associated spectra) for interpretation, we assume that our data have this ...
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Difference between steady state and equilibrium?
In semiconductor physics, what is the difference between steady state and equilibrium. How analysis of devices varies in these processes?
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What is decay associated spectra?
What is decay associated spectra?
Suppose we measure the fluorescence intensity over different wavelengths and over time, we get:
$$I(\lambda,t) = \sum_i^n \alpha_i(\lambda) \exp(\frac{-t}{\tau_i}).$...
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What happens if we give a single electron charge to a hollow metal sphere?
I found this related question: What happens to 5 electrons on a sphere?
But this question describes the case when there can only be 5 electrons on that sphere at all times. The answer linked to the ...
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