Density Definition and 1000 Threads

From the action ∫Ldt =∫ι√|g|d4x where |g| is the determinant of the metric .and ι the lagrangian density. For gravitational field why is this ι is replaced by the Ricci scaler R which yield field equations in vaccum.(Rij-1/2Rgij)=0 Is it that the lagrangian density corresponding to vacuum is the...

E(X) of probability density function f(x) is \int x f(x) dx E(X2) of probability density function f(x) is \int x^2 f(x) dx Can I generalize it to E(g(x)) of probability density function f(x) = \int g(x). f(x) dx ? I tried to find E(5 + 10X) from pdf. I did two ways: 1. I found E(X) then using...

Homework Statement Show that the neutron density distribution function at any point in a monodirectional beam of monoenergetic neutrons moving along the x-axis is given by $$n(x, \mathbf \omega) = \frac n {\pi} \delta( \mu -1)$$ where ##n## is the neutron density, ##\delta( \mu -1)## is the...

Dear Sirs, Maybe this is general knowledge, but I couldn't find the answer where I looked, so please bear with me. Consider a circuit consisting of a mechanical generator (some spinning magnets and coils) and a wire across the generators output. At some point the wire gets hot and starts a...

Hi everyone! I'm currently strudying some astrophysical equation of states, some stuff about Fermi's gas and I'm kinda confused about the relation between the energy density and the mass density, $$ \frac{\epsilon}{c^2}=\rho. $$ I don't get why they do not use whole $$...

Hi everyone, this is my first thread! I am currently undergoing a personal investigation that is based on one of the factors which effect the splitting of d orbitals in central metal ion by the charge density of ligands (in a complex ion). However, recently I got stumped by trying to...

MODERATOR'S NOTE: HOMEWORK INCORRECTLY POSTED TO CLASSICAL FORUM, SO NO TEMPLATE I need help with the following question: Please have a look at the question and my attempt at the solution. Alternative cooling systems are considered for a large computing centre requiring 1 MW of cooling...

Homework Statement Homework Equations While solving this problem at r >>a ,the corresponding potential due to the dipole is kpcosθ/r2(potential due a dipole) where k is the electrostatic constt. ...(1) If σ(θ) is the surface charge density induced due to external electric field. then the...

Homework Statement [/B]Homework Equations [/B] ∫Dperpendiculards=qenclosed freecharge D=ε0E+P The Attempt at a Solution D1+D2=q/2πr2 at a distance r from the centre How to find D2 which is at the lower boundary e.g inside the dielectric??

I don't know GR so while answering the question if you prefer not to use that, I would be happy. In the Friedmann Equations, is energy density has an effect on curvature or vice versa? Or they are separate things and they don't affect each other? For example can we have an energy density...

Homework Statement This post contains the answer to my thread of 10th August... [/B] in which I asked if anyone could point out how to derive ##\pi^{ij} = \sqrt {^{(4)}g} (^{(4)} \Gamma ^0 \,_{pq} - g_{pq} ^{(4)} \Gamma ^0\, _{rs} g^{rs}) g^{pq} g^{jq}## from ##\mathfrak {L}## = (4)R...

##E = \frac{1}{2}(kx^2+m \dot{x}^2)## ## \frac{2E - kx^2}{m}=\dot{x}^2## ##\frac{dx}{dt} = \sqrt{\frac{2E - kx^2}{m}}## or ## dt = \sqrt{\frac{m}{2E - kx^2}}dx ## ⇒##= \frac{1}{\sqrt{\frac{2E - kx^2}{m}}}dx## My Question please help me. 1. I know ##T = 2\pi\sqrt{\frac{m}{k}} .## but i don't...

Homework Statement Sorry, it's not an actual problem, it's just a statement I don't understand from my text - "The density of water vapor is less than that of dry air. Therefore, the higher the humidity (that is, the more water vapor there is in the air), the lower the density of the air. For...

Excuse me for bad wording in the title, but there is only so much you can do with the character limit. So, has there ever been a proposal for a mechanism through which negative energy density could be created? Or the only possibility considered so far was that it would have been created in the...

Hi :) Here's my problem along with what I've done. Here is the problem: That is the p.d.f. of a random variable X. I have to find the cdf. I don't know which I should do so I tried it two ways. First: $\int_{-1}^{1} \ \frac{2}{\pi(1+x^{2})} dx = {{\frac{2}{\pi} arctan(x)]}^{1}}_{-1}=1$...

