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0answers
17 views

What is normal fluctuation?

I was reading Statistical Mechanics (second edition) by Kerson Huang. On page 146, after equation 7.14, there is a reference to normal fluctuation. What is it? Here is the relevant part from the ...
2
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0answers
15 views

statistical property of light reflected from a coarse mirror

This is a problem comes up in my study in correlation reflectometry. I'm wondering if there is a straight-forward way to interpret the phase and amplitude of the reflected light from a perturbed ...
2
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1answer
58 views

Statistical Mechanics vs Statistics

Just how much of a representation of statistics do we get in a statistical mechanics curriculum. What are some of the useful facets of stat not in stat mech/quantum mech that physicists should really ...
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1answer
35 views

Counting the number of microstates that there are for a given configuration. How to prove this result?

I'm doing some statistical physics and I came across a result which I'm not sure how to derive. Any help? The answer turns out to be: Can anyone help with this derivation? Thank you :D
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1answer
43 views

Propagation of uncertainty - which formula? [duplicate]

Can someone explain to me when do I use this formula ...and when do I use this one?
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2answers
119 views

Why is propagation of uncertainties quadratic rather than linear? [duplicate]

1) Up until now, during practical work sessions, I always used these formulas for uncertainty propagation: if $C = A+B$ or $C = A-B$ $$\Delta C = \Delta A + \Delta B$$ if $C = AB$ or $C = ...
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0answers
15 views

Are the random variables in a delay embedded phase space uncorrelated and independent?

Consider a smooth manifold $M=R^d$ embedded in a higher dimensional space $R^D$ using Takens Attractor reconstruction where $D > 2d+1$. Let, the Random Variable $X \in R^d$ have a Gaussian pdf and ...
1
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1answer
50 views

Uniform $p$-values in $\chi^2$ fit?

I seem to have gotten myself confused about uniform $p$-values assuming the null hypothesis. This is related to how we interpret the results. Say I have a $\chi^2$-distribution which I got from ...
4
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1answer
69 views

What is the interpretatation of individual contributions to the Shannon entropy?

If $X=\{ x_1,x_2,\dots,x_n\}$ are assigned probabilities $p(x_i)$, then the entropy is defined as $\sum_{i=1}^n\ p(x_i)\,\cdot\left(-\log p(x_i)\right).$ One may call $I(x_i)=-\log p(x_i)$ the ...
0
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0answers
18 views

What does bispectrum mean?

I am working on a project that uses EEG signals of the brain to identify emotional states. While surveying the literature, I came across several references where "derived features of bispectrum" are ...
2
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4answers
238 views

Are “uncertainties” in Heisenberg Uncertainity just standard deviations? [closed]

Can someone confirm that the uncertainties in Heisenberg's uncertainty relation are really just standard deviations based on the expectation values? For example, the $\Delta x$ can be computed by ...
2
votes
1answer
35 views

Activity of a radioactive source - distribution of number of impulses per unit time

I have the following problem: The activity of a radioactive isotope was measured with the result $N=625$ impulses/second. If this measurement were to be repeated, state the interval where we can say ...
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2answers
40 views

Particle motion characteristic

I'm making a particle motion raffling normal numbers. The normal random numbers raffled are the angles of the directions that the particle is going. The particle speed is constant. Look how this is ...
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0answers
26 views

Regarding Chebychev and Gravity

I recently learned Chebyshev's Inequality (in statistics). He uses the inverse square to specify an upper bound to the proportion of entities of a set as it recedes on either side of the mean. I am ...
3
votes
1answer
23 views

Scale Factor on Error

I was gathering some data from the particle data group website and for many results it gives a value, an uncertainty and then a scale factor for the uncertainty. For instance, at here, where it gives ...
1
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0answers
44 views

How to calculate the correlation function for a discrete series of data [closed]

Using a simulation, I have generated a random field, which is basically a list of complex numbers. How do I calculate the correlation function of the field? To be more specific: which are the ...
1
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1answer
41 views

Derivation of Fermi level for T>0

I am working through the derivation of the Fermi level $ \mu_0$ for T>0. However, at one point in the notes I have, it states without any explanation that: $$ \int_0^\infty F'(\epsilon) ...
4
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1answer
181 views

