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...
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...
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?
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...
I'm trying to derive a formula but can't seem to work the algebra.
I need to combine these two:
V_{1}p_{1} + V_{2}p_{2} = N
V_{1} + V_{2} = V
to get this:
\frac{V_{1}}{V} = \frac{p-p_{1}}{p_{2}-p_{1}}
where p = N/V
If anyone could show me the steps that would be a huge help...
Simple question, and pretty sure I already know the answer - I just wanted confirmation,
Considering the Hermitian Conjugate of a matrix, I understand that
A^{+} = A where A^{+} = (A^{T})^{*}
Explicitly,
(A_{nm})^{*} = A_{mn}
Would this mean that for a matrix of A, where A is
a...
^ Exactly, that's what I'm thinking. I've consulted a textbook and it too has the statement "...the only essential requirement being that k has the same value in both parts of the solution, ie, the part depending on x and the part depending on y". So that would indeed indicate that one can't be...
Ever so sorry, I've missed something off in the transcription of the question: part (a) should read
Find the general solution to the equation d²X(x) / dx² = 0
Now i'm even more confused!!
Hmm, i'm not sure I understand. If I ignore the boundary condition when specifying a general solution for X, I would tend to write it as Ae^kx + Be^kx as that's the general solution for an ODE of d²X / dx² - k²X = 0 where k>0. Likewise, the gen. sol. for Y would be what I currently have for X...
Homework Statement
The edges of a square sheet of thermally conducting material are at x=0, x=L, y= -L/2 and y=L/2
The temperature of these edges are controlled to be:
T = T0 at x = 0 and x = L
T = T0 + T1sin(pi*x/L) at y = -L/2 and y = L/2
where T0 and T1 are constants...
Homework Statement
A thin square plate of side a has one corner at the origin and two sides along the positive x and y axes. If the density of the plate is given by p(x,y) = xy show that its mass is M=(1/4)a^4
If the distance of the mass element dM = pdS from the origin is r the moment of...