# Questions tagged [brownian-motion]

Brownian motion is a stochastic process, continuous in space and time, used in several domains in physics. It is the motion followed by a point which velocity is a white Gaussian noise. This tag sould be used for questions concerning the properties of Brownian motion, white Gaussian noise and physical models using these concepts, like Langevin equations. It should not be used for questions about discrete random walks.

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### For diffusion with a drift, what if the drift velocity is not a constant but varies with time?

Recently, I read some materials about diffusion with drift, and found that the mean squared displacement (MSD) of this process will be: $$MSD(t)=4Dt+v^2 t^2$$ Question: What if the drift velocity is ...
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1 vote
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### Finding equilibrium solution from Fokker-Planck equation for planer Brownian rotator

In Andrew Zwanzig's Nonequilibrium Statistical Mechanics, the author has given the expression of the equilibrium density distribution function for a planer Brownian rotator. Given the equations of ...
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### Pressure at a point around the corner in a conical fask [duplicate]

I have gone through this two very informative links in understanding pressure. Weight of fluid in a conical container act entirely on the base? Pressure is isotropic But in a long conical flask which ...
1 vote
44 views

### What is the correlation between Brownian noise's low frequency components and the actual movement of particles?

I do have some crude training in mathematics, but I'm not a physicist or engineer. So I'd appreciate a simple not too technical explanation. I conceptually understand how hitting a piece of wood will ...
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### Does Equipartition hold in overdamped dynamics?

We start with the Langevin equation $$m\frac{\mathrm{d}^{2}x}{\mathrm{d}t^{2}} = -\Gamma \frac{\mathrm{d}x}{\mathrm{d}t} +\sqrt{2\Gamma k_{B}T} \eta(t).$$ Now, we know that at $t \gg m/\Gamma$, the ...
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### Diffusion from a rod with constant concentration

Suppose I have an infinite rod that is suddenly brought into a medium where some substance starts to diffuse radially outwards from the rod. During this, the concentration in the rod is kept constant....
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1 vote
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### Mean squared displacement of a free Brownian particle moving in harmonic potential

For a free Brownian particle moving under harmonic potential ($\frac{1}{2}m\omega^2x^2$), the equation of motion can be written as, $$m\ddot{x}=-m\omega^2 x-m\gamma\dot{x}+R(t)\;,$$ where, $\gamma$ is ...
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### Discrete simulation of a Levy flight

I am trying to construct a discrete simulation of Levy flight in 1D and am wondering what is the best way to do so. For example, for pure diffusive random walk, one may assign probability of $1/2$ to ...
55 views

### Brownian noise variance

I have a question on a Brownian noise mean square which I get from the exercise (10-4) reference [p493, Athanasios Papoulis and Unni Krishna Pillai, “Probability, Random Variables and Stochastic ...
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### How to go from probability distribution to transitions probability distribution?

For the past few days I have been studying Advanced statistical mechanics. I am studying a Wiener process in general. Such a process is a non-stationaty time-independent Gaussian process. The ...
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### Is it possible to have an anisotropic temperature to a Brownian motion?

Resolving the Langevin equation. Tenperature is a scalar, is there a way to make it into vector?
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### How to explain Bernoulli's principle with Brownian motion?

Air pressure is generated by Brownian motion pushing against solid objects. The integration of all molecule collisions with the boundary is then the air pressure pushing against that object. But can ...
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