Brownian motion Definition and 84 Threads

I am studying lesson 41 (volume I) of the Feynman lectures on physics. You can find it at the following link https://www.feynmanlectures.caltech.edu/I_41.html#Ch41-S4 What I don't understand, first, is this consideration: "What is the rate of change of ##x^2## ? It is ##\frac{d...

Video on Brownian matter that got me thinking Brownian motion is a fundamental concept in physics, describing the random movement of particles suspended in a fluid. However, the apparent randomness of this motion is largely due to our limited understanding and computational power. As...

Hello, Why isn't the forces resultant on a "large" molecule (by small molecule: water for example) zero? The reason for this Brownian motion is the thermal agitation of the water molecule. If we talk about white and Gaussian noise in electronics (due to the thermal agitation of the electrons)...

A water molecule is as tiny as 0.3 Angstrom. I would expect that quantum effects play a role. I'm wondering if its Brownian motion in a fluid is determined only by classical thermodynamics or if its collisional processes must take into account also quantum scatterings or other effects like...

If we have charged particles having Brownian motion, would this motion be associated with (or produce) heat or electricity? Would it produce electromagnetic radiation (and if it would produce it, what type of radiation in the electromagnetic spectrum)? Could there be Brownian motion of charged...

It is said often that in 1905 Einstein “mathematically proved” the existence of atoms. More precisely, he worked out a mathematical atomic model to explain the random motion of granules in water (Brownian motion). According to that mathematical model, if the atoms were infinitely small and...

So the Langevin equation of Brownian motion is a stochastic differential equation defined as $$m {d \textbf{v} \over{dt} } = - \lambda \textbf{v} + \eta(t)$$ where the noise function eta has correlation function $$\langle \eta_i(t) \eta_j(t') \rangle=2 \lambda k_B T \delta_{ij} \delta(t -...

I know passive diffusion rates behave differently on the International Space Station relative to Earth (video of a contained flame experiment burning up there.) However, does the random walk of pollen particles etc. have slowed velocity in comparison to that on Earth? Has been bugging me for a...

I understand that based on what I have read online quantum computers are required to be close to absolute zero because it introduces less error. Is it because brownian motion due to thermal agitation of molecules reduces with temperature?

Greetings, I currently work my way through Langevin Dynamics which, in a certain limit, becomes Brownian Motion. I refer to this brief article on Wikipedia: https://en.wikipedia.org/wiki/Brownian_dynamics I understand the general LD equation given there. In order to obtain Brownian Dynamics...

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in fact the answer is given in the book (written by philippe Martin). we have $$ (\tau_1| A^{-1} | \tau_2) = 2D \ min(\tau_1 ,\tau_2) = 2D(\tau_1 \theta (\tau_2 -\tau_1)+\tau_2 \theta (\tau_1 -\tau_2))$$ So $$-1/2D \frac{d^2}{d\tau_1^2} (\tau_1| A^{-1} | \tau_2) = \delta( \tau_1 - \tau_2) $$...

For a standard one-dimensional Brownian motion W(t), calculate: $$E\bigg[\Big(\frac{1}{T}\int\limits_0^TW_t\, dt\Big)^2\bigg]$$I can't figure out how the middle term simplifies. $$ \mathsf E\left(\int_0^T W_t\mathrm dt\right)^2 = \mathsf E\left[T^2W_T^2\right] - 2T\mathsf E\left[W_T\int_0^T...

If you have enough information could you not determine with certainty the movements of pollen particles in water? In other words, if you were able to measure the movements the particles, then repeat the exact same experiment, with all things controlled, would the particles move in the same way...

Hi all, been a while since I studied physics but I saw something that I found strange, This device: https://researchfrontiers.uark.edu/good-vibrations/ from University of Arkansas A free floating graphene sheet extracting energy from brownian motion and converting that to electric current...

I am trying to understand how one can simulate the trajectory of a Brownian particle as a function of time. I am only able to do it with the assumption that I can simply generate random values of x and then take the cumulative sums of these values to get the trajectory of the Brownian particle...

Hello, Einstein evaluated the size of an atom by analysing a brownian motion, assuming the size of the molecules is a a factor. In order to demonstrate this concept, I want to put some powders with different sizes of grains on a vibrator and watch how a ball moves. What is the expected result...

