Thanks, I believe I have found the cause of my confusion.
The model problem is 1-dimensional (x is the only free parameter). This makes the gradient a scalar in the sense that it is a magnitude that can either be positive or negative.
This also makes the divergence and the gradient basically...
Background: I am currently reading up on homogenization theory.
I have a simple conductivity model (image attached). u is a scalar function (such as potential or temperature).
The textbook proceeds by giving a series expansion for the gradient of u (image attached). the problem is that the...
problem statement:
need to show:
||w||_p^2+||u||_p^2-2(||u||_p^p)^{\frac{2}{p}-1}\Sigma_i(u(i)^{p-1}w(i))
can be bounded as a function of
||w-u||_p^2
where p\in[2,\infty)
work done:
the expressions are equal for p=2, and i suspect that...
given a dictionary \Sigma = \left \{f(),g(),R(,),c_0,c_1,c_2 \right \} and a sentence \phi over \Sigma, I need to find an algorithm to translate \phi to \psi over \Sigma' where \Sigma' = \left \{Q(,,,), = \right \} (Q is a 4-place relation symbol), so that \psi is valid iff \phi is valid.
I...
tnx for the reply, but the groups are distinct, as I am interested in the number of ways to shuffle them around.
you can assume that n/k is an integer.
Hello,
I was given a question (not a HW question..) in which i was asked to calculate the number of ways to sort n numbers into k groups, where for any two groups, the elements of one group are all smaller or larger than the elements of the other group.
The answer is supposed to be...
Hello,
For a current project, I am searching for high operating temperature (200C-300C), Medium Strength (~80 Mpa UTS) and low cost plastics (or at least not extremely expensive).
So far the closest I found is nylon 6/6 reinforced with 30% carbon fiber. I also found something called Vespal...
hello,
I am trying to calculate the location of the center of pressure for a non slender cylinder with a cone shapes nose.
Referencing the internet and notes from a aerodynamics course, all the methods are for slender bodies.
unfortunately, my body is not slender. I am reluctant to go to CFD...
Thank you for the reply.
I am aware that bimetallic coils are used to drive the needle in a thermometer.
What I am asking is if this concept can be used to do heavier work, like spin a pulley (wheel), and If there are examples of such mechanisms.
I attached an illustration to further clarify.
Will this work? If so, How can i calculate the angle of revolution as a function of temperature gradient?
Hello,
I am looking at the possibility of turning a pulley using a bimetallic coil embedded inside.
How can I calculate the thermal "spring constant" of the coil, as a function of geometry and material properties?
Does anyone know of devices with similar actuation mechanisms?
thank you.
Yes, it is common knowledge among some of the more experienced engineers, although there is no concrete theory to back it up. I am just fact checking.
I understand that identical cross sections should have the same stiffness, but allegedly, the fabrication process itself (bending or extrusion)...