Hi, does anyone know density of Al0.1GaN. I have searched throught the internet but could not find anything. If possible send me some list of material properties to have some credible source of information for my work. Thanks.

I have a cylinder of some dimensions. I have a compressible liquid inside. Assuming a constant temperature, no atmosphere, no convection currents within, because it is in a cylinder, there will be no variations in density horizontally (the fluid will have time to settle). Now because there is...

Many times, the charge carrier density of a material is determined from a Hall effect experiment, from ##R_H=1/(ne)## (SI units). Where ##R_H## is determined from a measured voltage and other controllable parameters. As far as I know, this simple formula comes from the obsolete Drude's model...

Homework Statement Assuming you know the core mass, and other data about the sun, such as temperatures and pressures. Find the density at the very center of a star. Homework Equations I think this may be involved. P(r) = p(r)/µmH kT(r) The Attempt at a Solution [/B] I don't know where to...

What is the easiest way to calculate dark energy and matter density at any given age of the universe?

I am trying to estimate the distance of closest galaxy neighbor knowing the expression of number of neighbors into a volume ##\text{d}V##, the mean density ##n_\text{gal}## and the correlation function, i.e with this expression : ##\text{d}N=n_{\text{gal}}\,\text{d}V\,(1+\xi(r))## with...

Hello, I am asked to give the formal expression of the total number density of galaxies and explain why is this expression problematic in practice? From what I saw from my research and into my lectures, I have found the follwing relation which gives the number of galaxies ##N## with mass ##(m...

Vacuum or dark energy have energy densities. (Markus, a science advisor at Physics Forums in 2003, estimated that dark energy has an energy density of about 0.5 Joule per cubic km.) I assume that the structure of space-time has an energy density, that it was measured and that it can be...

Hi everyone, On Page 72 of S. Weinberg's Cosmology book, it's mentioned, just after Equation 1.9.16, that, for the universe matter density ρ(r) to be an analytic function near the origin (spherical symmetry), it has to be given near r = 0 by a power series of r2. I'm not a math wizard, so can...

Homework Statement A charge Q is uniformly distributed throughout a nonconducting sphere of radius R. Write the expression of the charge density in the sphere? Homework Equations Charge density ρ=dQ/dV Gauss's Law ∫EdA = E(4ϖr^2) The Attempt at a Solution If Q is uniform then ρ=Q/dV and the...

Homework Statement Given the above lambda system, is it wrong to say that the density matrix is of the form ## \rho = c_1|1> + c_2|2> + c_3|3> ## ? Hence when written in matrix form (basis of ##|i>##), ## \rho ## is a diagonal matrix who's elements are the ##c_i##s?

Hi! Given that the chamber is airtight and no air leakage occurs, is the design in the picture below possible? Can the pressure inside the chamber cause the button (black part at the top) to be "pushed"? https://imgur.com/a/wOSD30D Obviously the temperatures are over-exaggerated, but the...

Homework Statement I've been working through a paper by Alexey Golovnev, title 'ADM and massive gravity' arXiv.1302.0687v4 [gr-qc] 26 March 2013. I am hoping to use his result for the Einstein-Hilbert density to achieve my aim of finding a way to derive Equation 21.90 in MTW. I have worked my...

Studying probabilistic density, I know that a function that is integrated between two limits presents a probability. But how should I think to solve a problem where I need to determine the probability of a particle being seen being that its moment liner is a constant value

There is a Baez essay about the vaccum energy density, where he says: So did they do what I might naively think of doing, namely just plotting the redshift data over a few years? Or is it a more subtle method that directly measures the time derivative of the expansion? And if I understand...

Homework Statement "Given that the joint distribution of ##X## and ##Y## is ##f(x,y)=\frac{1}{2}(x+y)e^{-(x+y)},\text { for } x,y>0## and ##0## otherwise, find the distribution of ##Z=X+Y##." Homework Equations ##f_Z(z)=\int_{\mathbb{R}}f(x,z-x)dx##...

Dark energy density at this time is a constant and our universe is expanding (accelerating). This is expected to continue indefinitely. What would happen, if for some unknown reason, dark energy density started to decrease? If over time, in billion of years or longer, dark energy density...

