Science topic

# Brownian Motion - Science topic

Explore the latest questions and answers in Brownian Motion, and find Brownian Motion experts.

Questions related to Brownian Motion

I am maintaining an N2a cell line and I can see black dots that for the most part seem non-moving (a few seem to exhibit Brownian motion) but I am not sure if it's bacterial contamination, cellular debris or possibly something from the serum. The pictures are after I have washed the cells. Thank you for the help.

As these images shown, black dots seem adherent on my cell ,can be slightly observed under 400× magnification.They cannot be removed by PBS washing or medium repalcement ,and antibiotics ,including penicillin, streptomycin, gentamycin, neomycin , ciproflaxin and purchased myoplasma removing reagents are useless to them. These dots only exist on the cells and could be observed moving under 400× sight ,I am not sure if it is brownian motion. Colleagues in the same lab using same batch of serum or medium never find this phenomenon but we cultured different cells .

I m sure it is not bacteria contamination ,for no colony found on LB plate after 48h of incubation at 37℃ with cultured medium added on. If there 's possible that it is mycoplasma , which is resistant to mycoplasma removing reagents.

Could anybody give me some advice? really appreciate.

Electrical circuits for different experiments e.g Brownian motion, Hystesis Law and etc

It is well known that the Brownian motion and the related Wiener process have many different applications in different fields.

Roughly speaking, the Wiener process can be thought of as a function of two variables W(x, t).

Note that for each fixed x point W(x, t) = f(t) is a continuous function, often called a trajectory.

Various properties of such trajectories are known, one of them is that the function f(t) is not a function of finite variation in the Jordan sense, but f(t) is known to be a function of finite variation in Wiener sense, for some number p>1.

In the literature that I have access to, the connection between finite variation in the Wiener sense and Brownian motion ends with this last result.

I wonder what role the number p plays. Does the number p have any interpretation in physics, economics, or any other field?

I will be grateful if someone can refer to the literature that describes such interpretations of the number p.

Given that non-spherical particles (e.g., rods) will exhibit optical anisotropy due to their continuous rotational Brownian motion, and even if the scattering signal is concurrently obtained and then combined from multiple detection angles (MADLS), how reliable are the size measurements obtained from DLS/MADLS for non-spherical particles?

I can see how MADLS size measurements can be reasonable if the non-spherical particles do not change their orientation with time. But since rotational Brownian motion in unavoidable, I am not sure how/if that can be factored in the measurement and/or data processing.

The particles are Nanoparticles. How from their light scattering we can calculate their size

Hello,

Is it possible to observe Brownian motion of particles with a light microscope at 40X? I am asking for reasons relating to mammalian cell culture.

Thank you.

Hello,

Wondering if there are any physicists that can explain (very simply as I am a chem eng) whether a charged particle would move faster or slower through water than an uncharged particle. Perhaps this is somewhat explained by brownian motion?

For example, if I have an ionic solution (e.g. salt) would the particles move faster than a neutral solution or similar molecular weight? Or more simply would Na+ move more quickly than Na. Does the charge (pos vs neg) matter?

If you know any pubs that explain this that would be great too as everything I find is more looking at charged particles moving in an electric feild.

Thank you.

In the Dynamic Light Scattering (DLS) method, the exponential decrease of the autocorrelation function means the Brownian motion of particles in the dispersant. If it does not decrease exponentially (if it follows polynomial, zigzag, or linear manner), then what does it indicate regarding the particle motion?

I have done a numerical simulation of a nanofluid in a microchannel heat sink using Al2O3-water nanofluid. In this simulation, I used a single-phase methodology since I have all the thermophysical properties of the nanofluids from experimental data.

Is it still possible to quantify the effect of Brownian motion and Thermophoresis on my microchannel system? If yes, what do I need to do?

Thank you for your help

I am doing an experiment with colloidal solution of nanoparticles and would like to measure the Brownian motion velocity of these particles. Can I do it experimentally?

In probability theory,

**fractional Brownian motion**(**fBm**), also called a**fractal Brownian motion**, is a generalization of Brownian motion. Unlike classical Brownian motion, the increments of fBm need not be independent. fBm is a continuous-time Gaussian process*BH*(*t*) on [0,*T*], that starts at zero, has expectation zero for all*t*in [0,*T*],Besides temperature, particle size, and fluid viscosity, what other factors affect Brownian motion in a suspension?

