Statistical Definition and 582 Threads

Greetings All! I have what appears to be the most difficult question in the world based on the absence of even a single answer found on Google. I am looking for statistical ranking methods/rules/guidelines, etc. I work with data that is the result of taking continuous data (distance) and...

I need document or ebook talk about Nernst effect in statistical physics. who know that say for me? Gmail: manhkien_bka@gmail.com

I don't have the intuitive picture of thermodynamic 2nd law, in terms of statistical mechanics. That is, why should the number of microstates be maximized in equilibrium? Anyone gives an intuitive explanation? Thanks a lot.

According to quantum mechanics, every particle has an uncertainty of position and momentum. Particles have quantum vibrations. So is it possible for all the atoms in an object to vibrate at the same time in the same direction making the object as a whole move? If so, what kind of energy would...

Homework Statement 500 blue and 500 orange bacteria are placed in a growth medium. Each bacterium divides every hour. A predator eats exactly 1000 bacteria per hour irrespective of color. a) What is the ultimate probability distribution for the colors of bacteria in the growth medium? b) How...

\hat{\rho} = \begin{bmatrix} \frac{1}{3} & 0 & 0 \\[0.3em] 0 & \frac{1}{3} & 0 \\[0.3em] 0 & 0 & \frac{1}{3} \end{bmatrix} If I have this statistical operator I get i\hbar\frac{d\hat{\rho}}{dt}=0 So this is integral of motion and...

Homework Statement We have N particles, each of which can either be spin-up (s_i = 1) or spin-down (s_i = -1) with i = 1, 2, 3...N. The particles are in fixed position, don't interact and because they are in a magnetic field with strength B, the energy of the system is given by: E(s_1...

Homework Statement A classical particle with mass m is in thermal equilibrium with a fluid at temperature T. The particle is stuck to a harmonic ('Hookean') spring and can only move on a horizontal line (-\infty < x < \infty). The position of the particle is x = 0 if the spring is in its...

I'm starting a self teaching in statistical mechanics, so I would appreciate suggestions about the most appropriate textbook for this purpose. Thanks.

Homework Statement We have a surface that can adsorb identical atoms. There are N possible adsorption positions on this surface and only 1 atom can adsorb on each of those. An adsorbed atom is bound to the surface with negative energy -\epsilon (so \epsilon > 0). The adsorption positions are...

Quite a long title :D The fundamental assumption of statistical mechanics states, that all microstates of a system are equally probable. From what I know Liouvilles theorem should support this, but other than that I think it is just a pure assumption. Now I'm not really sure if I find it...

Homework Statement I have a set of data from the DAMA experiment in which a detector attempted to measure collisions with 'WIMP's [Weakly Interacting Massive Particles] as a candidate for dark matter. The detector records the time in days of a collision event. After binning the data and...

In A. Zee's book "QFT in a Nutshell" he glosses over the idea that the path integral approach and the partition function are related loosely by the correspondence principle, and alludes to some deep fundamental insight behind QFT. But then he moves on. Anyone know where I could read up more on this?

Hello all, I am currently doing statistical analysis of a knockout vs control mouse strain, investigating a gene that codes a protein that is hypothesized to be involved in learning and memory. To do the test, we ran mice in a morris water maze, which involves placing mice in a little...

hello - Do you know which programming languages have probability distributions available to use such as the binomial distribution (as an example). I guess I would like to limit my questions if it's necessary to languages that are either free or cheap - no specialty math packages for...

This might sound like a ridiculous question, but could someone please give an intuitive explanation of what a statistical model is? I have always thought that it was just a tool used to make inferences about data, but I was told very recently that this definition is not entirely correct. Could...

Hello everybody, I am a graduate physics student. I am trying to learn statistical physics and I have extreme difficulty in learning it. I do not find good books and don't get the ideas behind the concepts. the books I consulted where the Greiner, Kittel and Fliessbach. Books used in German...