The picture above has thrust density as a column and I am not too sure what that is. Can anyone explain to me what the difference between thrust and thrust density? Thank you for your answers!

What kind of ion sensor can I use in the range 1e19to 1e22 ions/m3? (corresponds to 0.1 to 5 pascals if non ionized) Does it exist any sensor based in the charge capacity?

Homework Statement A layer of liquid with density ##800~kg/m^3## floats on top of a volume of water. A block floats at the oil-water interface with ##3/4## of it in water and the rest of it in the liquid. What is the density of the block? Homework Equations Buoyancy =##vρg## where ##v##=...

Hi, I am wanting to confirm my understanding of the density matrix in quantum mechanics. Is it the wave function co-efficients squared - in other words the wave amplitudes squared which in turn are the probabilities and then these turn out to be placed into a matrix form with the squared wave...

In order to check if a quantum particle crosses a barrier or not, isn't calculating ##|\psi(x)|^2## enough in that particular region ? Why do we need to calculate probability current density for that matter?

The Compton wavelength of a particle is given by $$\lambda=\frac{h}{mc}.$$ One can construct an expression for the energy density ##\rho## of a particle of mass ##m## given by $$\rho = \frac{mc^2}{\lambda^3}=\frac{m^4 c^5}{h^3}.$$ What is the physical significance of the mass scale ##m## in the...

I've been reading a bit about the quantum confinement effect on nanowires, particularly how it changes the band structure. I'm trying to find an explanation on why the density of states splits into sub-bands. At the moment all I'm running into is 'because of the quantum confinement effect' which...

Homework Statement A charged isolated metal sphere of diameter d has a potential V relative to V = 0 at infinity. Calculate the energy density in the electric field near the surface of the sphere. State your answer in terms of the given variables, using ε0 if necessary.Homework Equations Since...

For continuos groups one introduces a density function for an invariant measure when summing over the group elements. I learned a little about these concepts in a pure mathematical book. I was thinking about their utility in physics.. I know they probably do.. What physical areas could these...

How can I find the relation between the radiance and the energy density of a black body? According to Planck's law, the energy density inside a blackbody cavity for modes with frequency ##\nu \in [\nu, \nu + \mathrm{d}\nu]## is given by $$ \rho(\nu, T)\mathrm{d}\nu =...

The MB energy distribution is: MB_PDF(E, T) = 2*sqrt(E/pi) * 1/(kB*T)^(3/2) * e^(-E/(kB*T)) How do I arrive at the density of states which hides inside the expression 2*sqrt(E/pi) * 1/(kB*T)^(3/2) ? I've only seen DOS that have "h" in them.. I want it to contain only E, pi, kB and T.. This is...

Do simple 2D Ising models have constant density of states? How is it calculated?

The Wikipedia entry on "White dwarf" has a table listing the densities (in kg/m3) of various objects/substances, and states that an earth-mass black hole has a critical density of 2 x 1030, about 13 orders of magnitude denser than atomic nuclei. Has such an enormous density been calculated...

Homework Statement Sphere 1 has net positive charge Sphere 2 has net negative charge Sphere 3 has net positive charge The ranking of net charge magnitudes are SPHERE 3 > SPHERE 2 > SPHERE 1 All spheres are conductors Sphere 2 is moved away from Sphere 1 and toward Sphere 3 so that 2 and 3...

Homework Statement If two balls, being identical in volume, but different in density (one ball is made of iron, the other of aluminum) roll down from an inclined plane, which will reach the bottom first and which will cover a larger distance after having reached the bottom? IMPORTANT NOTE...

Homework Statement The density of an object is given by its mass divided by its volume: ##p=\frac{m}{V}## Use a calculator to plot the volume as a function of density (##V=\frac{m}{p}##), assuming a mass of 8kg (m=8). In the follow-up question (part b): Evaluate ##\lim_{p \rightarrow 0}...

In general, when we say that in a fermionic gas the higher its density, the better we can consider it to be a plasma instead of gas?

Would a black hole whose density is lower than that of water, sink? The answer is likely over my head. So far, I've found 5 answers by "experts", with quite different opinions. For instance on this website, one reads . On IRC I was told by another expert that it would sink. Here are the...