Let's say I have a suspension and wish to increase the Brownian movement of its particles, is there a way I can do so without having to increase its temperature? What other things can I do to the suspension to achieve this (e.g. could I change the surface charges of the particles? Could I sonicate the suspension? Could I run an electric current through the suspension? Could I run a magnetic field around the suspension?)

Thank you.

Raum und zeit, space and time, were united by Minkowski in 1908 to elucidate Einstein’s special relativity. Time flows. Can the idea of the fourth dimension be generalized to any system that includes three dimensional space and one dimensional flow? One dimensional flow can include molecular motion, photons, wind eddies, Brownian motion.

Dear colleagues.

For the fungi-air system, I have difficulty defining the range of values that the molecular diffusion coefficient $D$ can assume. For fungi with 20-30 microns, ie 20-30 x 10^(- 6) m, some texts suggest the range from D=0.0001 m^2/h to D=0.1 m^2/h, but these values seem very low to me. Please, if anyone has measures or texts to suggest, I appreciate it.

Regards,

Dr. Paulo Natti

I understand that the Hurst exponent of the Gaussian white noise is equivalent to 0 theoretically, because of the definition of fractional Brownian motions, fBms.

Why do some papers say that the exponent is -0.5, not 0?

Why did Galileo build his analysis of the strength of animal bone for an animal of increased weight from a scaling standpoint and not a dimensional standpoint? The scaling he used is induced by dimension? Did dimensional capacity raise issues that seemed best avoided? Did the principle of dimensional capacity raise issues irrelevant for the new science of strength of materials? The dimensional standpoint seems involved in metabolic scaling, Brownian motion, and dark energy (expanding space), the cosmic scale factor, among other modern questions. Hence the question, implied in the article:

Preprint Size, scaling, and invariant ratios

Has anyone come across bacterial contamination which is very slow growing? only growing to cover the flask over 2-3 weeks (of media not changed)? Also not changing the pH of the medium, nor turning cloudy or yellow. Cells are still growing not dying. At first i thought it was just cell debris until i removed medium into a flask without cells and watched over weeks as the dots went from just afew per field of view to totally covering the flask. The dots, upon staring at them, move with brownian motion. I see in my FBS straight from the aliquot (2 different aliquot dates too). I have decontaminated incubators water bath, changed tips in pipette gun, etc. If this is coming from the FBS it just keeps turning up. Will preciptates from FBS jiggle around like brownian motion?

Kindly answer this question so that I can understand better about ( relationship between Brownian motion and temperature gradient on enhancement thermal conductivity) and what is the meaning of ( temperature gradient) in nanofluid ?

Hello every body,

I have got a set of GPS data containing the hourly locations of 74 terrestrial animals during the study period. Currently, I am looking over disparate models of movement modelings like BBMM. I need to study the interaction and movement pattern of each individual animal.

In addition, I will use Python for the implementation of the model.

Which model do you recommend?

Hello,

Recently I performed lentiviral transduction on several cell lines. On day one with the lentivirus, I observed black aggregates moving (dancing, vibrating) around my cells. These are only in cells to which I added virus.

When I harvested my lentivirus in the supernatant of my packaging cell line, I spun the supernatant (3000RPM for 15 minutes) to remove cellular debris, filtered it with a 450nm sterile filter, and then froze it at -80C. These steps should have removed bacteria, correct? Moreover, the aggregates are resistant to the 1% Pen/Strep in my culture media. They do not turn the media turbid, and they never seem to reach log phase.

**Could I be seeing the virus itself?**

Can lentiviruses form visible aggregates?

Could these be abiotic aggregates exerting Brownian motion?

I have seen this phenomenon before and as of now, no one has given me a satisfactory answer regarding the identity of the dots.

Thank you.

There are reasons to think so, if one connects theory for a variety of phenomena.

First there was a novel explanation for metabolism scaling by a 3/4 power of mass (Kleiber’s Law). That explanation emerged beginning in 2008 based on an animal’s circulatory system scaling by a 4/3 exponent of circulatory system volume. Metabolism scales by an inverse exponent, by a 3/4 power to maintain animal body temperature. In effect the entropy of the circulatory system is 4/3 the entropy of tissue supplied by the circulatory system.