For censored data. Random sample X1,...,Xn Censored such that x1,...xm are observed but xm+1,...,xn are not - we just know they exceed T. fx = exponential = theata exp(-theta.x) L = ∏ (from 1 going to m) f(x;theta) ∏ (m+1 - n) 1 - F(T;theta) Using F = int f I get L =...

Hello PF, I'm doing a Mohr's titration to determine Cl concentration. The volume I am working with is small, and it is not possible to obtain more. I have 2 uL of analyte to which I add 1 uL of indicator. Then, I add AgNO3 1 uL (0.014M) at a time until the endpoint is reached (color...

could we use three ensembles(microcanonic, canonic, grandcanonic) in cases of each problems? or can we solve any problem by using every one of these ensembles?

Problem: I have a sensor monitoring a process which is controlled by a feedback controller. This sensor fails from time-to-time and I need to replace it with a new one. I have always used the same type of sensor, say type A. Some sensor manufacturers are offering me an alternative sensor...

Homework Statement Consider a free-electron gas at a temperature T such that kT << E_f Write down the expression for the electron number desnity N/V for electrons that have an energy in excess of of E_f. Show by making the change of variables (E-E_f)/kT = x. that the number desnity is...

Statistical Mechanics -- Maximum Temperature We know that at zero degrees kelvin the only energy is zero point energy. As we heat a substance, the atoms move faster and faster. The question is, is there a maximum temperature since the fastest a atom can move is the speed of light?

why do we say that a classically behaved gas is non-degenerate and a quantum behaved gas is degenerate? I can't get why the word of "degeneracy" here can distinguish two kinds of behavior of gas.

For electronic devices that are made in large quantities, it's nearly impossible to test all the devices. How many samples do we have to test to get good confidence on the entire lot. Also, how do you select the samples for test - just pick them in random?

Having learned the fundamentals of quantum mechanics from Ballentine, I am now looking around for books on quantum statistical mechanics. However, I find most of them in-complete. I don't want to fuss, but I really liked Ballentine's approach and would like to continue with something similar. Do...

Hello, I just want to get people's idea on something: I am using MATLAB for doing statistical analysis since I am very much used to MATLAB than using other statistical software. Do you think MATLAB is good to use for that or do you think it has inherent disadvantages compared to other programs...

Homework Statement I'm working through an example from class and the textbook, but I'm confused about how the steps progress mathematically. The example involves the Gibb's partition for a paramagnet. \sum_{s} exp(\beta \mu B \sum_{i}^{N} s) Where s = -a,-a+1...a for each spin...

1. Homework Statement Given y = xz5 and x = zg find : (∂y / ∂x)z (∂y / ∂x)g 2. Homework Equations 3. The Attempt at a Solution I understand the concept of a partial derivative, but I've never seen one such that there is a variable held fixed, or one where ∂x is not changing...

Hello! I am currently doing my Extended Essay for Biology and I am not sure what stat test to use for my results. I am comparing audio frequency with the rate of antennal activity of the pill bug. I have found that from 0 Hz, the antennal movement also increases up to 400 Hz where it peaks...

Homework Statement The following set of analyses represent concentrations of chloride in blood serum (meq/L): 103,106,107,114. One value appears suspect. Determine if it can be rejected at the 95% confidence level. Homework Equations Mean Standard Deviation...

What are the classics in the area of (classical) statistical mechanics / kinetic theory? Is there anything as universally-lauded as, say, Jackson's Classical Electrodynamics or Goldstein's Classical Mechanics are in their respective fields?

Homework Statement Neutrinos are massless spin-1/2 particles (ignore their tiny finite masses). There are 6 types of neutrinos (3 flavours of neutrinos and 3 of anti-neutrinos), and each has just one possible polarization state. In the early universe neutrinos and antineutrinos were in...

Hi By some googling it seems like there exist some kind of expansion of the Taylor series for statistical functionals. I can however, not sort out how it is working and what the derivative-equivalent of the functional actually is. My situation is that I have a functional, say \theta which...

