Conditions Definition and 1000 Threads

Hello everyone :) I'm reading the book QFT - L. H. Ryder, and I don't understand clearly what are the generating functional Z[J] and vacuum-to-vacuum boundary conditions? Help me, please >"<

Here's the issue. I have two curves that are dependent on each other (part of a bigger solution set). The logic of my program requires that one of two conditions have to be met. Basically, two curves are rising in y as x increases. Either curve 1 will reach some value "first", or curve 2...

As far as I know, the classic paper applying the Hawking singularity theorem to our universe is this one: Hawking and Ellis, "The Cosmic Black-Body Radiation and the Existence of Singularities in Our Universe," Astrophysical Journal, vol. 152, p. 25, 1968...

Setting is like this: I have 52cards of 4 shapes. that's 13 each. I take one card out and put it in a hat. now with 51card I draw 3 consecutive cards. It happens to be that I picked 3 diamonds. Now I want to find the probability of the card in the hat be a diamond. My friend said it...

Homework Statement (Kleppner & Kolenkow - Introduction to Mechanics - 2.17) The first attached image shows a box on an incline which is accelerated at a rate a meters per second squared. \mu is the coefficient of friction between the box and incline surface. The questions are in the image...

Hello everyone and greetings from my internship! It's weekend and I'm struggling with my numerical solution of a 1+1 wave equation. Now, since I'm eventually going to simulate a black hole ( :D ) I need a one-side open grid - using advection equation as my boundary condition on the end of my...

Hey folks, I have an orbit in the circular restricted three body problem with initial conditions [x(0), 0, z(0), 0, y'(0), 0] I'm following this paper http://adsabs.harvard.edu/full/1984CeMec..32...53H on how to correct these initial conditions given the state transition matrix at a...

I am trying to set up for an experiment, and I need to know the time dependence of the temperature of the front surface of an assembly of plates. The assembly has a heater on one side and is exposed to a gaseous environment (of constant known pressure and temperature) on the other. I am...

I wasn’t sure where to put this, I decided that really it could only go here in general discussion. Although the discussion involves matters of the human genome and the growing knowledge of it, the issue is not biological, it’s social. In any case… So, there was a program broadcast here in...

It has come up a few times in recent threads here that the energy conditions on the stress-energy tensor (weak, null, dominant, etc) traditionally used to prove global results (e.g. the singularity theorem, the positive energy theorem, geodesic motion theorems*) are problematic: they allow more...

Hey folks I'm looking into halo orbits and I have a question about how to find the initial conditions from the third order approximation solution... A good run through of the third order solution calculation is found in this paper...

Homework Statement MnO_4^{-} + 8H^{+} + 5e^{-} \rightleftharpoons Mn^{2+} + 4H_2O 1. Explain why the presence of an acid is necessary for aqueous permanganate ions to function as an oxidizing agent. 2. Give two reasons for the aqueous permanganate ions acting as an oxidizing agent in acidic...

Hello, I was wondering under what conditions does free fall need to comply to in order to take effect? I am pretty certain that for an object to be in free fall it needs to be void of any friction, but what about air resistance? Or is air resistance a form of friction? Thank you in advance.

Homework Statement The normal vector of each of the following planes is determined from the coefficients of the x-, y-, z- terms. pi1: a1x+b1y + c1z + d1=0 pi2: a2x+b2y+c2z+d2=0 pi3: a3x+b3y+c3z+d3=0 Define the extended vector for each plan as follows: e1= [a1, b1, c1, d1] e2= [a2, b2, c2...

Please teach me this: The parameters(mass,interaction constant) in classical Lagrangian can be freely changed in classical framwork,but how about in quantum framework?Then why we can freely arrange the renormalization conditions,because I think that we do not know whether the parameters can...

Could you please check if these are the Dirichlet conditions? 1. f(x) is periodic. 2. f(x) has a finite number of maxima and minima over one period. 3. f(x) is single valued, except at a finite number of discontinuities over one period. 4. \int^{-L/2}_{+L/2} \left|f(x)\right| dx is finite...

If I could be inside the LHC Atlas detector during a proton bean collision what would I see? Would there be a huge flash of light? Would I be killed, if yes how fast? Or would there be nothing to see?

Homework Statement n is given by: ∂2Θ/∂x2=1/α2 ∂Θ/∂t , where Θ(x, t) is the temperature as a function of time and position, and α2 is a constant characteristic for the material through which the heat is flowing. We have a plate of infinite area and thickness d that has a uniform...