The same 4/3 scaling of entropy occurs in an intermediate step of Stefan’s Law (1879); the derivation was worked out by Boltzmann but the most accessible derivation is that of Planck in his text book on heat. Since Stefan’s Law applies to black body radiation and the universe can be considered in the large as a black body cavity, the involvement of Stefan’s Law is, at least, intriguing.

In 1859 and 1860, Rudolf Clausius gave a demonstration in connection with the kinetics of gas molecules that in effect says that lengths stretch by 4/3 in stationary three dimensional space compared to four dimensional space with motion. If Clausius’s derivation is modified to apply to photons instead of gas molecules, then 3 dim space itself would stretch by 4/3 relative to 4 dim space consisting of 3 dim space + light motion.

In 1926, Lewis Fry Richardson measured that wind eddies scale by 4/3, an observation similar to that of Clausius in 1859 and 1860. In 1941, Andrei Kolmogorov provided mathematical derivations.

In 2000 or so, the fractal envelope of Brownian motion was determined using sophisticated mathematics (stochastic Lowner evolution) to be 4/3.

Common mathematics appears to connect all of the foregoing. That suggests that the 4/3 ratio arises, for comparable circumstances, as a universal law.

In other words, by connecting different phenomena that all relate to 4/3 scaling, one can infer a general law.

Since 4/3 scaling appears to be a general law, it should not be surprising if it applies at a cosmological scale.

It is therefore intriguing that the ratio of energy densities for Omega_r / Omega_M for r radiation and M matter, has been measured at about 0.70 / 0.30. This is very close to the ratio of cosmological energy densities that would result from 4/3 scaling for energy E: E/ (1)^3 : E / (4/3)^3 = 4^3 / 3^3 = 0.7033 / 0.2967. In fact the survey of type 1A supernova by Betoule et al in 2014 measured Omega_M as 0.295 which is exceptionally close indeed to what theory suggests.

It is moreover interesting that the 1998 observations inferred that type 1A supernovae were about 10 to 15% farther away than expected based on luminosity about 3/4 as bright as would be expected for a flat universe. But 3/4 luminosity is equivalent to being 4/3 as far away if two reference frames, one 3 dim and the other 4 dim, are assumed consistent with 4/3 scaling. The 10% to 15% estimates were based on the implicit assumption that looking out into the universe looks out on a single 3 dim space, not two reference frames of 3 and 4 dim.

So. Do the dots connect?

In DLS method, the time dependence of scattered light intensity is used to obtain autocorrelation function (usually characterized by about 100 points). Then this function is fitted, and the inflection point of the fit corresponds to the characteristic time of the process in the sample. If we assume that this process is the Brownian motion of particles, then we can calculate characteristic size of these particles (regarded as hydrodynamic size; assuming spherical particles, and taking into account viscosity and refractive index of the medium).

Is it possible to achieve the estimate of this particle size with accuracy better than 1 nm for particles, say, of 10 nm? I suspect that it should be inherently limited by accuracy of the fit for the autocorrelation function.

The fundamental solution to the Diffusion Equation in one dimension is

c(x, t)=1/(4(pi)Dt)^1/2 e^( - (x - xo)^2/4Dt) ,

where D is the Diffusion constant of the diffusing particle, t is the time, x is the position along the x-axis, and xo is the initial position of the diffusing particle.

In the above equation, the center (mean) of the pulse is taken to be stationary at x = xo.

If the pulse were to drift in one direction along the x axis so that its center (mean) moved with velocity v to the right, the moving pulse would be expressed mathematically as

c(x, t)=1/(4(pi)Dt)^1/2 e^( - (x - vt)^2/4Dt) ,

where v is the velocity of the center (mean) of the pulse along the x-axis.

However, if the center (mean) of the pulse were moving randomly, so that it undergoes Brownian Motion, how would c(x, t) be expressed so that it could be evaluated (numerically) for each given (x, t) pair?

Any information related to the answer of this question would be greatly appreciated.

I'm experimenting the modeling/simulation of some processes using the Perlin noise, of which I've gain only some basic understandings. According to this article (https://flafla2.github.io/2014/08/09/perlinnoise.html), the gradient vectors control the distribution of the resultant map (I'm only concerned with 2D maps), if the 4 corner gradient vectors converge, there will be a region of local maximum, and vice versa. So if I want to have some inference on the distribution, I believe these vectors are the way to go. My question is how to bind the orientations of the 4-corner-vectors of some selected cells with the probability of there being an local maximum? Suppose for some cells, I want there to be near-permanent positives. And for some other cells, the probability of seeing a local maximum/minimum is controlled by observational values.

