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3
votes
1answer
112 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 ...
0
votes
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 ...
9
votes
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 ...
4
votes
4answers
6k views

What are distinguishable and indistinguishable particles in statistical mechanics?

What are distinguishable and indistinguishable particles in statistical mechanics? While learning different distributions in statistical mechanics I came across this doubt; Maxwell-Boltzmann ...
10
votes
2answers
751 views

Use of Monte-Carlo simulation in High-energy Physics

I've been doing some research into the analysis used in particle physics when determining the significance of a finding (e.g. the recent Higgs candidate was announced as a boson in the 125-126 ...
0
votes
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 ...
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
votes
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 ...
2
votes
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 ...
3
votes
2answers
6k views

How to combine the error of two independent measurements of the same quantity?

I have measured $k_1$ and $k_2$ in two measurements and then I calculated $\Delta k_1$ and $\Delta k_2$. Now I want to calculate $k$ and $\Delta k$. $k$ is just the mean of $k_1$ and $k_2$. I thought ...
3
votes
1answer
159 views

Combining uncertainties - multiple measurements

I am trying to understand how to combine uncertainties when they are dependent and independent from each other. Using this formula : $$\delta z = \sqrt {\Biggl(\dfrac{\partial f}{\partial x} \delta ...
1
vote
0answers
55 views

Weighted average whenever a variance is 0? [closed]

So I have data for the number of times a certain event happens. Each column is a different event and each row is one trial. A sample of data would look like \begin{bmatrix} 1& 4& 7& ...
5
votes
1answer
254 views

Advanced data analysis in Physics experiments

Before answering, please see our policy on resource recommendation questions. Please try to give substantial answers that detail the style, content, and prerequisites of the book or ...
2
votes
2answers
179 views

Physics Standard Deviation

I am a physics enthusiast and I have a question: Why is it meaningless to express the '$\pm$' (standard deviation) value as a percentage?
4
votes
1answer
264 views

How do I calculate the experimental uncertainty in a function of two measured quantities

I am performing an experiment where I'm measuring two variables, say $x$ and $y$, but I'm actually interested in a third variable which I calculate from those two, $$z=f(x,y).$$ In my experiment, of ...
1
vote
0answers
85 views

What could be the distribution of an explosion energy of a mining-grade and seismic exploration explosives?

Seismic exploration involves the excitation of seismic waves using the industrially made explosive charges. What could be the distribution of explosion energy of such a charges? My guess is that it ...
1
vote
0answers
115 views

Canonical form representation of a Linear Gaussian CPD

I'd like to know how a linear Gaussian conditional probability distribution can be represented to a canonical form. For example, let X and Y be two sets of continuous variables, with |X| = n and |Y| ...
0
votes
1answer
68 views

Can a distribution with sharper energy maximum than the exp-function give an equivalent theory?

Because for many particles the distribution $\varrho\sim\mathrm e^{-\beta\ H}$ has an extremely sharp maximum, the expectation values of the canonical ensemble agrees with that of the microcanonical ...
1
vote
1answer
177 views

Paper in physics - calculations; rounding or not?

I'm currently a high schooler, and I'm writing my first scientific paper. The result is fairly simple, and it is nothing too special, but I see it as a nice way to prepare myself for the academic ...
3
votes
1answer
176 views

Notations for statistical / systematic / numeric errors?

I constantly see the notation $$ 5.143(13) $$ for specifying that a value was measures / calculated to be 5.143 with an estimated error of 0.013. I have come to wonder though, just how commonly ...
1
vote
2answers
308 views

Drude theory of electrical conductivity

I was just trying to calculate the electrical conductivity for a Fermi-Dirac distribution and a Maxwell-Boltzmann distribution, and I ended up with the same result: $$\sigma=\frac{ne^{2}\tau}{m}$$ ...
1
vote
0answers
299 views

Combining errors to calcuate the total error (standard deviations)

I have a measurement method for which I want to study the measurement error by an error budget. Therefore, I listed all possible errors (error sources) (lets say $x_1, x_2, x_3,\ldots$). For each ...
2
votes
0answers
147 views

Bose-Einstein condensation in 3D

I have read in many books that BEC takes place in momentum space and in only 3-dimensions. What is meant by this statement?
6
votes
0answers
138 views

Statistical analysis of data in Physics

Analysis of data is integral in bridging the gap between theory and experiment. My question is about the two major methods of approaching the analysis - Bayesian and Frequentist. How much do the ...
-1
votes
0answers
74 views

How to determine spatial color distribution? [closed]

Is there an easy way (i.e. free or open source tool) to determine the spatial color distribution (i.e "intensity") in a picture or in a region of interest of this picture? Let's say I used a laser or ...
2
votes
1answer
124 views

Integral related to particle diffusion

In the context of particle diffusion, I am trying to understand the equations that describe Brownian motion as a macroscopic process. Assume $N(x,t)$ is a number concentration and $D$ is a diffusion ...
1
vote
0answers
91 views

Fitting of data to a model

Imagine that I have some observable value predicted with a theory for some process to be: $1+a x + b x^2$ and observed value is 1.3 with an error 0.2; a and b are some numerical constants. I also have ...
2
votes
1answer
313 views

Coherency matrix of partially polarized light doesn't contain all information on polarization state?

