Thank you for your reply.
So if ##L'## is the stretched length as described by you, then the needed equation above follows immediately. I am, however, still not sure about that ##L'##. Can you explain where your last equation comes from (as shown below; I have added parenthesis where I thought...
Homework Statement
Reading the very first chapter of Weinberger's First Course in PDEs, I stumbled over the derivation of the tensile force in the horizontal direction. The question was posted already in this thread: https://www.physicsforums.com/threads/one-dimensional-wave-equation.531397/...
Rotationally invariant in this context means that
T_{ij} = T'_{ij} = R_{ip} R_{jq} T_{pq}
For example, for the Kronecker delta this is pretty straight forward to show:
\delta_{ij} = R_{ip} R_{jq} \delta_{pq} = R_{ip}R_{jp} = \delta_{iq}\text{,}
where we have used that R_{ij} are orthogonal...
It is pretty straight forward to prove that the Kronecker delta \delta_{ij} is an isotropic tensor, i.e. rotationally invariant.
But how can I show that it is indeed the only isotropic second order tensor? I.e., such that for any isotropic second order tensor T_{ij} we can write
T_{ij} =...
Alright, thanks for the explanation. This leaves me with two questions:
T and S are not viewed as a pair of generalized forces/coordinates in this context?
What is the argument for needing n+1 variables in order to completely determine all thermodynamic properties?
I am trying to understand why I can specify the specific volume v of a fluid element as a function of the equilibrium pressure, p, and the equilibrium entropy, s. This is for example done in this article http://www.sno.phy.queensu.ca/sno/str/SNO-STR-95-051.pdf , on this website...
One page 5 in Landau & Lifshitz Fluid Mechanics (2nd edition), the authors pose the following problem:
The authors then go on to give their solutions and assumptions. Here are the important parts:
For the condition of mass conversation the authors arrive at (where ρ_0=ρ(a) is the given...
Can somebody please change the name of “Lifgarbagez”? It hurts my eyes reading this. The man's name is Lifshitz, which is pretty close to the Russian Лифшиц.
Somebody is going to patent "the moon" or "mars" (or rather something like "travelling to an extraterrestrial astronomical formation by rocket-propelled means), and then going to sue the hell out of you because they thought of that first. :-D
As regards the sustainability: your are absolutely...
You misunderstand me. I am myself considering going into the financial industry if my plans for landing a spot in academia fails.
I am also not as ignorant as to believe that the financial system as such is the root of all evil.
However, I very strongly believe that the current system is...
Well, that's the funny thing - what does it mean that "everyone can agree"? If you look at the situation after the 2008 crisis, the Europeans wanted to enact much stricter rules on the financial markets (well, except the British, but since they are economically completely incompetent, that's to...
This goes a little too far in this thread, but: what you describe there is not capitalism, but a (genuine) free market, which is kept free and open. Often they go together, but are not the same thing. If you put your emphasis on free markets and personal freedom - and here you have to especially...