Could anyone give me some hints how to handle this?

I would use the variance in the Brownian motion using equipartition theorem to calculate the trap stiffness, but I could not understand how I choose the points that is representative to be used for the calculation,

shall I use the just after calibration of position detector, or the straight-line on which beads are trapped by light before I start the real experiment.

As both values of variance differs and the difference is big enough to create different results (SD=2.1, 5.8 nm).

Does difference between these values mean something wrong in the our optical tweezer

Do you know of any interactive apps that allow users to setup simple 2D simulations, such as:

- repulsive gas,

- liquids,

- brownian motion,

- polymer solutions,

- etc.

?

dX= u

_{ }dt + s dw- u is referring to drift
- s(sigma) is referring to volatility

suppose I have data for 3 years. how can I estimate (u and s)

These are examples of the 4/3 law so called by Hunt 1998. Lewis Fry Richardson’s 1926 measurements of wind eddies and Kolmogorov’s 1941 proof. John James Waterston’s 1845 on a gravitating plane. Clausius 1858 on 3/4 mean path lengths. Boltzmann’s 1884 derivation of Stefan’s law. Kleiber’s 3/4 metabolic scaling. The 4/3 fractal envelope of Brownian motion in Lawler 2001. Brittin and Gamow 1961 on photosynthesis, an implicit reference. In cosmology energy density varies with distance as 1/a^3 for matter and 1/a^4 for radiation. Jafar and Shamai 2007, perhaps, on cell phone transmission towers. The 4/3 law has two guises. First, a system with 4 dimensions has 4/3 the degrees of freedom of one with 3 dimensions. Second, lengths in a 4 dimensional system are 4/3 longer in the 3 dimensional system. The 4/3 law may account for dark energy.

we have some cost data of the equipment. about 3 years.

Often in astrodynamics we need conducting a high order integration of orbits in higly pertubed dynamics (the n-body problem augmented by the solar radiation pressure, J2, atmosphere, low-thrust, etc.). Some problems that I investigate require precise trajectory propagating. Does anybody know a very precise method of order, say, 30, 35, 40?

Particles will show random motion under a microscope. Is there an approximate equation to describe the mean translation velocity as a function of experimental parameters such as size, viscosity and temperature? Thanks!

I am trying to estimate the 3D position of a point in space by measuring acceleration.This can easily be done by computing the integral of the integral over time of each component of the acceleration vector.

The question is how to statistically characterize the noise. If I assume uncorrelated zero-mean Gaussian noise on the acceleration, the error on the velocity will be a zero-mean Brownian motion, and the error on the position will be the integral of a Brownian motion.

Do anyone know any literature on how to statistically characterize the integral of Brownian motion?

I thank you in advance

If the value of Hurst exponent is in the range of 0.55-0.65, then can theoretically random walk hypothesis be strongly rejected? As literature reports studies where time series having Fractional Brownian Motion correspond to higher ( in the range of 0.85-0.95) Hurst exponent values. Similarly for anti persistent pattern if Hurst Exponent Value is in range of 0.40-0.45 what can be inferred?

Bio-molecular system interaction by tiny field from UV how problematic for its thermal stress development?

turbulent flow

I am using Brownian motion dynamics in my equation.two particles are connected through linear spring.I want to generate random force for these two particles using Gaussian distribution.Since this is three dimensional problem so it has 3 independent components.in order to get different value at each run i need to use different seed at each time step.my question is that how we can get different seed for each run?

Nanoparticles dispersed in liquid are known to undergo Brownian motion. I feel that from time to time, two individual nanoparticles can come close enough to spaces of 1-3 nm and form transient dimers, before separating. I was wondering if there is any method to model this interaction time in terms of the concentration of nanoparticle,distance between the nanoparticles, solvent viscosity and solution temperature. Can anyone please suggest me where I should start looking for the same?

Regards

Rifat Kamarudheen

At first the viscosity is following simple trend i.e viscosity is decreased when temperature is increased which might happen due to increases in Brownian motion of droplets.

However beyond a certain temperature limit viscosity is increasing. Upon physical identification the emulsion seems to be stable at higher temperature.

