Recent content by babagoslow

That is what I am calculating. As we know, for a sphere, V(r), A(r) and it's easy to calculate \frac{dA}{dV} = \frac{dA}{dr} \frac{dr}{dV}. But what happens when these two quantities are functions of more than one variable, ie, V(a,h), A(a,h)? Then how would we calculate \partial A/\partial V?

Yes, that's right, the cap is not on a given sphere. There are two parameters.

a , h are also related by a contact angle \theta. But you can't express a spherical cap uniquely in just that one variable. I guess I don't really understand what you meant. From what I understand a spherical cap is uniquely described by at least two parameters - one possible combination is the...

Dear Pasmith, I have been looking at this problem again and in fact I don't think it is possible to find the derivative dA/dV like you mentioned. Let x\equiv a/h. A^3 = V^2 f(a/h) = V^2 f(x) 3A^2 dA = 2V dV f(x) + V^2 \frac{df}{dx} dx The complication comes in when you are trying to solve for...

Thanks for the advice HallsofIvy and pasmith! Pasmith, yes, you were right, I was able to evaluate the derivative by expressing the functions in terms of f(h/a). Thanks for the insight!

Jakeness, I was glad to read your posts and see your thinking. I think you are sensible and you'll definitely avoid some of the rather horrible fates that await some PhD graduates. One tip I can give you is to go to Google Scholar, and in the search box, type in, for example "label:complex...

I would say familiarise yourself with calculus and/or linear algebra if your basics aren't up to scratch. The gap will naturally be much larger if you're transferring to a better university. I'm not familiar with the US-style honours system – in my school honours just means you write a senior...

If dV, dA were just functions of one variable, it would be straightforward. But here there are two variables, and perhaps I would have anticipated a chain rule of the form \frac{dA}{dV} = \frac{\partial A}{\partial a}\left( \frac{\partial a}{\partial V} + \frac{\partial h}{\partial V} \right) +...

Computational physics is a huge field that can range from statistical analysis (for instance, time series of the stock markets), to agent based models (traffic control, economic simulations, and other complex systems), to doing the heavy duty work in various theoretical branches of the natural...

Homework Statement Consider a spherical cap, for which the surface area and volume is A(a,h) = \pi(a^2 +h^2) V(a,h) = \frac{\pi h}{6}(3a^2 +h^2) What would the aspect ratio dA/dV be? The Attempt at a Solution Clearly we would have dA = 2\pi a da + 2\pi h dh dV = \pi ha da +...

If I have a hot wire, the distribution of its temperature with respect to radius (from the center of the wire) and time follows the heat/diffusion equation. However, now consider two wires, or even an array of many such wires. Say we can ignore the z coordinate and treat them as a point...

Hi Pasmith, thanks, I understand it now!

I'm trying to implement a numerical code for the diffusion equation with moving boundaries. I have no problems with the numerical implementation, but with the transformation of coordinates. In spherical coordinates, the diffusion equation is \frac{\partial c}{\partial t} = D...