The electric field of quasi-monochromatic, partially polarized light can be expressed by the following random process (Goodman, Statistical optics) ...
2
votes
0answers
149 views

How long would it take for a container in vacuum to leak half of its air? [closed]

Let's say I know the size of the container, size of the hole the air leaks through, pressure the air is under and temperature of the air if that helps anything. Is it possible to calculate this only ...
3
votes
1answer
103 views

Time of Measurement Vs Number of Measurements

Let's say that an experiment has to determine the number of cosmic muon at sea level. The appropriate equipment is ready to measure the counting rate. I can think of two ways Count for 10 minutes, ...
2
votes
2answers
176 views

Error in variance

I've been exploring techniques in statistical physics, specifically applying them to spin ices. I'm in the canonical ensemble. By using the fluctuation dissipation theorem you can extract useful ...
2
votes
1answer
399 views

Experimental measurement of volumetric flow rate

The other day I with my team had to measure the volumetric flow rate through a pipe only using a 2000 mm$^3$ volumetric flask and a chronometer. The end of the pipe discharged to the atmosphere. As we ...
-1
votes
1answer
93 views

How many measurements should be done? [closed]

I am measuring time of a computer operation. The operation should run roughly same time each time I measure it. How many times should I measure it to get good average and standard deviation?
0
votes
2answers
359 views

Microsoft Excel not graphing $x = y^{1/2}$

The experiment was relating the period of one "bounce" when you hang a weight on a spring and let it bounce. I have this data here, one being mass and one being time. The time is an average of 5 ...
2
votes
1answer
157 views

Underlying physical basis of an exponential distribution

My data set of upper atmospheric cloud occurrences $N$ versus their thickness (or optical brightness, say $B$) show an exponential variation over more than two orders of magnitude - that is $N$ varies ...
4
votes
2answers
100 views

What's the physical difference between the quantities $\langle v_{i}v_{j}\rangle$ and $\langle v_{i}\rangle\langle v_{j}\rangle$?

What's the physical difference between the quantities $\left\langle v_{i}v_{j}\right\rangle $ and $\left\langle v_{i}\right\rangle \left\langle v_{j}\right\rangle $? Where $\left\langle ...
1
vote
5answers
525 views

Are Uncertainties in Measurements Important?

In the first lecture of MIT's Classical Mechanics Prof. Lewin highlights the importance of uncertainties in measurements by quoting "Any measurements, without the knowledge of uncertainty is ...
0
votes
1answer
123 views

What is a long-tailed distribution for physicists?

What is the most common definition of long tailed distribution for physicists? I am looking for definition and examples. Examples should have arguments why the distribution is or is not long tailed. ...
0
votes
2answers
76 views

Has anyone studied a statistical scaling law for the universe? [closed]

How do named objects in the universe scale? Is there a predictable curve for an ordered list, say {atom, animal, planet, solar system, galaxy, etc}? Can you then use the analysis to predict when the ...
1
vote
1answer
81 views

Initial separation of neutron star/black hole binaries?

How would I go about finding the distribution of initial separations (i.e. the lengths between the centres of mass) of stars that make up binary systems. I am interested in neutron stars and stellar ...
2
votes
2answers
9k views

Physical interpretation of y-intercept in a Current vs Voltage graph

So I collected current and voltage data from a simple circuit with a power source and a resistor, using a multimeter. I created a graph for this data using excel and got the y-intercept (which is ...
2
votes
1answer
489 views

Maxwell-Boltzmann velocity PDF to CDF [closed]

I asked on Math.SE and was advised to try here instead. I need to draw from a Maxwell-Boltzmann velocity distribution to initialise a molecular dynamics simulation. I have the PDF but I'm having ...
1
vote
0answers
91 views

Pareto efficiency and Standard Model parameters

Pareto Efficiency is a well understood concept in economics, which basically is a condition where no one actor could be made better off without some one being made worse off. This condition allows ...
2
votes
0answers
301 views

Probability and probability amplitude [duplicate]

What made scientists believe that we should calculate probability $P$ as the $P = \left|\psi\right|^2$ in quantum mechanics? Was it the double slit experiment? How? Is there anywhere in the ...
0
votes
1answer
65 views

Statistical error in a regression

I measured some voltage values ($x$) and some corresponding frequencies ($y$). I know that the voltage can only be measured within an uncertainty $\Delta x$. And the uncertainty of $y$ shall be ...
5
votes
2answers
466 views

statistics for photon counts in photomultiplier

It seems that a common statistical model for the count numbers of a photomultiplier is a Poisson distribution whose parameter $\lambda$ equals to the square-root of the number of counts.(e.g. ...
1
vote
4answers
2k views

Statistics in physics

What are the uses of statistics in physics? I am about to embark upon a study of statistics and I would like to know what the particular benefits I gain in physics.
2
votes
1answer
140 views

Peak deconvolution [closed]

I need some help understanding how much information I can pull out of this data. I have a sample made up of two materials. Materials A and material B. Then I took a picture of the sample. The two ...
5
votes
2answers
1k views

Averaging decibels

Wikipedia: The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level. If I ...