Hi,

I work with MDCKs. Typically, we put Pen/Strep into our media. Recently, one of my transfections has been determined by the lab to be contaminated. This has made me worried. How do you tell if you have contamination? Obviously, I plan to do a Mycoplasma test on my cells since those are basically invisible. But what other ways can I tell?

The media does turn yellow after the cells have been in it for about two days (assuming I do not change it). But I'm pretty sure that's just exhaustion of media. I haven't observed any slowed growth. It takes about 2 days from thawing to confluence or from split to confluence. Their morphology hasn't altered, either. They look fibroblastic when growing and then nestle into nice little cobblestones when done.

I

**do**see little black irregular dots oscillating at 40x. However, it seems like this is just Brownian motion as they don't really go in a specific direction. And there aren't many, even after two days with no media changes. There's probably one for every two cells? If I did see something swimming/darting around, I'd toss everything immediately. The lab says it isn't contamination.Throwing the cells into wells has them all turn the same color at the same time at the same rate, too!

Imagine a very small particle in air (I call it Brownian particle, maybe its not correct). This Brownian particle is "dances" (or oscillates) in air due to air molecules. BUT! When this particle is oscillates it should create some wave around himself. Because during oscillating the particle strikes air molecules and we can imagine this particle sound source. I know that this oscillating is not coherent but there is some oscillating and it should be some wave around this oscillating Brownian particle. Am I right? I searched any information about this wave but I cant find. I liken these waves to pilot-waves of walking droplet.

I am looking for a simple software that is able to track single and individual (dilute) particles and to retrieve diffusion coefficient values out of it.

The system is the simplest possible: micron-sized particles undergoing 3D diffusion in water or 2D brownian motion when attached to a planar surface.

1) What parameters are important for recording a time lapse?

2) Any suggested (user friendly) software for non experts?

3) How does one retrieve diffusion coefficient values from the tracks?

Thank you in advance,

Rafael

I am working on the natural convection in nanofluids in a square cavity in the temperature range of 30 - 90 degree Celsius. Which type of thermocouples will be best suited to measure the temperature of nanofluids by considering the fluctuation in temperature due to the Brownian motion of nanoparticles.

Can I use the T-type thermocouples?

What will be the effect of thermocouple's tip diameter on the measurement of temperature?

to support chaos theory in brownian motion.

I am trying to figure out why the output of fractional Brownian motion as described by Richard Voss (

*Random fractal forgeries. In: Fundamental Algorithms for Computer Graphics, R. A. Earnshaw (eds.). Springer-Verlag, Berlin. 805-835. ISBN-13: 978-3-540-54397-8*) is characterized by periodicity.In particular, the images produced according to its Fractal Forgeries paradigm always come with an x=y axis of symmetry.

**What is the mathematical or numerical reason for that?**

I am wondering about how an aqueous suspension of superparamagnetic nanoparticles would behave if an externally applied uniform magnetic field were applied. With no magnetic field, I assume the particles will move in a random motion as they collide with eachother and the water molecules--normal Brownian motion.

But what if the particles were inside a solenoid type of apparatus? For example, the suspension was inside a glass capillary tube with a current carrying wire wrapped lengthwise around it.

My question is, the instant you apply current and establish that magnetic field, how will the motion of the SP nanoparticles change?

Without the magnetic field, each particle has 6 degrees of freedom (translational motion about x, y, z axes and rotational motion also about x, y, z). If the x axis be taken as passing through the center of the horizontal capillary tube, then which of the 6 types of motion will be affected once the solenoid is activated?

My thought is that translational motion will not change. But the particle will be restricted to only rotating about the x axis (aligning itself with the magnetic field) and no longer rotate in the y and z. Is that right?

This is probably a map algebra problem. I have a 2D map with values ranging 0.0 to 1.0 spread all over it. The algorithm that produces them is an application of the fractional Brownian motion. The map measures 101x101 pixels or cells.

My problem: I want to find in the map the regions (or islands) which values exceed a given threshold, e.g. 0.3 (we can call them the hotspots). I then want to calculate the number of pixels or cells that fall within the boundaries of that island. Given that there might be more than one island, I could end up with:

- Situation 1: 1 island with, say, 1000 pixels or cells;
- Situation 2: 2 islands with 500 pixels or cells each;
- Additional combinations.

