Recent content by cathalcummins

Hi there!I'm working on a physics problem where there is a liquid droplet (not necessarily spherical) on a plane. Transforming from cylindrical coordinates to bispherical: (r,\phi,z)\mapsto (\xi,\eta,\varphi;a) such that r={\frac {a\sin \left( \eta \right) }{\cosh \left( \eta \right) +\cos...

I'm modelling low Re flow of liquid past a sphere close to a sliding wall with COMSOL. I'm trying to extract the drag dependence on distance from the wall. Problem: The other walls of cube are causing noticeable effects on drag (even though Cube length = O(10*r)) as I get closer to the centre...

Hi all, The problem at hand is a bubbly flow in a cylinder: I'm using an FEM to identify how the walls effect the drag on bubbles in a flow. To test my results I want to set up an infinite cylinder with randomly distributed spheres and then average the Navier-Stokes equations over the entire...

That sounds about right, thank you. Fortunately, since I wrote the last post, I discovered that the method was failing for a different reason. The "initial profile" I used to start the relaxation procedure was a very poor choice.

Hi there, I am working on a problem in Fluid dynamics. I've written a code in MATLAB which finds the shape of the free surface of the liquid based on Newton Relaxation. The code is fairly robust and produces good results which agree with current papers on the same problem. Unfortunately...

After searching long and hard I discovered that the "identity element" symbol may be inserted into a LaTeX document via the bbold package. However, loading this package conflicts with the amsmath/assymb package which I use to give me blackboard font Real numbers etc as above. My question is...

That has cleared the picture up considerably - I was aware of the connection between the "unit vectors" and was more concerned with v_n v_m= v_{n+m} idea. With regards the underlying field in each case; it seems a little much to use a different field for each conversion and expect it to go...

As far as conversions between bases go: is there any advantage representing a number as a vector in an n-th dimensional vector space? So, say I wish to represent the number 73 in base 10, it'd be 73=7\times \vec{v}_1+3\times\vec{v}_0 where \vec{v}_n=10^n, so its representation is on...

Homework Statement If \omega \in \Lambda^{r}(V^*) and \nu \in \Lambda^{s}(V^*) show that \omega \wedge \nu \in \Lambda^{r+s}(V^*) Homework Equations \omega \wedge \nu (v_1,... ,v_r,v_{r+1},... ,v_{r+s})= \frac{1}{(r+s)!} \Sigma_{\sigma}(-1)^\sigma...

If we were to generalise this to general 3-forms. \omega \in T^{0}_{3} such that T_{ijk}=-T_{jik}. The thing I am trying to prove is that n-forms form a vector space, and to find the dimension of this space. To make generalisation easier, could you please clarify the following reasoning. Would...

Looking back on this question, I suppose I could cut out all the texing and just simply ask: If I show that \exists a \Lambda \in O(1,3) which the Schrodinger Equation does not transform covariantly under, is this enough to say that the SE isn't Lorentz Covariant. Because trivially, if I take...

This is a question involving the semantic on the statement "The SE is not Lorentz invariant" I'm trying to prove that the SE isn't Lorentz Invariant. I think I've showed it. I'd just like some input on my argument. Under the change of coordinates: x^\mu \mapsto...

Doing space time symmetries through Group theory. I completely understand how do derive, say SO(2), from its generators. And I understand how, as so(3) obeys the same commutation relations as Angular Momentum, that Angular Momentum is just the generator of rotations. Now, I wish to use the...

Thank you George. I was unsure of my reasoning. However, I did mention implicitly that L^{\downarrow}_{+} doesn't contain the identity when I said: Thank you again. Much appreciated.