Model Selection in Physics [closed]

My high-level understanding of the scientific method is that it can be summarized in the following steps, in no particular order: Make conjectures & hypotheses (theory) Make predictions ...
0
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1answer
61 views

A parameter to quantify instability in flight

Suppose I have plotted the body angles of a flying aeroplane.I have two such plots. One of a normal plane, and the other plot in which a primary sensor of the aeroplane is removed. So with the absence ...
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3answers
92 views

We don't know when a nucleus will decay. Then how can find its half life? [duplicate]

I mean how can we say that in 5730 years, 1/2 the no. of C14 nucleus will decay because in reality we don't know when a particular nucleus will decay
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2answers
237 views

Arrhenius Fit: Linear or exponential form?

I have a seemingly easy question about performing an Arrhenius fit to the equation $$y = A \times \exp \left( -\frac{E_A}{RT} \right)$$ I can either fit this in the exponential form using a ...
1
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1answer
39 views

Uncertainty of approximately sinusoidal voltage measurement

Say one is interested in measuring the mean value an approximately sinusoidal voltage with an instrument that has an accuracy of 0.01 V, according to its spec sheet. 10 periods of the oscillation have ...
3
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3answers
713 views

Should a Gaussian Curve Always Be Drawn Symmetrically?

This question is more about the appearance of a curve that comes up while I am analysing my data rather than an actual physics question, but I think it's relevant. I have analysed some data from an ...
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1answer
91 views

Probability distribution of phase-space reconstructions

I am unable to find resources regarding the probability density and distribution of non-linear chaotic systems in phase space. For example, if a discrete one-dimensional system, say the logistic ...
0
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1answer
54 views

Resolution of experiment is lower than the detector, so how to weigh the data?

I am attempting to create an atomic model based on data from a transmission electron microscope (TEM). Basically you shoot electrons at bunch of identical molecules stuck to a grid, and look at the ...
0
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1answer
32 views

Help Understanding Gaussian Particle Distribution

I have a simple enough problem. I want to mathematically describe a Gaussian particle distribution of $N$ total particles with a spot size of 0.1 (sigma). I need a function that will tell me the ...
0
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1answer
33 views

To find the probability? [closed]

The mass of the earth is 5.975 X 10^27 g of average atomic weight 30.00 g. The fraction (by weight) of the earth that is gold has been estimated to be 3 X 10^-9. The atomic weight of gold is about ...
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0answers
184 views

how to draw mechanical engineering problems [closed]

Hello I'm not entirely sure if this is on topic, but does anyone know software (or methods) to draw mechanical engineering schematics? (For statics/dynamics, so things like beams joints, rollers, ...
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0answers
28 views

Why can't we use the Neyman-Pearson likelihood ratio directly?

If you have a bunch of events and would like to choose a cut to distinguish background and signal, you can take the likelihood ratio $$ \lambda(\vec x) = \frac{f(\vec x| s)}{f(\vec x| b)} $$ and the ...
1
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1answer
129 views

Error calculation for experimental data

I have the list of experimental values: $$\{w_i \pm \Delta w_i\},$$ where $w_j$ is a mean value and $\Delta w_i$ is an error. I want to calculate the second list $\{a_i \pm \Delta a_i\}$ according to ...
4
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1answer
238 views

How is the theory of partial coherent light related to quantum-mechanics?

Background Let me start this question by a long introduction, because I assume that only few readers will be familiar with the theory of partial coherent light and concepts like a mutual coherence ...
4
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0answers
107 views

Is frequency or Bayesian interpretation used in quantum mechanics?

In quantum mechanics, we discussed about probability. There are two kinds of interpretations: frequency and Bayesian. Which one is actually used in quantum mechanics? My impression is, it doesn't ...
2
votes
1answer
131 views

From where randomness comes from and why it exists? [closed]

I recently began to study statistics and probability and I have two questions: Where does randomness come from? What is the source of randomness? Why does the randomness exist? Is it possible to ...
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0answers
171 views

What is known about Higgs LHC machine learning algorithm for identifying Higgs events?