Since I must be able to distinguish between the various situations, I was thinking of somehow weighing the total number of cells with respect to the number of islands. How could I do this, other than considering the average number of cells (which I see as a trivial solution)?

Please take a look at the picture for a better explanation of what I mean by islands or regions.

I would appreciate it if you could give me some direction, along with some relevant references. Thank you!

I have a series of 2D maps with values ranging 0.0 to 1.0 spread all over. The algorithm that produces them is an application of the fractional Brownian motion. Each map measures 101x101pixels or cells.

The algorithm producing these maps uses a discretized Inverse Fast Fourier Transform (FFT) in the spectral domain. The maps have a varying mean (0.0 to 1.0) but share a fixed variance which is σ

^{2}= 1.My question: it is said (check the attached link) that applying Moran's I to determine the clustering of a geographic dataset is sensitive to the dataset distribution, especially if the distribution is skewed. Since my algorithm produces maps which distribution is not consistent across all maps,

**what could be a robust algorithm for determining the clustering of my maps?**The aim is to find a method in which no influence is played by the shape of the distribution on the p-value of the clustering coefficient.

I am interested to know whether the forces that cause brownian motion can help keep larger particle suspended in a fluid even though they are too large to show the movement.

Brownian motion can be see in starch grains that are approx 1micrometre in diameter.

What is the maximum size of particle before they can no longer exhibit Brownian Motion?

Platelets are 2 micrometres in diameter and are only marginally more dense than plasma. There are studies of the effects of Brownian Motion in flowing fluids to mimic its effect in vivo, but I cannot find any reference to it being studied in plasma at rest.

Has anybody seen any studies of Brownian Motion in Platelets at rest in non-flowing plasma?

Hi,

I am trying to write a code for fBm in Python. I am following the

**SpectralSynthesisFM2D**pseudocode written by**Dietmar Saupe**in "*The Science of Fractal Images*", Springer-Verlag, 1988 (page 108). This pseudocode uses the spectral synthesis approach instead of the diamond-square algorithm.I got stuck at lines 25-27, where the pseudocode calls something like

**A[][].imag**, which has not been defined. I failed to "translate" this into a Python command.Could anyone please help? Thanks!

I am trying to calculate the Hurst-Exponent for time-series I created (stock price). I tried to use DFA, DMA und GHE and wrote everything in python.

To test if I implemented it correctly I generated a fractional Brownian motion with an algorithm from here http://arxiv.org/pdf/1308.0399v1.pdf (p28-29) with several Hurst-Exponents. I found a matlab code for the GHE here:

The problem I face is that the H-values for my different methods differ quite a bit. For example fBm(H=0.3): DMA:0.286, DFA:0.336, GHE:0.309 , whereas the matlab-code has a precision of about 1%.

My first question is: Is it normal that the values differ this much? Might there still be an error somewhere in my code? I usually get at least under 10%.

Second: The H-value seems to depend a lot on how I chose the scaling window. If I use a series with length=2^16 how big should my windows be?

For DFA I cut them into 2^4..2^13 parts. For DMA and GHE I tried a lot of things like 5,6...,20 or 10,20,..100 or 10^1...10^5.

Is there a proper way to assign the windows? How do I get the exact H-value?

Is there even an "exact" value?

I really appreciate any help.

Im trying to plot the dynamic brownian motion variance for my movement dataset using:

plot(Timestamp(var), getMotionVariance(var), type='s')

I received this error:

error in evaluating the argument 'x' in selecting a method for function 'plot'

This error wasn't cropping up before but now it is.

I have attached the file below.

Also, I want to plot the variance against time. How may I do so?

My timestamp is in the format: 4/17/2015 12:00

I wonder to know how accurate might be an estimate of fractal dimension for a specific fBm?

I've created a bunch of fractals with the

**same**known value of H, inside a loop and tried to estimate their fractal dimension but it seems there are some variations around the estimated values in comparision to the original H (or dF) that I started with!Is this normal? Is there any approach or method to get more accurate estimations?

Molecules of usual gas move stochastically. This stochasticity is a result of interaction between gas molecules (collisions of molecules). Let us imagine that molecules of the gas interacts by means of some force field. In this case the character of stochasticity of molecular motion changes. Let us take into account, that the wave function is a method of description of any ideal fluid motion (See “Spin and wave function as attributes of ideal fluid.”