In standard, run-of-the-mill, one-dimensional scattering problems (e.g., finite square wells), we calculate transmission and reflection amplitudes by (in part) making sure that our wave function \psi satisfies the following conditions at discontinuities of the potential: (1) It is continuous...

I am trying to model the diffusion of fluorophores in a cell with a source in the middle by solving the appropriate differential equation. I can solve the PDE easily enough, however as I haven't done DE's in a while, I need a refresher on how to apply the appropriate boundary conditions for my...

I am trying to solve the following heat equation ODE: d^2T/dr^2+1/r*dT/dr=0 (steady state) or dT/dt=d^2T/dr^2+1/r*dT/dr (transient state) The problem is simple: a ring with r1<r<r2, T(r1)=T1, T(r2)=T2. I have searched the analytical solution for this kind of ODEs in polar coordinate...

Hello all! :smile: I am wondering: Since we derive the equilibrium constant by minimizing the Gibbs free energy, it means that me are taking advantage of the fact that at the minimum, we have (dG)_{T,P,m}=0. Does this mean that in order to determine the products of a reaction using the...

Homework Statement Find the standard matrix for the linear transformation T: R^3-->R^3 satisfying: T([1 2 2]) = [1 0 -1], T([-1 -4 -5]) = [0 1 1], T([1 5 7]) = [0 2 0] All of the vectors are columns not rows, I couldn't type them correctly as columns. The Attempt at a Solution I...

Under what conditions is Faraday’s Law independent of Ampere’s Law? I want to say that this is so only in the static case, however this isn't right (or at least there's more to it). What am I missing?

a steel rod, 40mm in diameter and 1.00m long is pinned at each end calculate the euler bucking load Answer: using PE = pie sqaured 210x10cubed kN/mm x 1.25 x 10power 5mm to the 4 divided by 1000mm sqaured =259.1kN b) indentify three other possible end fixity conditions for the...

vw= Velocity of Wave vm= Velocity of Wave Source fw= Frequency of the Wave fd= Frequency of the Wave relative to Detector as Wave Source is also moving q= Infinity For the wave frequency detected by a detector at rest as the wave source* is moving towards it, there is: fd=( vwfw )/(...

Hi, How can I solve the diffusion equation in one dimension: u_t=ku_{xx} ; -\infty < t < \infty , 0<x<\infty With the boundary conditions: u(0,t)= T_0 +Acos(wt) u(x\rightarrow \infty,t) \rightarrow T_0 Thanks!

Hey guys, I'm having a conceptual problem implementing the Crank-Nicolson scheme to a PDE with nonlinear boundary conditions. The problem is the following: u_t + u_{xxxx} = 0, u(0,t) = 1,\quad u_x(0,t) = 0, \quad u_{xx}(1,t) = 0, u_t(1,t) - u_{xxx}(1,t) = f\bigl(u(1,t)\bigr). Taking m...

What will be the limiting conditions?

Homework Statement Hi guys, I'm having trouble understanding the finite potential well, in particular the boundary conditions The well under scrutiny has potential V(x)= 0 for |x|<a and V(x)=V_0 for >a Homework Equations \frac{d^2\psi}{dx^2}=-\sqrt{\frac{2mE}{\hbar^2}}\psi=-\alpha^2\psi...

It's just the final part (e) that I don't get, I have the rest but just for completeness I thought I'd put it in (iii) Let f : (0,infinity) -> R be a function which is differentiable at 1 with f '(1) = 1 and satisfies: f(xy) = f(x) + f(y) (*) (a) Use (*) to determine f(1) and show that f(1/x)...

I wrote a program that uses the FEM to approximate a solution to the heat conduction equation. I was lazy and wanted to test it, so I only allowed Neumann boundary conditions (I will program in the Dirichlet conditions and the source terms later). When I input low values for the heat flux, I...

I've seen equations for Fanno flow and Rayleigh flow but I am confused on how to use them properly. Fanno Flow \frac{P}{P^{*}}=\frac{1}{M}\frac{1}{\sqrt{\left(\frac{2}{\gamma+1}}\right)\left(1+\frac{\gamma-1}{2}M^2\right)}...

I have seen lots of simulations using the shallow water equations, and every one I've seen involves having some sort of initial displacement in the water, resulting in a propagation of waves through a medium of either constant or variable depth, as a function of position. However, can you...

