# 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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### Why is Wiener process a homogenous but not a stationary stochastic process?

I found the claim that wiener process is an example of a stochastic process which is homogeneous but not stationary in the book 'The Theory of Open Quantum Systems' by Breuer and Petruccione. (Section ...
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### Brownian motion and the heat equation

Einstein showed that the Brownian motion provides a solution to the heat equation. As written here, the relation between the brownian motion and the heat equation can be shown by the taylor series. ...
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### Diffusion of a particle between two immiscible liquids

I am trying to find a model, or construct my own to describe the diffusion of a particle between layers of immiscible fluids with different densities. The particle size is much larger than the sizes ...
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### Diffusion of Ink in Water

I am investigating the diffusion of ink in water. A drop of blue ink is dropped to the center of a round plate of radius $R$. Say the drop of ink has an initial radius of $r=r_0$ (the very edge of the ...
39 views

### What is meant with overdamped motion?

I'm learning about Brownian motion. I use the approximation of overdamped motion. I read that the average acceleration is $0$ then, but I don't really understand the concept. So, what does overdamped ...
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### Determining probability density function in Brownian motion simulation

Theoretically, the probability density function of brownian particle would be a function satisfy the diffusion equation in the form of: \begin{equation} \rho=\frac{N}{\sqrt{4\pi Dt}}e^{\frac{x^2}{4Dt}}...
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### Assumption of equipartion theorem in Langevin equation

To show Einstein's diffusion relation, one can develop the mean square displacement from the Langevin equation as shown in https://en.wikipedia.org/wiki/Equipartition_theorem#Brownian_motion In this ...
198 views

### Is the Feynman's path integral a density?

The Feynman-Kac path integral formula is used to solve parabolic equations related to stochastic processes. Considering the probabilistic expression, the solution is indeed not a density. However, ...
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### Unbounded time derivative of the brownian motion and Newtonian dynamical models

The second order dynamics model $dx_s = v_s ds$, $d v_s = dw_s$ where $w_s$ is s standard Brownian motion is an example of Langevin dynamics. Note that the Brownian motion in this case models a white ...
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### Brownian dynamics simulations in confined geometries [closed]

I am currently trying to implement a 2D Brownian dynamics simulation in confined geometries (corrugated channels, of the form $A\cos(2 \pi x) \ + B\$ in this case). The concept is to compute the ...
84 views

### How long does it take for oil to coalesce in water?

I was studying the process of coalescence in emulsions. We considered $N$ bubbles of liquid 1 floating in liquid 2. The result we derived, is that if there are some dissipative forces (diffusion) the ...
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### Question about the autocorrelation function of the fluctuating force in the Langevin model for Brownian motion

According to the Langevin model, we have, for the motion of Brownian particles, $$\frac{dv}{dt} = -M\gamma v + \zeta(t)$$ with $\zeta(t)$ the random force acting on the particle due to fluctuations. ...
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### Statistics of 1D discrete random walks

I have already asked this question in Math.SE. Let $P(n)$ be a probability distribution on the integers. Suppose a random walker starts off at the origin and, at every positive integer time, takes a ...
5k views

### How does Brownian motion prove the existence of atoms?

I have heard many people say that the existence of atoms is proven by Brownian motion. Now, I understand how an atomic theory would suggest the existence of Brownian motion. However, who is to say ...
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### What is the decoherence rate and the thermal de Broglie wavelength in quantum Brownian motion?

I know that when the thermal de Broglie wavelength is on the order of the interparticle distance, the gas must be treated as a Fermi gas or a Bose gas, depending on the nature of the gas particles. I ...
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### Why the distribution of Fluctuationg force in brownian motion has gaussian distribution?

I am reading the Zwanzig's book and I have a confusion about the average of the fluctuating force and its distribution. As it says $F(t)$ is a random variable that means it has a probability ...
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### How to improve this simple Brownian motion simulation by adding viscosity?

I've written a 0th order Brownian motion simulator to envision how a particle of smoke might appear to move under a microscope. There will be missing $\sqrt{2}$'s and $\frac{\pi}{2}$'s since I haven'...