Density Definition and 1000 Threads

Does anyone knows the name of the probability density function f(y) =aeby-cy2

I think Flux density is flux/Volume. Or is it flux/ Area Please be kind to help

Hi,I'm reading about critical density and I'm a bit confused about it's derivation.Solving the Einstein equations using the cosmological principle we get the (second) Friedmann equation: $$ \bigg( \frac{\dot{a}}{a} \bigg)^2...

I don't understand the exact meaning of flux. Please be kind to help.

According to the wiki entry on Planck units, https://en.wikipedia.org/wiki/Planck_units, the energy density of the universe, 1.8 × 10−123, is 1/16th the cosmological constant, 2.9 × 10−122. Is there a theoretical reason for this precise relationship?

I am studying two level atoms interacting with fields in order to study Dicke Superradiance. From Loudon's book, the Optical Bloch Equations for a two level atom interacting with a field say (with rotating wave approx): $$\frac{d\rho_{22}}{dt}=- \frac{d\rho_{11}}{dt} = -\frac{1}{2}...

This is a question from a mathematical statistics textbook, used at the first and most basic mathematical statistics course for undergraduate students. This exercise follows the chapter on nonparametric inference. An attempt at a solution is given. Any help is appreciated. Exercise: Suppose...

In the Lambda-CDM model, the density of galaxies goes decreasing and should even vanish in the far future. I would be grateful if someone could point me to a paper where this is calculated.

In Sydney Coleman Lectures on Quantum field Theory (p48), he finds : $$D\mathcal{L} = e^{\mu} \partial _{\mu} \mathcal{L}$$ My calulation, with ##\phi## my field and the variation of the field under space time tranlation ##D\phi = e^{\mu} \frac{\partial \phi}{\partial x^{\mu}}## ...

Hi, there. I am working with a model, in which the dimension of the Hilbert space is infinite. But Since only several states are directly coupled to the initial state and the coupling strength are weak, then I only consider a subspace spanned by these states. The calculation shows that the...

When I plug in the numbers I get ##2.9513\cdot 10^{-5}C/m^2##, not ##17.6\cdot 10^{-6} C/m^2##. Can someone point out where I'm going wrong?

Hey everybody, :smile: I have a joint density of the random variables ##X## and ##Y## given and want to find out ##P(X+Y>1/2)##. The joint density is as follows: $$f_{XY}(x,y) = \begin{cases}\frac{1}{y}, &0<x<y,0<y<1 \\ 0, &else \end{cases}$$ To get a view of this I created a plot: As...

I am only asking about part (b)(i) and (b)(ii). Below is the explanation for (b)(i). What is going on in the above? I understand up till the 3rd line, about the left/right hand circular motion. What is the "upward motion" the solution mentioned? Is it suggesting that ions are moving...

Hey guys! Sorry if this is a stupid question but I'm having some trouble to express this charge distribution as dirac delta functions. I know that the charge distribution of a circular disc in the ##x-y##-plane with radius ##a## and charge ##q## is given by $$\rho(r,\theta)=qC_a...

I’m trying to calculate how many Joules are stored in the Hyperion tree, the worlds tallest (115.84 m). However, I cannot find the mass of said tree, and am trying to find it by multiplying density by the volume (530 m^3) because if p=m/V then p•V=m, but I cannot find the density of the tree, so...

hi need help in physics HW: given current density [J][/→]=[J][/0][x][/Λ] and rotating frame with given surface vector: $$ A^→ = A_0(cos(wt)x^Λ + sin(wt)y^Λ$$ in need to calculate I(t) i tried I = ∫J*dA but i don't know i to technically do the math please help me

Summary:: Is the magnetic flux density B constant? Is the magnetic flux constant? I am working on a project design for Uni and I am stuck. In a magnetic circuit is either the magnetic flux or the magnetic flux density B constant? This magnetic circuit has all different cross section areas and...

Suppose that a particle evolves from point A to point B. The state of the particle can be written as $$\rho=\sum \left | m\right >\rho_{mn}\left< n\right | .$$ Because the basis is evolving as the particle travels, I am considering applying the Heisenberg picture to the density operator. Let...

Hello I've made a small program that does FFT, Fast Fourier Transform on a signal from radio receiver (RTL SDR), and parabolic antenna. Of course, the output is amplitude depending on frequency. I want to use it to detect and measure 1420MHz radiation from space. But I'm not sure on what's the...

