Recent content by samuelandjw

Suppose an impurity particle/atom with 5 valence electrons is induced into a bulk material whose atoms have only 4 valence electrons. The "excessive" electron of the impurity particle can be promoted to a higher energy state such that we can say the impurity particle/atom is "ionized". In this...

I think my real problem is: when the boundary condition on the bottom edge is T(x,0)=f(x), BC on left edge is T(0,y)=0, BC on right and top edges are perfect insulation (suppose we don't care about the values on the four corners), is it correct to obtain the Fourier coefficients using...

I think you can write the y-component solution as \cosh(k_n(a-y))

Thanks for your reply. That post does not seem very useful though.

Not really. IMHO, the value on the corner is not particularly important. And, C1 is not equal to C2.

The length of the side of the square is a. The boundary conditions are the following: (1) the left edge is kept at temperature T=C2 (2) the bottom edge is kept at temperature T=C1 (3) the top and right edges are perfectly insulated, that is \dfrac{\partial T}{\partial x}=0,\dfrac{\partial...

Thanks for your reply. We can surely say that J_1(x),J_2(x) are positive functions between x=0 and x=1 because the first nontrivial zeros are larger than 1. One has to somehow use the information of the location of zeros to reach this conclusion. Suppose we don't have this information, is it...

Use the orthogonality relation of Bessel function to argue whether the following two integrals are zero or not: \displaystyle\int_0^1J_1(x)xJ_2(x)dx \displaystyle\int_0^1J_1(k_1x)J_1(k_2x)dx, where k_1,k_2 are two distinct zeros of Bessel function of order 1. The textbook we are using is...

Thanks! Starting from the result is indeed easier!

Sorry about the typo. But my problem remains. Could you show a bit more on the decoupling process?

Hi, Suppose we have these two functions and their z-transforms are P(r,z)=\sum_{t=0}^{\infty}P(r,t)z^t and F(r,z)=\sum_{t=0}^{\infty}F(r,t)z^t. Now we are going to transform the following convolution of P and F: \sum_{t'\le{t}}F(r,t')P(0,t-t'). The result is said to be F(r,z)P(0,z). But I don't...

The article on SA describes an alarming tendency in some fields of physics, but don't confuse tendency with what it is now. If you changed you title to "Will physics be a junk science", at least fewer people would be pissed off. Moreover, "soft" science is not junk science. I don't know...

Thanks for your reply. In my problem, g_i is given and arbitrary, so in general g_i is not a constant sequence.

Hi, The problem is to solve (1-g_{i+1})P_{i+1}-P_{i}+g_{i-1}P_{i-1}=0 for P_{i} with boundary condition P_{i}=P_{i+L}, g_{i}=g_{i+L} Can anyone provide any guide of solving this type of recurence equation? Thank you!

Hi, I have been searching the internet for some gentle introductions of Fibonacci chain, but so far I haven't found anything. I wonder if anyone can recommend some good introductions to me, e.g. a book, an article... Thank you.