Recently many LHC-affiliated organizations and otherwise announced the Higgs ML learning challenge (in May) running over the summer. There are many competing teams and significant results posted ...
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1answer
56 views

What is the experimental uncertainty of an ensemble measurement? [duplicate]

Let's say you measure the time it takes for 10 oscillations of a mass undergoing simple harmonic motion to within ± 0.01s, what is the uncertainty of the period of one oscillation?
1
vote
1answer
278 views

Why is uncertainty divided by $\sqrt{3}$?

Why do we have to divide uncertainty of the measurement by $\sqrt{3}$? For example we have the uncertainty of the measurement with a ruler being the smallest scale of 0.01cm, and it is not our ...
0
votes
1answer
120 views

Calculating kWh from time series of kW

I have a time series of kW where each sample is measured at regular intervals (10 seconds). Could anyone explain to me how could I calculate the total power consumed (kWh) over an hour? Thanks
2
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5answers
256 views

What's the difference between $10\%$ of $10\text{ cm}$ and $1\text{ cm}$?

I overhead a physics professor at my university on the phone: I interviewed that student you sent me, but he didn't know the difference between increasing the length of a $10\text{ cm}$ rod by ...
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0answers
35 views

What can I say about compatibility between predictions and results?

If I have these theoretical predictions: \begin{align} \omega_{p_1} = 4.5132 \pm 0.0003~\text{rad/s} && \omega_{p_2} = 4.5145 \pm 0.0002~\text{rad/s}\\ \omega_{b_1} = 0.0707 \pm ...
2
votes
1answer
1k views

Kolmogorov-Smirnov test vs Chi-squared test

What is the difference between the Kolmogorov-Smirnov test and the Chi-squared test? When should we use one instead of the other? I was reading this article, and I got confused a lot. It is hard to ...
1
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0answers
28 views

Quantity with approximate lognormal distribution

I am studying a quantity $x$ for which $\log( x)$ is nearly (although not exactly) lognormal. What would be the appropriate "typical" value: the mean $\langle x\rangle$ or rather ...
0
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0answers
29 views

Sum of independent errors [duplicate]

During a physics lab we stumbled upon a little problem. The measuring device was unstable, oscillating between two values. We were told to write down the average with the half-difference between the ...
1
vote
1answer
54 views

What is the correct way to handle significant figures when calculating compound uncertainties? [duplicate]

When processing experimental data, and calculating an uncertainty value in multiple steps, should intermediary uncertainties be used to a certain number of significant figures or kept to the full ...
3
votes
1answer
113 views

Autocorrelation of noise - negative correlation

I am investigating autocorrelation of electrical noise as part of an undergraduate experiment (as detailed in http://physlab.lums.edu.pk/images/a/ab/Correlation.pdf). I sampled noise voltages using an ...
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10answers
342 views

Could one measure a stick to an arbitrary precision by having its length estimated by enough people?

I remember reading somewhere that the problem of exact time-keeping on ships could have been solved a lot earlier than it was if somebody would have had the idea of keeping time with a whole array of ...
1
vote
1answer
113 views

Measuring a fluctuating quantity: Instrument error vs. uncertainty, or both?

Say I am measuring a quantity $x$ in physical system whose true value is approximately sinusoidal in time. I have an instrument to sample this quantity, for which the manufacturer gives an accuracy ...
1
vote
1answer
135 views

Error propagation of statistical error

I have a pulse profile (binned photon counts versus phase) of a star, and for each count rate I have its statistical error. I want to calculate the so-called pulsed-fraction ...
0
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2answers
115 views

Function for curved line in log-log-plot

I've done experiments on the thermo-viscoelasticity of liver tissue and the following results ...
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2answers
52 views

Why does chemical potential smaller than zero mean nondegeneracy and vice versa

In Mudelung's book, Introduction to Solid-State Theory, I have a confusion about the statement. Here, $x$ should be $\frac{\mu}{k_B T}$. I am cofused about his statement. Why does $x<0$ mean ...
2
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0answers
66 views

Statistical Mechanics: Most probable orientation of grain particle in gas chamber?

I'm in an introductory statistical mechanics course, and we've been posed the following situation: Long-shaped dust particle (so imagine something like a grain of rice) is placed in a gas chamber (so ...