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4
votes
3answers
310 views

Guessing what a simple partial differential equation is describing physically

Is there an easy way to look at a partial different equation and get a sense of what kind of phenomena it is physically describing? I have an equation that looks like this: ...
1
vote
3answers
146 views

Schrödinger equation derivation and Diffusion equation

I am aware of the debate on whether Schrödinger equation was derived or motivated. However, I have not seen this one that I describe below. Wonder if it could be relevant. If not historically but for ...
137
votes
3answers
40k views

Surviving under water in air bubble

An incredible news story today is about a man who survived for two days at the bottom of the sea (~30 m deep) in a capsized boat, in an air bubble that formed in a corner of the boat. He was ...
36
votes
7answers
14k views

How can two seas not mix?

How can two seas not mix? I think this is commonly known and the explanation everyone gives is "because they have different densities". What I get is that they eventually will mix, but this process ...
1
vote
0answers
32 views

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 ...
1
vote
1answer
901 views

Characteristic length for the diffusion equation (temperature)

The background: I'm doing some simulation work involving the diffusion equation in 1D. Specifically I have some temperature profile, constant thermal conductivity and fixed temperature at each end of ...
6
votes
4answers
482 views

Do particle velocities in liquid follow the Maxwell-Boltzmann velocity distribution?

The Maxwell-Boltzmann velocity distribution arises from non-reactive elastic collisions of particles and is usually discussed in the context of the kinetic theory (for gases). There are various ...
2
votes
3answers
492 views

Finite difference formulation of the heat equation with thermal conductivity in 1D

This may seem trivial, but I'm having some trouble deriving the finite difference form of the heat equation with a thermal conductivity function $a(x)$ depending on $x$: $$\frac{\partial u(x, ...
1
vote
1answer
92 views

Gillespie's stochastic framework valid for particles in aqueous solution?

Gillespie proposed a stochastic framework for simulating chemical reactions which is predicated on non-reactive elastic collisions serving to 'uniformize' particle position so that the assumption of ...
1
vote
1answer
180 views

How does air escape from a pneumatic tire?

Obviously, it is caused by the difference in pressure between the inside of the tire and its surrounding environment; but how specifically is the air escaping?
0
votes
0answers
51 views

Temperature dependence for specific thermal diffusivity in the diffusion formula

I recently found this answer about the diffusion equation (nice one actually), but have one doubt about the temperature dependence of this formula. If the "packet" of energy (terminology suggested ...