Hi folks :smile: I have an experiment in which I take an image of a flame. I then run a software routine that tells me what the concentrations of OH (hydroxyl) is at different heights above the flame. I first have to give it a calibrated image of a flame with known data and it then is able...

I was reading the solution to a statistical mechanics problem and this showed up: http://imageshack.us/photo/my-images/196/grddar.jpg/ S2N-1 = the area of the 2N-1 dimensional unit sphere. Could anyone shed some light on how these expressions equal each other, I am quite dumbfounded :(.

Homework Statement Consider a system composed of 2 harmonic oscillators with frequencies w and 2w respectively (w = omega). The total energy of the system is U=q * h_bar * w, where q is a positive negative integer, ie. q = {1, 3, 5, ...}. Write down the number of microstates of the system...

Homework Statement Give an physical explanation to why the specific heat capacity goes to zero as temperature goes to zero. Homework Equations The Attempt at a Solution I was simply thinking that around absolute zero the average kinetic energy of the particles should be zero...

Homework Statement You have a latice of particles that all have spin 1, but they can change the direction of their spin so constraint \left|S_j\right|=1. There is only interaction with the closest neighbours so we have the following hamiltonian: H = -J \sum_{\left\langle ij \right\rangle}...

Hi PF I was wondering about the problem of quantum gravity, and maybe the reason why we struggle so much with a formulation of quantum gravity is, that spacetime itself is the source to all quantum phenomena. The evidence is, that with the standard model, we describe the quantum phenomena...

Maybe this is the first post I enroll.(I wanted to change my id because I am not expert actually but I don't know how to change my id.) Anyway the main points of this post are as follows: Hello, I am an undergraduate student in Asia. Soon I have to apply for graduate, but I have no idea. I...

Hi everyone! Here's my problem of the day: Let's take a box containing 3 identical (but distinguishable) particles A B C. Let this be a canonical ensamble. Suppose that A has energy \varepsilon_0 and both B and C have energy \varepsilon_1. We thereforre have 2 energy level, n_0,n_1...

I read that entropy is a measure of disorder. Or in other words, unpredictability. So if I have a fair 50/50 coin. It is at maximum entropy (unpredictability). If I have a two headed coin I have zero entropy. It seems that the more possible unpredictable states, the higher the entropy. Now...

When we study a classical system of distinguishable particles, we use parameters \epsilon_{j} for the energy states and n_{j} for the number of particles in \epsilon_{j}. But clearly, the energy states are not discrete in classical systems. Surely, this is nonsensical. Why are we doing this then?

Recently, I was reading the Dixon (Annals Math. Stat. 22, (1951) 68-78) method for extreme (outliers) values. He considered that there are n ordered values (x1, x2, ...xn) of an analytical measurement. The values belong to a normal distribution. He defined two equations: 1. For Critical value...

Homework Statement Trying to solve 2(a) on this problem set...

When did statistical studies become important for the study of physics? Could someone cite something for me to read which would put this question in a historical context? I’m doing research on Arpad Elo (1903-1992). He did a master’s degree in physics (I assume before 1926), and then...

So, I found myself in need of an elective course, and I have taken all of the maths that I can possibly take (except for things further in the sequences). I signed up for a Stats course, and after tonight (the first day of the course) I realize that there is very little I will probably take...

I'm trying to understand why various statistical distributions are so common. For the most part, all I can find online is how to calculate and manipulate them... I did finally find a couple of refs that helped with Gaussians, this being one: http://stat.ethz.ch/~stahel/lognormal/bioscience.pdf"...

Homework Statement find the equation of state which gives the relationship between P , V , N and T C and b are constants Ω = CebNV2(EV)N Homework Equations P/T = (ds/dV)E,N The Attempt at a Solution so i just use s = klnΩ ? then i get ds/dV = k2bNV so P = k2bNVT ? that's it? btw, what...