This a really simple question: If I have, say, 2 ions close to one another, and measure their repulsion very precisely, is the force constant, or is it a series of little pushes caused by individual virtual photons? I know there are many misunderstandings about virtual particles, but I'm not...

For observation of Brownian motion, the mass and the size of the Brownian particle should be very small. Within what range the size and mass of the Brownian particle should lie?? Can a particle with small mass and bigger size and vice versa can undergo Brownian motion??

Homework Statement Consider the diffusion of a drop of ink in a water vase. The density of the ink is ## \rho (\vec{r}, t) ##, and the probability ##P(\vec{r}, t)## obeys the diffusion equation. What is the relationship between ##\rho (\vec{r}, t)## and ##P(\vec{r}, t)##? Homework...

Homework Statement I have a free Brownian particle and its coordinate is given as a function of time: And its first moment, or mean, is given as But what kind of probability density was used to calculate this first moment? Homework Equations I know that the first moment is calculated...

All, I'm looking for a reference to help guide one of my students- a motivated physics undergrad. I would like him to work through a derivation of the mean-squared displacement of a particle undergoing free Brownian motion (free diffusion) and then for a particle held in an optical trap. All...

Hello all! Can you please provide some guidance with this problem? 1. Homework Statement Calculate the air pressure at 3000m above sea level assuming that the molecular weight of air is 29 and the ambient temperature is constant against height. Homework Equations Stokes-Einstein equation. In...

Hi, Imagine we have few particles with different diameters in fluid flow. so, can we neglect brownian forces at certain particle diameters? Actually I'm looking for a criteria in which we can neglect the effect of brownian forces in fluid flow. Thanks :-)

Hi, I need urgent answers. Basically, I don't have background in Markov and I don't need to learn it now actually. But I have to solve the questions below somehow. If somebody can give detailed answers to the questions below (From beginning to the final solution with explanations), then I will...

I am graduate student in engineering. In course of my research I have encountered an integral of this form ##\int_{t'}^{t} e ^{-b t_1} dt_1 \int_{t'}^{t_1 } e ^{b t_2} dt_2 \int_{t'}^{t_2 } e ^{-b t_3} dt_3 \int_{t'}^{t_3} e ^{b t_4} dt_4 ... \int_{t'}^{t_{n-1}} e ^{b t_n} dt_n ## I am trying...

I'm trying to understand the derivation of the expression for the random Brownian force on a particle in a medium with coefficient of viscosity η. It turns out it is gaussian over some timescale, with a standard deviation that depends on the temperature and the viscosity. I'd like to read a...

I was reading about ferrofluid and I was wondering how you would go about calculating the maximum size of a particle that could be suspended by Brownian motion in a fluid? Can a denser fluid suspend larger particles?

I am trying to derive the Probability distribution of Geometric Brownian motion, and I don't know how to find the variance. start with geometric brownian motion dX=\mu X dt + \sigma X dB I use ito's lemma working towards the solution, and I get this. \ln X = (\mu - \frac{\sigma...

Hi. I have a doubt on the derivation of the correlation function for the velocity and position in Brownian motion from the Langevin equation. I have that for a brownian particle: ##\displaystyle v(t)=v_0e^{-\frac{\gamma}{m}t}+\frac{1}{m}\int_0^{t}dse^{-\frac{\gamma}{m}(t-s)}\xi(s)## (1)...

Hi, I am trying to answer the following question: Consider a geometric Brownian motion S(t) with S(0) = S_0 and parameters μ and σ^2. Write down an approximation of S(t) in terms of a product of random variables. By taking the limit of the expectation of these compute the expectation of S(t)...

not sure if this is the right section to post this question, but i was wondering in what class i would learn about brownian motion. I took undergraduate thermodynamics and i feel that it could be mathematically described with the material already covered in my thermo class, but is there a class...

Homework Statement In an experiment to demonstrate Brownian motion in a gas, a brightly illuminated cell containing smoke is viewed under a microscope. The observer sees a large number of bright specks undergoing random motion. Which one of the following statements about this experiment...

