Recent content by Like Tony Stark

"Newtonian and Variational Formulations of the Vibrations of Plates With Active Constrained Layer Damping" by Chul H. Park and Amr Baz. See eqs. 21, 35, 36 and appendix.

Hi. I'm not sure if I understood your comment correctly, but in my post I wrote both the author's results and mine. We differ in K_{12} and K_{15}. On the other hand, what you said about using \cos\left(\frac{m\pi x}{a}\right) \sin\left(\frac{n\pi y}{b}\right) instead of X'(x)Y(y) is the same...

Hello, This is not homework but I am trying to replicate some results I found in a paper. In short, the situation is as follows. The following equation is given: A_{11e} \frac{d^2 u_1}{dx^2} + (A_{12e} + A_{66e}) \frac{d^2 v_1}{dxdy} + A_{66e} \frac{d^2 u_1}{dy^2} + \frac{G_2}{h_2} \left( u_3...

I tried using the Wigner matrices: $$\sum_{m'=-2}^{2} {d^{(2)}}_{1m'} Y_{2; m'}={d^{(2)}}_{1 -2} Y_{2; -2} + {d^{(2)}}_{1 -1} Y_{2; -1} + ...= -\frac{1-\cos(\beta)}{2} \sin(\beta) \sqrt{\frac{15}{32 \pi}} \sin^2(\theta) e^{-i \phi} + ...$$ where $$\beta=\frac{\pi}{4}$$. But I don't know if...

I've already calculated the total spin of the system in the addition basis: ##\ket{1 \frac{3}{2} \frac{3}{2}}; \ket{1 \frac{3}{2} \frac{-3}{2}}; \ket{1 \frac{3}{2} \frac{1}{2}}; \ket{1 \frac{3}{2} \frac{-3}{2}}; \ket{0 \frac{1}{2} \frac{1}{2}}; \ket{0 \frac{1}{2} \frac{-1}{2}}; \ket{1...

Yes, I know that ##\vec{S_1} \cdot \vec{S_2}=\frac{1}{2} [S^2-(S_1)^2-(S_2)^2]##. That means that the energy levels are: $$E=-\frac{\lambda}{2h^2} \delta(x) [s(s+1)-s_1(s_1+1)-s_2(s_2+1)]$$ $$E=-\frac{\lambda}{2h^2} \delta(x) [s(s+1)-\frac{11}{4}]$$ with ##s=\frac{1}{2}, \frac{3}{2}##...

1) The Hilbert space for each particle and the system are: ##H_1={\ket{\frac{1}{2} \frac{1}{2}}; \ket{\frac{1}{2} -\frac{1}{2}}}## ##H_2={\ket{1 1}; \ket{1 0}; \ket{1 -1}}## ##H=H_1 \otimes H_2## 2) I'm not sure what "considering the total Hamiltonian" means, but I think that the two CSCO...

Thanks for your answer! Let's see if I've understood... So, for ##\alpha## I have to calculate ## \frac{\partial V}{\partial T}=\frac{\partial}{\partial T}## ##\frac{-aVT^{5/2}e^{\frac{\mu}{RT}}}{P}##, for constant ##P## Then, for ##c_P##, I have to calculate ##\frac{\partial^2 A}{\partial...

Thanks! I have arrived to ##c_P=\frac{2T^2}{9B^3P}## and ##\alpha=\frac{NT^2}{9B^3P^2V}##. But when I replace this identities in the expression for ##\mu## I get ##\mu=0##

Hello! It's from a purely thermodynamics class. The reference book in my course is Callen's Thermodynamics.

Hi All the expressions for calculating the properties are given in terms of ##S##, ##V## and ##N##. Should I find the energetic representation and then apply the formulas, or is there another way? Then, for finding the energetic representation, I know that ##A=U–TS–\mu N## But I want all these...

Hi ##\mu=\frac{\alpha TV–V}{N c_P}##. So, firstly, I have to calculate ##\alpha## and ##c_P##. So ##\alpha=\frac{1}{V} \frac{\partial V}{\partial T}## at constant ##P##. I can write ##U=PV##, then I replace it in the equation of ##T##, solve for ##V## and then I differentiate with respect to...

I've attached images showing my progress. I have used Maxwell relations and the definitions of ##\alpha##, ##\kappa## and ##c##, but I don't know how to continue. Can you help me?

Ok But apart from the elastic force, is the solution ok?

So should I consider just one degree of freedom?