# 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.

141 questions
Filter by
Sorted by
Tagged with
0answers
24 views

### Work done by the drift term of Ornstein–Uhlenbeck process

Consider a particle obeying the Ornstein–Uhlenbeck process: $$dx_{t}=\theta (\mu -x_{t})\,dt+\sigma \,dW_{t},$$ where $x_t$ is the position of the particle at time $t$, $W_t$ denotes the Wiener ...
1answer
26 views

### Interaction energy of two brownian spherical particle in liquid [closed]

Let us consider two hard sphere in finite volume. Their motion is Brownian. What can we say about interaction energy? Is it less then $kT$? I know that we can describe this system by Langevin ...
0answers
30 views

1answer
147 views

### 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 ...
0answers
52 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 ...
1answer
55 views

### 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. ...
1answer
67 views

### 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 ...
7answers
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 ...
0answers
33 views

### 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 ...
0answers
35 views

### 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 ...
1answer
143 views

### 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'...
1answer
225 views

### Derivation of diffusion equation from Fokker-Planck equation

I need your help, could you please explain me the sentence "The diffusion equation is the Fokker-Planck equation for the Brownian motion". I have tried to use some assumption and transform a ...
2answers
298 views

### How can I include variable particle number in a Brownian dynamics simulation?

I programmed a Brownian dynamics simulation in two dimensions. (Coarse-grained proteins on surfaces with interaction potentials i.e. patchy particles.) Now I want to allow particles to leave or enter ...
1answer
104 views

### Smoluchowski theory of Brownian Motion

I am studing Brownian motion, in particular I am reading the book "Brownian Motion, Fluctuation, Dynamics and Application" by Mazo. Now I am dealing with Smoluchowski theory, but I am having some ...
1answer
88 views

0answers
105 views

### Quantum Brownian Motion - Calculation of moments [closed]

The master equation of quantum brownian motion is derived as \begin{equation}\frac{d}{dt} \hat{\rho_s}(t) = -i[\hat{H_S} + \frac{1}{2}M\tilde{\Omega}^2 \hat{X}^2 , \hat{\rho_s}(t)] -i\gamma[\hat{X}, \{...