mathtrek

I'm struggling with understanding the Einstein Summation Convention with respect to Lorentz transformations. Is anybody able to point me in the direction of some easy to read resources on the subject? Thanks in advance!

I'm wanting to calculate the experimental uncertainty in the following function: N = f(x,y) = a*exp(-x/y) where a is a constant. I've applied the following technique: For z = f(x,y), Δz = sqrt[ (∂f/∂x * Δx)² + (∂f/∂y * Δy)² ] And calculated: ΔN = sqrt [ ( (-a/x)*exp(-x/y)*Δx )² + ( (ax/y²)*exp(-x/y)*Δy )² ] However this is giving me an error far in excess of what I should be getting... can someone advise where I've gone wrong?

Hmm, well after further research it does seem that for an ideal gas that, indeed, α = 1/T and β = 1/P. However, reconsidering the question - it's directing the use of the Carnahan and Starling equation to estimate these coefficients. Would that imply that one doesn't use the Ideal equation..?

^ Yeah, just been introduced. My concern is that the calculation is far too simple - I was lead to believe it would be far more involved... I'm just wondering if I've dreadfully oversimplified it and in doing so have missed a crucial step

Hoping for a bit of insight with a problem I've been tasked with... I've tried using Z = PV/nkT and then the CS expression for Z: Z = (1+η+η²-η³) / (1-η)³ however we find α = 1/T and β = 1/P which seems far too easy. Could someone please offer a suggestion of which direction I should be looking in? Any help would be greatly appreciated!!

Ever so sorry, i've transcribed the first part of the question incorrectly. Part (a) should read (a) Find the general solution to the equation d²X(x) / dx² = 0 ...making me even more confused!

Got this (rather tricky) separation of variables problem: Expanding the LaPlace's equation, I get my two ODEs: d²X / dx² - k²X = 0 d²Y / dy² + k²Y = 0 Because one of the boundary conditions has a sin(pi*x/L) term in, I've written the general solution for d²X / dx² - k²X = 0 as: X(x) = Asin(kx) + Bcos(kx) (think that's right...) However I'm having major problems with part (b)... my natural assumption would be that the entire general solution reads as: T(x,y) = [Asin(kx) + Bcos(kx)][Ce^ky + De^ky] However using that I can't zero enough terms given my boundary conditions to get anywhere. HELP!!!!

Hi all, I'm working out various Fermi Temperatures of substances (potassium, neutrons in a neutron star etc) and have come to Liquid 3He (density 81kgm-3). I've been told that these are not electrons when considering liquid Helium, but I'm at a loss of how to proceed. Has anyone got any ideas? Thanks!

Hi all, having difficulty with this problem: A B0 star has a luminosity of ~ 16000 L(solar) and a mass of ~ 16 M(solar). Can you estimate the time on the main sequence for this star simply from considering the rest mass energy of the core of the star (~10% of the total, and fusion burns with an efficiency of about 0.7%) and its luminosity? Not really sure where to start, am very new to Astro stuff...

Update - ok! managed to work it out. Good old Mosely's law!

Having some difficulty with a subatomic problem concerning K-alpha lines: "Light from the K-alpha line of an unknown material X is compared with the K-alpha line of Carbon. The wavelength ratio is lambda(x)/lambda© = 0.148. What is the matieral X?" I've got no idea where to go with this one. The only time i've used K-alpha lines is in regards to changes of energy levels. I know E=hf=hc/lamba, but i don't see how that helps

Hi all, We've just been studying the Hall Effect and it was noted that magnetic field detectors which use the Hall Effect are based on semiconductors. Is there any specific reason for this? All I can seem to find is that the voltage measured for semiconductors is much larger, and from the Hall Effect equation V(H) = IB/net this would indicate that a larger B field could be measured...

^ The rate of flow of charge, Q/t. I see what you're saying, I just wondered if perhaps there was more to it... the question was set after a full derivation of Drude's formula for the conductivity making me think it was more complicated

Hey all, am having difficulty with this question: Calculate how many conduction electrons pass through a given area per second when a current of 1A flows. I've used these formulae: Current density, j = i/A (i=current, A=cross sectional area) Current desntiy, j = nevD (n=no of electrons per unit volume, e=charge on electron, vD=drift velocity) I've taken an element of volume of length vDt and cross-sect area, A. I've surmised then that the total number of electrons in that area will be N=nAvDt. All of those electrons will then cross a plane in 1 second, so i've equated j=i/A=nevD, and substituted n from the earlier (bold) equation - n=N/AvD. However, that produces a result of N=i/e=1/e ... doesn't look right! Help!!

Badly worded question, isn't it? pdV is p (ro - density) times the volume element dV. The square of the distance of the mass element from the z-axis - i assume means the distance from the mass element to the z-axis, all squared...

Hi all, Have been having some problems with the following math problem I was given last week: A solid cube of mass M and side a has one corner at the origin and three sides along the positive x,y and z axes. The square of the distance of the mass element dM = pdV rom the z-axis is x^2 + y^2 so that the moment of inertia of the cube around the z-axis is given by I = integral (x^2 + y^2) pdV taken throughout the volume V of the cube. If the cube has constant density, prove that I= (2/3) Ma^2 Any help/tips would be most appreciated!