*J. Math. Phys*.**40**, 256 -278, (1999). Electronic version http://gasdyn-ipm.ipmnet.ru/~rylov/swfaif4.pdf ). Is it possible to choose such a force field, that the gas with such interaction between molecules be described by the Klein-Gordon (or Schroedinger) equation? In other words, is it possible a classical description of quantum particles?If Markov and Martingale are properties of Brownian. What is Wiener then? How Markov is different from Martingale.

Hello all, I am investigating the sedimentation behavior of colloidal particles at different temperatures and using different grain size distributions. Sedimentation kinetics are affected by the inter-particle, gravity, and Brownian forces. I need to experimentally measure an index that can describe the Brownian effects, or theoretically estimate a value that correlate Brownian forces to the others. Any suggestions.

In the attached paper from the Gauge Institute, the definition of differential in e-calculus is (see page 8):

F'(x)={f(x+e)-f(x)}/e (1)

where e is defined as an infinitesimal (i.e. it should be smaller than any number but greater than zero).

From this definition in (1) it should be clear that as e approaches zero, it is assumed that the function of f'(x) has the form of a slope (linear). But this assumption has problems in real data of many phenomena, i.e. when the observation scale goes smaller and smaller then it behaves not as a linear slope but as brownian motion. Other applications such as in earthquake data, stock market price data, etc. indicate that each data includes indeterminacy (I).

I just thought that perhaps we can extend the definition of differentiation to include indeterminacy (I), perhaps something like this:

F'(x)={f(x+e)+2I-f(x)}/e. (2)

The I parameter implies that the geometry of differential is not a slope anymore. The term 2I has been introduced to include unpredictability/indeterminacy of the brownian motion. And it can split into left and right differentiation. The left differential will carry one I, and the right differential will carry one I.

Another possible way is something like this:

F'(x)=(1+I).{f(x+e)-f(x)}/e (3)

Where I represents indeterminacy parameter, ranging from 0.0-0.5.

Other possible approaches may include Nelson's Internal Set Theory, Fuzzy Differential Calculus, or Nonsmooth Analysis.

My purpose is to find out how to include indeterminacy into differential operators like curl and div.

That is my idea so far, you can develop it further if you like. This idea is surely far from conclusive, it is intended to stimulate further thinking.

So do you have other ideas? Please kindly share here. Thanks

Start with a reflexion domain being a polygon A1 A2 ...An, with n summits

A simple computation using formula line 7 page 57 shows that if d(An, An-1)-->0 then P (B5(0)=An)-P(B5(0)=An-1)-->0 as n-->infinity

and P((B5(t+s)€E/B5(0)=An))-P((B5(t+s)€E/B5(0) =An-1))-->0 as n--> infinity

Which allow to derive the distribution of the relected process in a bounded domain with smooth boundaries.

Thanks

Bernard Bellot

l

I want to run Brownian Dynamics simulation and wonder which software package is more popular?

How does it vary with concentration, temperature, size of atom?

My question is related to diffusion process.

I need to run an atomistic molecular dynamics simulation of a system in which some neutral gold atoms are randomly distributed in water box. I need to see how the gold atoms behave in water with time. But for running the simulation I need correct polarizable forcefield for gold atoms in water. There are some papers in which forcefields of various types of gold surface are present, but not for single gold atoms. Can anybody provide me any clue about the polarizable forcefield of single gold atom in water?

Looking for main QoS parameters (loss probability, queue length, mean delay and response time) for FBM input, Pareto input, FARIMA input and other known proccesses.

Although we can see the result from Brownian motion that small particles in the fluid actually have random movement, which means these fluctuations are unsymmetrical, I still don't know why in statistics we can say in small intervals of time these fluctuations would be unsymmetrical?

When or where do we use both?

Thanks.

Due to the non-conservative nature of radiation pressure force, it can be used for the cooling of atomic motion.

can anybody explain to me about :

1 - When the nanofluid is heated the nanoparticles experience stronger Brownian motion ?

2- Stronger Brownian motion leads to increase the amount of aggregation ?

3- Aggregation causes thermal conductivity enhancement ?

Random motion of gaseous molecules was one of the assumptions used to facilitate derivation of gas laws. Yet it is currently accepted as real displacements (vibrations in cases of solid and liquid) of molecules in space. Could someone explain on what basis this assumption became a real fact?