Conditions Definition and 978 Threads

What is the condition for a spherically symmetric solution represents a black hole? ##ds^2=\exp(\nu(r))dt^2-\mu(r)^{-1}dr^2-r^2 d\Omega^2## it is enough that it is fulfilled that ##\nu## and ##\mu## are nulled in the same value of r??. There are other conditions?

I was reading the paper entitled "The Rayleigh—Taylor instability in astrophysical fluids" by Allen & Hughes (1984), and they discuss relativistically hot plasmas in the context of weak magnetic fields which are presumed to have no dynamic influence, so they take a fluid approach. In this paper...

Homework Statement A particle is represented by the following wave function: ψ(x)=0 x<-L/2 =C(2x/L+1) -L/2<x<0 =C(-2x/L+1) 0<x<+L/2 =0 x>+L/2 use the normalization condition to find C Homework Equations ψ(x) must be...

Hello, I don't know how to compute that number, but probably is a kind of reference value... Q: How many ion-pairs are there in normal conditions* in the air? (This is not homework, it is just out of curiosity.) Thank you for your time. Regards, ORF * 1 atm, 300K.

Hi, I have some confusion about the jump conditions for an electric field across an interface between two materials with different properties. In general, we have the two jump conditions across an interface: n.(ɛE)+ - n.(ɛE)- = σ...

Homework Statement A Jet is heading due east: its nose points towards the east direction, but its trajectory on the ground deviates from the east direction due to a sideways component of the wind. The plane is also climbing at the rate of 100 km/h (height increase per unit time). If the plane's...

-If we have string of length L that has fixed ends, then we can easily find frequencies with which this string can oscillate: We just need to solve wave equation: ∂2y/∂x2=1/c2*∂2∂t2 (c is determined by strings properties (linear density and tension), with Dirichlet boundary conditions...

Homework Statement and Homework Equations[/B] I was working on a math project involving certain simulations and a quarter circle. The equation of the quarter circle I used is y = r - SQRT(r^2 - x^2). Where r is the radius of a circle and x is greater than 0. The purpose of this is to model is...

Homework Statement You have been asked to provide a strategy for achieving radiation dose reduction for a radiology procedure in the X-ray Department. The procedure involves the slow insertion and careful positioning of a small metal catheter into the artery of a patient using fluoroscope. The...

Here's the problem: I don't see why there should be only finitely many nonzero a_z in b. I was able to prove uniqueness assuming that there only finitely many nonzero. I was able to show b implies d and b implies c, c implies a.

Hi I would like to know if there is any physical or medical scientific tests I can take to know/confirm my energy levels/body energy levels and will level when it comes to motivation. the reason for wanting to take these tests is that I have a severe mental brain neurological disability known...

I am solving the Laplace equation in 3D: \nabla^{2}V=0 I am considering azumuthal symmetry, so using the usual co-ordinates V=V(r,\theta). Now suppose I have two boundary conditions for [V, which are: V(R(t)+\varepsilon f(t,\theta),\theta)=1,\quad V\rightarrow 0\quad\textrm{as}\quad...

Hi at all, I'm tring to solve Schrodinger equation in spherically symmetry with these bondary conditions: ##\lim_{r \rightarrow 0} u(r)\ltimes r^{l+1}## ##\lim_{r \rightarrow 0} u'(r)\ltimes (l+1)r^{l}## For eigenvalues, the text I'm following says that I have to consider that the...

I'm reading "Division Algebras and Quantum Theory" by John Baez https://arxiv.org/abs/1101.5690 In the last paragraph of section 5 (Applications) he says the following "SU(2) is not the only compact Lie group with the property that all its irreducible continuous unitary representations on...

Hello PF community, I am currently self-studying electrodynamics from Griffiths textbook, and I'm at a point where the book discusses electrostatic boundary conditions. If someone can please check if my reasoning is right. So, as I am approaching an infinite, uniformly charged plane (let the...

I am unsure how to choose the boundary conditions for a system of PDEs or for a single PDE for that matter. The situation I am stuck with involves a system of 4 PDEs describing plasma in a cylinder. The dependent variables being used are Vr, Vt, Vz, ni, and the independent variables are Rr...