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Hello, I found this article. In equation (1) the authors wrote that the current operator is given by : ## - \frac{\delta H}{\delta A} ##. I just would like to know if this relation is a just definition or if it can be derived from more fundamentals considerations ? Thanks !

Hi, I was wondering if compacting a particle p, you could create an even more dense one. In my theory, you would have a particle of any material, (for example: copper) and you combine it with another copper particle, if you compacted it enough, would the density of the two particles be added up...

I don't know where to start. This chapter is incredibly confusing for me.

hi guys i have a question about the derivation of the density of states , after solving the Schrodinger equation in the 3d potential box and using the boundary conditions ... etc we came to the conclusion that the quantum state occupy a volume of ##\frac{\pi^{3}}{V_{T}}## in k space and to...

In Principles of Lasers by Svelto, while deriving the Planck radiation formula, equation 2.2.3 says $$I_{\nu} = \frac {c_0} {4n} \rho_\nu$$ where ##I_\nu## is the spectral intensity at some hole in the cavity wall (energy per time per area per frequency), ##c_0## is the speed of light in...

I did (1300)(9.81)(0.67) and got 8544.51 N/m^2 but unsure if that was the correct route to take. Please confirm or deny if I was approaching it in the correct way!

So first I found rate of heat change using the above equation, with T=883K, e=1, SA= 6*l^2=21.66 Now dQ/dt=746593.71 W Now I am not sure entirely what to do next. They give density so I likely have to get the mass from that, M=pV,=1.9^3*4037=27689.783 kg. My issue is that I don't know how to...

Given a probability density distribution ##P(\vec{x})##, for what named distributions is the following true: \begin{equation} \begin{split} P(\vec{x}) &= P_1(x_1) P_2(x_2) ... P_n(x_n) \end{split} \end{equation}

In ΛCDM, H(t0) = 70km/s/Mpc, Ωd(t0) = 0.3, Ωr(t0) = 0 and ΩΛ(t0) =0.7, so that Ω(t0) = Ωd(t0) + Ωr(t0) + ΩΛ(t0) = 1and the universe is spatially flat. I want to know the t and z when the matter density equal to the vacuum energy density. By total energy density equation, I think Ωd(t) +...

Hi, In Problem 9.12 of Griffiths Introduction to Electrodynamics, 4th edition (Problem 9.11 3rd edition), in the problem, he says that one can calculate the average energy density and Poynting vector as using the formula I don't really understand how to do...

I know I need to measure the density of 7-Up. I can measure its volume, but I don't know how to find its mass. I also need to determine the composition of sugar in water, and compare 7-Up solution to the known sugar/water mixtures -- I don't know how to do these. Thanks.

When I was reading this page to understand Archimedes' 'story' I got a question: http://hyperphysics.phy-astr.gsu.edu/hbase/pbuoy.html#buoy According to the example shown, Archimedes found the density of crown by finding the apparent weight. What if he had just measured the volume of water...

The wave function ψ(x) of a particle confined to 0 ≤ x ≤ L is given by ψ(x) = Ax, ψ(x) = 0 for x < 0 and x > L. When the wave function is normalized, the probability density at coordinate x has the value? (A) 2x/L^2. (B) 2x^2 / L^2. (C) 2x^2 /L^3. (D) 3x^2 / L^3. (E) 3x^3 / L^3 Ans : D

I have a problem where I am given the density of states for a Fermion gas in terms of momentum: ##D(p)dp##. I need to express it in terms of the energy of the energy levels, ##D(\varepsilon)d\varepsilon##, knowing that the gas is relativistic and thus ##\varepsilon=cp##. Replacing ##p## by...

Hello All Typical 'artist's impressions' of the Asteroid Belt show a large density of matter, see the attached view. Many unmanned spacecraft (and hopefully soon some manned ones) have crossed this belt, without encountering any asteroids, so how close is this view to the truth? Is there any...

Performing force balance on the two balls, I obtain ## T+\frac{4\pi}{3}g \rho_3 R_1 ^3 = \frac{4\pi}{3}g \rho_1 R_1^3 ## ## T+\frac{4\pi}{3}g \rho_2 R_2^3 = \frac{4\pi}{3}g \rho_3 R_2^3 ## from which I obtain ## \rho_3 = \frac{\rho_1 R_1^3 + \rho_2R_2^3 }{R_1^3 + R_2 ^3 }## and ## 2T...

