Recent content by beth92

Homework Statement A capillary filled with water is placed in a container filled with a chemical of concentration C_{0} , measured in number of molecules per unit volume. The chemical diffuses into the capillary of water according to the following relation (where x is distance along...

That makes sense - would it be correct then to say that: rather than necessarily having 0 on the right hand side for the above equation, I have B_{i} where B_{i} is: -2 for the four points on the corner of the grid -1 for points along the edge 0 for all other points Thanks for the quick reply

Homework Statement I need to (computationally) solve the following linear elliptic problem for the function u(x,y): \Delta u(x,y) = u_{x,x} + u_{y,y} = k u(x,y) on the domain \Omega = [0,1]\times[0,1] with u(x,y) = 1 at all points on the boundary.Homework Equations [/B] I know that I...

Just finished writing out the whole problem - thanks so much. I think the main issue was the temptation to substitute the B-1b with x0 but as soon as I just put in Ax everything came together. And yeah I agree it should definitely be k not k + 1 so I'll just add a note there. Thanks again!

Still can't seem to get anywhere...in the above equations wouldn't it be x1 - x = nx0 - m ? I feel it would be more useful to express the difference between x0 and x as m = (x0 - x) as you can then just look for equation (2) as xk+1 - x = m * nk. Either way, in order to iterate the algorithm for...

Homework Statement The question relates to iterative refinement. The idea is that the computer generates a solution to the linear system Ax=b which is inexact (due to roundoff errors), denoted by x0. You then iterate the algorithm given in (1) until it converges to (something much closer to)...

That makes perfect sense now, thanks a lot!

This is part b) of an assignment question. In part a) we were asked to derive the Fokker Planck relation for the biased random walk. The answer is: dP/dt = -vdP/dx + D d2P/dx2 Where the first term is the drift term due to the biased motion and the second term is the diffusion term. Then...

I'm writing up an experiment I did for a lab course and I am calculating the error in quantity V. I have two runs and have ended up with a value of V for each one, as well as an error. Ie, I have V = 0.1145±0.0136 for Run 1 V= 0.1146± 0.0134 for Run 2 I got my errors through some tedious...

Hmm okay. So can I just say that ψ is a superposition of two states ψ1 and ψ4 and that the time independent Schrödinger Equation then becomes: H(ψ1+ψ4) = En*(ψ1+ψ4) which, due to the fact that H is additive means that: H(ψ1)+H(ψ4) = E1ψ1+E4ψ4 And therefore En is not an energy...

Homework Statement We are considering the Superposition state: ψ(x,t) = 1/2 u1(x)e(-i/hbar)E1t + √3/2 u4(x) e(-i/hbar)E4t We had to verify that ψ is a solution of the time dependent Schrödinger Equation, which I have done. Next we are asked to show that ψ is NOT an energy eigenfunction...

Homework Statement For the magnetic field B=k/s3 z determine the magnetic vector potential A. For simplicity, assume that A does not have a component in the s direction. (I don't know if this is relevant but this was a follow up question to one in which I was required to find the...

Okay, thanks! I think I've figured it out.. From Lorentz we have t=γ(t'+v/c2x') So if we have two times in the S frame t1 and t2 then the interval t2-t1=Δt=γ(t'2-t'1)+γ(v/c2(x'2-x'1)) We know that S' observes the events at the same time so t'1=t'2 Also from Lorentz: x=γ(x'+vt')...

I'm doing a similar problem at the moment, and I don't quite understand why you've set t' to 0?

Homework Statement For a Foucalt Pendulum: Relative to horizontal Cartesian x and y axes fixed to the Earth (with x as East) the equations of motion for horizontal motion are: x′′ + ω02x -2ωy′ = 0 and y′′ + ω02y + 2ωx′ = 0 [where x′, x′′, y′, y′′ are first and second time...