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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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 ...
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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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Method of inserting random numbers in the numerical calculation of mean-squared displacement for brownian particle
I am trying to plot Mean-Squared-Displacement for a passive Brownian particle. For that I'm using the discretized over-damped version of the Langevin equation as: $$x(i+1)=x(i)+\sqrt{\frac{2.k_BT.\...
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Viscous stress, and closed dynamic equations for density and velocity fields of an Ornstein-Uhlenbeck process?
Context
I am trying to write simple derivation of hydrodynamic definition of viscous stress $\partial^{2}_{x}v$ based on OU-process which is
\begin{align}
\dot{x} &= v \\
\dot{v} &= -\gamma v +...
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Self-similarity of the diffusion equation
I am going through this book Simulation of Complex Systems. In the chapter on Brownian Dynamics, we considered a "free diffusion" given by the Stochastic differential equation: $$\dot{x}(t)=...
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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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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 ...
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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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Onsager relation in the Casimir Paper
My question is about the paper On Onsager's Principle of Microscopic Reversibility by Casimir (see page 346, second column).
The relations between forces and currents have the form
$$\dot x_1 = l_{11}...
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Asymptotic form of solution to biased random walk
(Cross post from math.stackexchange)
Consider a continuous time biased random walk on a 1D lattice. The random walker walks with rate $k_\mathrm{R}$ to the right and with rate $k_\mathrm{L}$ to the ...
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Energy exchanges between a Brownian fluid and particles
In the context of the dynamics of polymeric models, and specifically the dumbbell model, one of the forces acting on a dumbbell spring is said to result from "a time smoothed Brownian force" ...
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