Conditions Definition and 1000 Threads

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...

Homework Statement Consider a plane monochromatic wave incident on a flat conducting surface. The incidence angle is ##θ##. The wave is polarized perpendicular to the plane of incidence. Find the radiation pressure (time-averaged force per unit area) exerted on the surface. Homework Equations...

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...

Hi guys, I am kind of stuck in this assignment. I have to design a flap wave maker in a half pipe (L=35m,Water height 0.5 m )I have read a lot about linear wave theory and another theories but all these involves wave tanks with a planar bottom so what I want to know is how does the curved bottom...

Hello, What could be wrong when the total inertia matrix of a robotic manipulator is non invertible when under certain values of the joint angles? Thank you

Homework Statement Use Friedmann equations to show that if ##\dot{a} > 0##, ##k<0## and ##\rho>0## then there exists a ##t*## in the past where ##a(t*)=0## Homework Equations [/B] Friedmann : ##(\frac{\dot{a}}{a})^2=\frac{8\pi G}{3}\rho-\frac{k}{a^2}##The Attempt at a Solution [/B]...

Homework Statement Homework Equations $$\frac{dy}{dx}=f(x)~\rightarrow~dy=f(x)dx~\rightarrow~y=\int f(x)dx$$ $$F=ma,~a=\frac{dv}{dt}$$ The Attempt at a Solution $$-\frac{mgR}{s^2}=mv\left( \frac{dv}{ds} \right)\rightarrow~v^2=\frac{2gR}{s}+C$$ $$v_0(s=R)=\sqrt{2gR}\rightarrow~C=2g(R-1)$$...

Homework Statement Find an equation of the plane that passes through the point (1,2,-2) and that contains the line x=2t,y=3-t,z=1+3t. Homework EquationsThe Attempt at a Solution I know that a plane is determined by a base vector and a normal vector, and the equation of the plane is ##\vec{n}...

Homework Statement Let f : R → Rn be a smooth function. Give necessary and sufficient conditions on f so that the antiderivative F(x) = ∫f(t)dt (from 0 to x) is periodic with period p ≠ 0 Homework EquationsThe Attempt at a Solution My initial thought is that as long as f is periodic then F...

Homework Statement Hello, For two waves to be coherent, they must have the same frequency right? Does this on its own implies a constant phase different between any point on one wave and any on the other. So, for example, if we had two waves with different wavelengths and velocities but equal...

Homework Statement In a lab experiment we ran the simulation of 3 different flight conditions into a program that produced graphs of the oscillations in them conditions and we have to do a comparison of the SPO (short period oscillations) characteristics for the 3 flight conditions which are...

The answers is b) ab≠1, but I have no clue how to get to that answer... Can someone help me? :D

http://imgur.com/a/xIydC The answers is b) ab≠1, but I have no clue how to get to that answer... Can someone help me? :D

Homework Statement Ive looked through several published journals online trying to find an experiment that I can use as background research for my report, something I can compare my findings to but I am just wasting lots of time that I could be doing the rest of my report so what I am trying to...

Whittaker (1st Edition, 1902) P.132, gives two proofs of Fourier's theorem, assuming Dirichlet's conditions. One proof is Dirichlet's proof, which involves directly summing the partial sums, is found in many books. The other proof is an absolutely stunning proof of Fourier's theorem in terms of...

Homework Statement Two lossy homogeneous dielectric media with dielectric constans ϵrl = 2, ϵr2 = 3 and conductivities a1= 15 (mS), σ2 = 10 (ms) are in contact at the z = 0 plane. in the Z>0 region a uniform electric field E1 = 20i - 50k exists (i and k being unit vectors in the x and z...

Homework Statement Deriving an s-domain equation for the following inputs a) &b) The Attempt at a Solution I understand how to derive the equation for an input with zero initial conditions (part a) but I'm not sure what to do when there are non-zero initial conditions (part b)

Working through a paper about whose rigor I have my doubts, but I am always glad to be corrected. In the paper I find the following: "We now investigate the random variable q. There are the following restrictions on q: 1) The variable q must characterize a stochastic process in the test...

I've been trying to come up with wave equations to describe the motion on vibrating rectangular (more specifically, square) membranes. However, most paper I find assume fixed edges. What are the boundary conditions I need to apply to the 2D wave equations in order to have an free boundary in a...

I'm trying to read this paper. Right now my problem is with equations 3.16 and 3.17. I understand that in equation 3.16 we're putting some boundary conditions on the fields, but I have two problems with these boundary conditions: 1) The fields depend on both ## t_E ## and ## x##, i.e. ##...

I have a couple homework questions, and I'm getting caught up in boundary applications. For the first one, I have y'' - 4y' + 3y = f(x) and I need to find the Green's function. I also have the boundary conditions y(x)=y'(0)=0. Is this possible? Wouldn't y(x)=0 be of the form of a solution...

Homework Statement Consider the following problems In #2, they start the solution by saying: r(t)=u(t-1) in #3, they start by saying that r(t)=t-tu(t-1) I understand how to solve the problem once you get r(t), I just don't understand how they decide what r(t) is going to be.