I want to begin by writing the problem and drawing its sketch to make things clearer on what is being asked for. Given : In the sketch shown to the right, the density profile of air with increasing ##z## is given by ##\rho=\rho_0 \exp(-z/z_0)##. Since we know the value of atmospheric pressure...

Hi everyone. Using the Green function, I want to obtain the density of states of a one-dimensional (linear) lattice. Depending on the problem conditions, we will have an iterative loop with 4,000 data for the energy component and a iteration loop with 2,000 data for the wave number component. In...

PROGRAM DensityOfState IMPLICIT NONE INTEGER :: omega , t0 , a0 ,kx omega=1 ; t0 =1 ; a0=1 REAL :: kx , eta , w , ek eta=0.0015 REAL,PARAMETER :: pi=3.14 COMPLEX , PARAMETER ::i=(0,1) COMPLEX :: Energy COMPLEX :: Density COMPLEX :: GreenFunc...

Using the ideal gas equation ##PV = nRT\Rightarrow PV = \frac{m}{M} RT## where ##m,M## are the mass and molecular weights of the gas respectively. This yields ##\frac{m}{V} = \frac{PM}{RT} = \rho##, the density of the gas at a point with pressure ##P##. If only we can obtain the variation of...

Hi, I have a question about probability transformations when the transformation function is a many-to-one function over the defined domain. Question: How do we transform the variables when the transformation function is not a one-to-one function over the domain defined? If we have ## p(x) =...

Hi, I have question about finding marginal distributions from 2d marginal pdfs that lead to the probabilities being greater than 1. Question: If we have the joint probability distribution ## f(x, y) = k \text{ for} |x| \leq 0.5 , |y| \leq 0.5 ## and 0 otherwise. I have tried to define a square...

Hi. For some background, I am running molecular dynamics simulations of silica fracture in LAMMPS. Each point represents the location of a broken bond. I would like to find regions where many bonds are breaking, which I speculate would be locations of crack formation. These computations are...

The current density is given by the formula ##J_e = (n\mu_n + p\mu_p)qE = \sigma E; \sigma \text{=conductivity}## ->eq1 The resistivity of intrinsic germanium is 60 Ohm-cm, the equation 1 becomes ##J_i=n_i(\mu_n + \mu_p)qE## ->eq2 ##J_i=60 \text{ ohm-cm} ## Applying the standard equations...

So I'm confused what the Saturation Flux Density is referring to. Defintion says it is when you no longer get an increase in H-field when increasing external B-field. So, does the satuation flux mean the core can only create fields UP TO that saturation flux, or that it can make a stronger...

In cosmology the deceleration parameter defined as the $$q_0 = \frac{1}{2}\sum_i\Omega_{i,0}(1+3w_i)$$ Is there a similar expression for the jerk parameter (##j_0##) ?

this figure form ( https://en.wikipedia.org/wiki/Effective_mass_(spring%E2%80%93mass_system) ) massive spring ; m K.E. of total spring equal to ## K.E. = \frac{1}{2} \sum dm_i v_i^2 = \frac{1}{2} \sum \rho dy (Vy/L)^2## V is the speed at the end of the spring and V are same speed of mass M...

I don't understand why ? ## \Psi ∇ ⋅ (A \Psi^ *) + \Psi ^* ∇ ⋅ (A \Psi ) = 2 ∇ ⋅(A \Psi ^* \Psi) ## form ## ∇ ⋅ (fg) = ∇f ⋅ g + f(∇ ⋅ g) ## Attempt at a Solution ## \Psi ∇ ⋅ (A \Psi^ *) + \Psi ^* ∇ ⋅ (A \Psi ) = 2 ∇ ⋅ (A \Psi ^* \Psi) - ∇\Psi ^* ⋅ A\Psi - ∇\Psi ⋅ (A\Psi ^*) ##

There is a section in the BJT explanation the charge density and the corresponding electric field graphs. But i was not sure how the electric field is derived and hence i started deriving it. Please correct me if my understanding is wrong in posting the question It is an ##npn## BJT. My...