Recent content by raintrek

1. PhD Physics student need help on career planning

Hi everyone - I'm hoping for a bit of impartial advice about career prospects for a couple of different options I'm considering. I graduated from a Masters degree in Physics back in 2009 and since then have been mostly travelling and working, albeit in an unrelated industry (medical...
2. Polymer random walk question

I understand the mean square end-to-end distance of a polymer of stepsize b and number of units N is given by \left\langle R^{2}\right\rangle = \sum_{i,j=1}^{N} \left\langle r_{i} r_{j}\right\rangle + \left\langle \sum_{i \neq j}^{N} r_{i} r_{j}\right\rangle And that the cross terms drop...
3. Probability distribution function / propagator

I have the following equation: \frac{1}{2N^{2}}\int_{s} \int_{p} \left\langle (\textbf{R}_{s} - \textbf{R}_{p} )^{2} \right\rangle which describes the radius of gyration of a polymer. (the term being integrated is the average position between beads p and s) This is shown to be...
4. Kinetic theory question

The molecular flux (number of collisions per unit area per unit time) in Kinetic theory is given by F=\frac{1}{4} n \bar{c} where c bar is the average molecular speed and n is the density of molcules in the gas phase (molecules/m^3) I was wondering about the origin of the 1/4 term ...

6. Calculus question

Homework Statement I have the following expression: cos\theta = \frac{\vec{a}\cdot \vec{b}}{ab} (this is simply taken from a dot product rule for two vectors) However I need to find \nabla_{\vec{r}i} \theta Is there a way I can do it without involving differentials of arccos and...
7. Tricky differentiation

Hmm, I've transcribed the problem straight from the question sheet. I too had that thought. I'm not sure I follow you with your methodology though. If I try to solve the equation using the standard quotient rule, it gives me zero - is there a reason for that?
8. Tricky differentiation

Homework Statement Find \frac{dU_{ave}}{d\beta} where U_{ave}=\sum_{k}\left(\frac{U_{k}exp(-U_{k}\beta)}{exp(-U_{k}\beta)}\right) Homework Equations The Attempt at a Solution My answer is supposed to be -(U_{ave}^{2})+(U_{ave})^{2} However I keep getting zero. I can...
9. Probability / Energy question

Homework Statement - Initial conformational potential energy = 2500 J - NVT Metropolis Monte Carlo simulation, T = 300 K - New conformational potential energy = 5000 J What's the probability this will be accepted within the Metropolis scheme? Homework Equations Acceptance...
10. Dipole Moment interaction

LOL, ok probably talking to myself here. Still playing around with this, taken it further, although I'm pretty sure my final answer here is wrong... http://voy.trekcore.com/working.jpg [Broken]
11. Dipole Moment interaction

OK, I've got a little bit further (this seems brutal!) I've been able to see that the separations of the charges mentioned above are: q1 & -q2: \sqrt{(d+rcos\theta)^{2}+(rsin\theta)^{2}} -q1 & q2: \sqrt{(-d+rcos\theta)^{2}+(rsin\theta)^{2}} Simplifying: q1 & -q2...
12. Dipole Moment interaction

Homework Statement Consider two dipoles with moments u1 and u2 arranged as in the following diagram. Each dipole is depicted as two charges of equal magnitude separated by a distance d. The centre-to-centre separation of the two dipoles is the distance r. The line joining the two dipole...
13. Unit cells (crystal structure)

I'm trying to clarify for myself the difference between a Unit Cell, a Primitive Unit Cell and a Conventional Unit Cell. As far as I know, Primitive Unit Cells contain only one lattice point and are the smallest possible unit cell Unit Cells are the crystal's smallest building block, and...
14. Entropy at different temperatures

^ Well the E/T term in the entropy would automatically go to infinity at 0K...
15. Entropy at different temperatures

I'm having difficulty with this problem: Consider a two state system consisting of N distinguishable and indeppendent particles where each particle can occupy one of two states separated by an energy E. What is the entropy of the system at: (A) T=0 (B) T=infinity I'm assuming this...