Homework Statement I am trying to solve a system of 2 ordinary differential equations using matlab. However, I am not able to get numerical solutions from the code despite having keyed in all possible solutions. Homework Equations The equations I am given are: dx/dt=A(x/t)+By...

I am facing some difficulties solving one of the questions we had in our previous exam. I am sorry for the bad translation , I hope this is clear. In each section, find all approppriate matrices 2x2 (if exists) , which implementing the given conditions: is an eigenvector of A with eigenvalue...

Homework Statement If ##a_n## counts the number of ways to climb a flight of n stairs if one can take 1, 2, or 3 steps at a time, then ##a_n = a_{n-1} + a_{n-2} + a_{n-3}##. What are the three initial conditions? Homework EquationsThe Attempt at a Solution I would say that ##a_0 = 1## since...

Ideal gas behavior condition is high temperature and low pressure, right? so is the book's answer to 10(a) ii wrong? https://scontent-kul1-1.xx.fbcdn.net/v/t34.0-12/14996536_1455768127770250_1228715611_n.jpg?oh=750e2555f8229aa9a4eeb17e3e80b1fb&oe=5829A2EE...

I'm trying to solve some statistical mechanics. This problem appeared. ##\frac{f\left(0\right)}{f\left(a\right)}f\left(x+a\right)=f\left(x\right)## Any idea as to which function will satisfy this equation?

The difference between Planck's Law and the Rayleigh-Jeans' Law is, in Rayleigh Jeans, the average energy per mode is ##kT##, whereas in Planck, it is ##\frac{hc}{λ(e^\frac{hc}{λkT}-1)}##. These average energy formulas are multiplied by another formula to give either Planck's Law or the...

Hi everyone, This is my first time posting here I am looking to get some help with Abaqus, I wish to compare two models and find the residual stress which causes a original model to deform to the other. The deflection between the two models can be calculated by other software. I plan to do...

Three conditions must be met in order for the Poisson Distribution to be used: 1) The average count rate is constant over time 2) The counts occurring are independent 3) The probability of 2 or more counts occurring in the interval $n$ is zero Simply, why must these conditions be met for valid...

So I am studying conditionals in proposition logic, and I have discovered that there are a variety of ways to phrase a conditional "if p, then q" in English. Some of the harder ones are... p is sufficient for q a necessary condition for p is q q unless ~p (where ~ is the not operator) p only...

Hi all. I don't have as much experience with thermal analyses in ANSYS, and I can't quite figure out a problem that I'm working on. I'm trying to find the temperature distribution in a box that has a circle in the center. I want to define constant temperature b.c.'s at the walls and the circle...

When dealing with heat transfer, there are cases where Q can be expressed by C*ΔT, for some proportionality constant C. However, in isothermal processes for example, this formula would lead to a mistake, for any value of C (because it would imply Q=0, which is not true generally speaking). What...

So this is kind of a speculative question but it is something I have long wondered about. I know that if I were to suddenly find myself transported backward in time, say 5000 years, or transported to a primitive Earth like planet, chances are that I would probably die in no time at all. I...

Hello, I have some sort of problem which I would like to explore. We have yet to touch it in the class in the university, but it seemed like a crazy idea when i stumbled upon it. Let there be a very long pipe with an inner radius of 1.08 meters and outer radius of 1.1 meters. The material of...

Hi all! I have to calculate the natural frequency of the system. Any idea of boundary conditions of this case? There is beam supported by two springs on the left side.

I'm facing some difficulties in using "boundary conditions" in a simple wavefunction. The wavefunction I'm considering is $$\xi(x,t)=A sin (k x \pm \omega t +\psi)$$ The minus or plus are for progressive or regressive waves. The indipendent parameters are 4: ##A##, ##k##, ##\omega##, ##\psi##...

If we have an infinite square well, I can follow the usual solution in Griffiths but I now want to impose periodic boundary conditions. I have \psi(x) = A\sin(kx) + B\cos(kx) with boundary conditions \psi(x) = \psi(x+L) In the fixed boundary case, we had \psi(0) = 0 which meant B=0 and...

We have a blowing performance measurement test (from ANSI B175.2) we perform to calculate flow rate and velocity with. The calculation spreadsheet is attached. The inputs are: Nozzle Diameter (m) blow force (N) atmosphere temperature (°C) atmosphere pressure (hPa) atmosphere humidity (%) air...

I am working in ℂ3 in this question. (If it will make it easier, we can work in a bounded subspace.) Suppose you have, in each of the three complex planes whose Cartesian product make up the space in question, a set of points. (You do not have knowledge of generators of these sets, or whether...

Hi there, I'm trying to simulate a vibrating plate with free edges. If i consider a consider a plate with fixed edges, the eigenvectors of the matrix bellow (which repesents the Laplacien operator) with S as a nxn tridiagonal matrix with -4 on the diagonal and 1s on either side (making the...