The LHC is supposed to create conditions similar to the big bang. Although energy densities, temperatures and other conditions may be similar to those theorized in the big bang and soon thereafter, are the conditions of space and time the same now as then? If time and or space were fundamentally...

Hi! As a part of a mathematical construction I used the rate of change of F(s) with s, i.e. dF/ds. F and s are smooth functions. The problem is that s(u,v,w) is a function of u, v & w and actually I need to find the rate of change of F with respect to u, v & w. The question is: what does...

Hi everyone! I'm trying to find a smooth function that can replace the intersection of a continuous piecewise function made up of two lines of different slopes, one of which starts at the origin. Right now, I'm trying to find a logarithmic function that goes from the origin (or close to it)...

I am using Gaussian elimination to solve the airy stress function, but I am having difficulty implementing boundary conditions. A good synopsis on the problem of identifying boundary conditions is given here (section 5.2.1): http://solidmechanics.org/text/Chapter5_2/Chapter5_2.htm Given that...

Homework Statement For every set S and every metric d on S, which of the following is a metric on S? A. 4 + d B. ed + 1 C. d - |d| D. d2 E. square root of d Homework Equations none The Attempt at a Solution I've ruled out A. because d(x,x) does not equal 0. I've ruled out C. because it's...

When a PN juction is in the open circuit condition, my textbooks says the following. "The voltage measured between the terminals is zero. That is the junction Voltage Vo does not appear across between the diode terminals.This is because of the contact voltages existing at the...

Greetings, everyone! The problem below is actually a task on Numerical Methods. But I have difficulties making a mathematical model. Homework Statement Let us have a longitudinally homogeneous system of a pipe of radius R and a propeller of nearly the same radius inside it (we shall...

Homework Statement Consider \frac{\partial u}{\partial t} = k\frac{\partial^2u}{\partial x^2} subject to u(0,t) = A(t),\ u(L,t) = 0,\ u(x,0) = g(x). Assume that u(x,t) has a Fourier sine series. Determine a differential equation for the Fourier coefficients (assume appropriate continuity)...

Homework Statement Base metal zinc (Zn) reacts with concentrated hydrochloric acid (HCl) forming gaseous hydrogen and zinc chloride. STP conditions: pressure p = 101,3 kPa , temperature t = 0C. The equation of state for ideal gas: pV = nRT R = 8,314 J /(mol K) Homework Equations Write...

So, I do not think I did this properly, but if f(-x)=-f(x), then u(-x,0)=-u(x,0), and if g(-x)=-g(x), then ut(-x,0)=-ut(x,0). According to D`Alambert`s formula, u(x,t)=[f(x+t)+f(x-t)]/2 + 0.5∫g(s)ds (from x-t to x+t) so, u(0,t)=[f(t)+f(-t)]/2 + 0.5∫g(s)ds (from -t to t) f is odd, and so is...

Calculus of variations problem. I want to make stationary the integral of (1+yy')^2 dx from 0 to 1. I know what the Euler-Lagrange differential equation turns out to be, but how do I interpret the limits of integration as initial conditions for the diff eq? also, can i use laplace transforms to...

Hi, Assume the following action: \int d^4 x L[\phi,A]+ \int d^4 x A_{\mu} (x) J^{\mu}(x) What are the conditions on the form of action to have space/time translational invariance for a two point function: \left\langle J_{\mu}(x) J_{\nu}(y) \right\rangle = G_{\mu \nu}(x-y)...

Hey So i need to write down the first order necessary condition (F.O.C). and i need to find out where does a stationary point exist I know how to solve for the F.O.C when i am given an equation in the standard quadratic polynomial form but here the equation is f(x) = 1/2 xT Qx - cTx where T...

Hello I have a question about coupled oscillators and what initial conditions affect what constants of integration. In the book I have, A.P. French Vibrations and Waves, the guesses at solutions are chosen at random and sometimes do include a phase shift, while sometimes they dont. For...

I am sometimes just not sure how to go about solving magnetics problems and applying the right boundary conditions. I was hoping for a little advice. For example in an infinitely long cylinder (along z-axis) with radius a, and a permanent magnetization given by: \vec{M} =...

Homework Statement I'm told these are (1) f(x) is a periodic function; (2) f(x) has only a finite number of finite discontinuities; (3) f(x) has only a finite number of extrem values, and I've got a function 1/(3-x) which I'm asked to give reasons why it doesn't satisfy the...