Homework Statement [/B] Determine the Green's functions for the two-point boundary value problem u''(x) = f(x) on 0 < x < 1 with a Neumann boundary condition at x = 0 and a Dirichlet condition at x = 1, i.e, find the function G(x; x) solving u''(x) = delta(x - xbar) (the Dirac delta...

There are few thing I'm not sure of and be happy for clarifications. In general: at steady state, what are the electric-field,potential, and current boundary conditions between a conductor and a dielectric medium? more specific: a) When dealing with a perfect conductor there exist a surface...

Homework Statement I'm trying to do all the calculations for the attached paper, and I'm having trouble with the boundary conditions for P polarization. My question is, how can I arrive to those conditions? The problem is 2D, an infinite dielectric cylinder coated with a layer of graphene...

Hi, I am wondering if there exists some general initial conditions for solving the Schödinger eqn. for 1D free electrons ? Thanks!

Homework Statement I'm trying to find the boundary conditions for the following problem: A plate with length 2L is placed on supports at x = L/2 and x = - L/2. The plate is deforming elastically under its own weight (maximum displacement bowing up at x = 0). Both ends of the plate are free...

Hi, I am trying to solve an ODE, however, the initial conditions are not known. From PDE examples, which are quite different, I see that some examples have initial conditions given by functions, and not by constants, i.e:: y(0) = x^2 I may have not modeled the problem correctly yet, however, I...

I am studying online course notes from University of Waterloo on 'Analytical mathematics in geology' in which the author describes a 'modified Fourier transform' which can be used to incorporate 3rd kind of boundary conditions. The formula is ## \Gamma \small[ f(x) \small] = \bar{f}(a) =...

Hello! I am reading a derivation for Fermi pressure and the author assumes that the electrons in a box are cooled so much that they occupy all the states in the momentum space from p=0 up to a maximum value of p. Then after he obtains a formula for the pressure, he simplifies the formula...

https://www.sciencedaily.com/releases/2000/06/000602074805.htm The article says that the zeno effect only applies to certain systems while the anti zeno effect applies to all systems. Is this true?

I would like to know if there is any formula for calculating the necessary conditions for certain elements to undergo nuclear fusion. I know that before the quantum tunnel effect was proposed, theoretically nuclear fusion reactions shouldn't occur in the Sun; with the increasing energy (affected...

Homework Statement My notes state the Lemma as shown above. I believe one of the underlying conditions is that the arc we integrate over must be +ve oriented (anti-clockwise) in the Upper and Lower half of the Complex Plane. However my notes doesn't mention whether or not the result holds...

Homework Statement Find E1, E3, and ps2 Homework Equations boundary conditions The Attempt at a Solution (these are class notes)[/B] I understand how to find E1, but I am a bit confused about the reasoning behind finding E3... Why do we leave the 2x(hat) for E3...? I though that only...

Hello, My question is very simple but I do not have a lot of experience with simulation. I want to write some code to simulate a lattice with boundary conditions and then I will perform calculations with the Hubbard model to find different kinds of properties of interest. I would like to know...

What are the ideal conditions in which circuit analysis or analysis of an electrical system is done?I know that the air friction,friction between materials is ignored in ideal systems, such as for ohms law applications.What else is ignored in analysis of ideal electrical systems?

Homework Statement A particle with mass m and spin 1/2, it is subject in a spherical potencial step with height ##V_0##. What is the boundary conditions for this eigenfunctions? Find the degeneracy level for the energy, when it is ##E<V_0## Homework Equations Radial equation \begin{equation}...

[Moderator's note: moved to new thread and edited slightly for context.] Hello to everybody, i just arrived at PF and I would like to know if i may set a couple of questions. First: It's possible for paired electrons to interract if one of them (or the two of them) is (are) in a black hole...

Homework Statement I am working on a code that sends a 6480 x 10 data set into a 64800 line LAT / LON / DATA gridded set. In part of my code, I'd like to have 2 conditions in 1 DO statement and I am not sure if it is possible.Homework EquationsThe Attempt at a Solution [/B] DO x = 1...

Homework Statement Let p: E-->B be a covering map. Let E be path connected and B be simply connected. Prove that p is a homeomorphism. Homework EquationsThe Attempt at a Solution I'm really struggling with this. Can anyone give me any insights? B is simply connected so any two paths with the...

