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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 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 ...
354 views

### 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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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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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, ...
1 vote
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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 ...
436 views

### 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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### 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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