Hello EVERYBODY! :) I have a question: Does the frequency of virtual particles (apparition/disappearance) match with nucleus random path - known as Quantum Browniαn Motion? Thank you in advance! ;)

1. Problem is in the Attachment This link will help your figure these question...

I hope you can bear with me as I warm up to my question regarding Brownian motion. I am currently studying physics on my own and am watching a series of lectures on Quantum Theory. Obviously I am just some guy with an interest in physics and I have no clue. Apparently, Brownian motion is the...

Hi! I need some help at the following exercise... Let $$B$$ be a typical brownian motion with $$μ>0$$ and $$x$$ ε $$R$$. $$ X_{t}:=x+B_{t}+μt$$, for each $$t>=0$$, a brownian motion with velocity $$μ$$ that starts at $$x$$. For $$r$$ ε $$R$$, $$T_{r}$$:=inf{$$s>=0:X_{s}=r$$} and...

Apparently : What significance does brownian motion has to do with coal explosion?[Brownian motion or pedesis is the presumably random moving of particles suspended in a fluid (a liquid or a gas) resulting from their bombardment by the fast-moving atoms or molecules in the gas or liquid.] Now...

Homework Statement Is the process \{X(t)\}_{t\geq 0}, where X(t)=\rho B_1(t)+\sqrt{1-\rho^2}B_2(t) Standard Brownian Motion? Where \rho\in(0,1), \ B_1(t) and B_2(t) are independent standard brownian motionsHomework Equations The Attempt at a Solution Obviously X(0)=0. Now let 0\leq...

I computed the distribution of B_s given B_t, where 0\leq s <t and \left\{B_t\right\}_{t\geq 0} is a standard brownian motion. It's normal obviously.. My question is, how do I phrase what I've done exactly? Is it that I computed the distribution of B_s over \sigma(B_t)?

Good day! I am reading the paper of Marc Yor ([FONT=arial]www.jstor.org/stable/1427477). equation (1.a) seems unfamiliar to me since the $ds$ comes first before the exponential part; $$ \int_0^t ds \exp(aB_s + bs). $$ Can you please help me clarify if there is a difference with the above...

Suppose that \sigma(t,T) is a deterministic process, where t varies and T is a constant. We also have that t \in [0,T]. Also W(t) is a Wiener process. My First Question What is \displaystyle \ \ d\int_0^t \sigma(u,T)dW(u)? My lecture slides assert that it's equal to \sigma(t,T)dW(t) but I'm...

We all know that \int_0^t dB(s) = B(t), where B(t) is a standard Brownian Motion. However, is this identity true? \int_{t_1}^{t_2} dB(s) = B(t_2) - B(t_1)

Hi all, When random walk takes the steps at random times, and in that case the position X_t is defined as the continuum of times t≥0, isn't this concept/phenomenon/rule is Brownian motion (Weiner process)? At http://en.wikipedia.org/wiki/Wiener_process in section "Characterizations of the...

I read somewhere that the "path of history" measured in some way can be modeled as Brownian motion with a mean collision time. There's been several very *specific* models such as: http://onlinelibrary.wiley.com/doi/10.1002/asm.3150030303/abstract However, what I'd like to know is that...

Suppose I have a large particle of mass M that is randomly emitting small particles. The magnitude of the momenta of the small particles is \delta p (and it is equal for all of them. Each particle is launched in a random direction (in 3 spatial dimensions--although we can work with 1 dimension...

Hello, how do we apply the idea of the Lagrangian to a Brownian motion? I guess what I mean is what is the Lagrangian functional form for a Brownian motion? Thanks

Hi! Probably I am just confused, but why for the exact solution of the geometric brownian motion dX_t = \mu X_t dt+\sigma X_t dW_t we have to apply Ito's lemma and manipulate the expression obtained with dlogX_t? Couldn't we directly use the espression dX_t / X_t = dlogX_t in the equation dX_t /...

Can someone please explain how the standard deviation is relevant when we are talking Brownian motion? And why is statistics important when we want to understand the movement of a brownian particle?

I need to show that (Wt)2 is a brownian motion So let Vt = (Wt)2 I need to first show that Vt+s - Vs ~ N(0,t) Vt+s - Vs = (Wt+s)2 - (Ws)2 = (Wt+s + Ws)(Wt+s - Ws) (Wt+s - Ws) ~ N(0,t) But is (Wt+s + Ws) ~ N(0,t)? If it is what happens when I multiply two RV's that are normally...