Hey! :o We have $3$ lines with equations $a_{i1}x+a_{i2}y+a_{i3}=0$, $i=1,2,3$. I want to show that $\det ((a_{ij}))=0$ iff the lines are pairwise parallel of they have a common point. We have that $\det ((a_{ij}))=0$ iff we have a zero row. That would mean that we have linear independency...

I'm currently reading class notes from an introductory waves course, written by the professor himself. I'm stuck in the Fourier analysis part, because he gives the formulas for the nth mode amplitude of a standing wave with fixed ends and then states some properties which I can't really make...

I've been playing around with Maxima and it's ctensor library for tensor manipulation. I decided to have a crack at deriving Schwarzschild's solution for the interior of a constant-density sphere. I've managed to derive a static, spherically symmetric solution, but am struggling a bit with the...

Is there website that shows recent El Nino -vs-La Nina conditions in concise form? - or is the intensity of El Nino too vague a concept to quantify?

Q) A conducting sphere of radius R floats half submerged in a liquid dielectric medium of permittivity e1. The region above the liquid is a gas of permittivity e2. The total free charge on the sphere is Q. Find a radial inverse-square electric field satisfying all boundary conditions and...

This question is based on page 71 of Thomas Hartman's notes on Quantum Gravity and Black Holes (http://www.hartmanhep.net/topics2015/gravity-lectures.pdf). The Euclidean Schwarzschild black hole $$ds^{2} = \left(1-\frac{2M}{r}\right)d\tau^{2} + \frac{dr^{2}}{1-\frac{2M}{r}} +...

Hi, I need to solve Laplace equation ##\nabla ^2 \Phi(z,r)=0## in cylindrical coordinates in the domain ##r_1<r<r_2##, ##0<z<L##. The boundary conditions are: ## \left\{ \begin{aligned} &\Phi(0,r)=V_B \\ &\Phi(L,r)=V_P \\ & -{C^{'}}_{ox} \Phi(x,r_2)=C_0 \frac{\partial \Phi(x,r)}{\partial...

Homework Statement [/B] Inside a sperical dielectric mass there is a electric dipole on the center of the sphere. The sphere has radius a. This dieletric sphere is inside and on the center of a conductive spherical shell of radius b. The problem asks to find the potentials and then the...

Homework Statement Let ##A,B## be subgroups of a finite abelian group ##G## Show that ##\langle g_1A \rangle \times \langle g_2A \rangle \cong \langle g_1,g_2 \rangle## where ##g_1,g_2 \in B## and ##A \cap B = \{e_G\}## where ##g_1 A, g_2 A \in G/A## (which makes sense since ##G## is abelian...

Homework Statement Question attached Homework Equations The Attempt at a Solution part a) ##ds^2=\frac{R^2}{z^2}(-dt^2+dy^2+dx^2+dz^2)## part b) it is clear there is a conserved quantity associated with ##t,y,x## From Euler-Lagrange equations ## \dot{t}=k ## , k a constant ; similar for...

[FONT='inherit']the function y_p is a particular solution to the specified nonhomogeneous equation. Find the unique solution satisfying the equation and the given initial conditions. $y'' + 7y' = 7x$ $y_p=\frac{1}{2}x^2-\frac{1}{7}x$ $y(0)=y'(0)=0$ $r^2+7r=0$ $r=0$ $r=-7$

Hi For a book I'm writing, i try to write a very very very detail proof of self-buckling. I did it almost by taking inspiration of: https://en.wikipedia.org/wiki/Self-buckling But i really really don't get how we arrive to, that when, x=0 as we obviously must have: \dfrac{\mathrm{d}^2...

It won the the Qualcomm Tricorder X Prize, after a 5 year design mission.

The standard proof to show carnot efficiency cannot be exceeded is to couple a supposedly more efficient engine to a carnot refrigerator, and show that it would violate second law. However, isn't it true that we can make the same argument with any arbitrary efficiency? Some discussions on...

(Mentor note: moved here from noon homework thread hence no template) I was studying vibration of a one-dimensional monatomic chain and the textbook used periodic boundary condition (PBC). I wanted to justify the use of PBC, so I came up with this: atoms deep inside the crystal sees an...

Homework Statement Hy guys I am have a problem with the last part of this question. part d), ii) I get the general formal which I have displayed below, but what I done understand is if I take the limits as show in ii) I get ##0=\ \infty## which obviously I am doing something wrong. Have I...