DQW

I'd held off on comments about the previous section because there was no prior indication that it had reached completion ..and so I waited. Let me point out, that the above equation is not a vector equation. Either of the following could be, though : [math](1)~~\vec{F} = \frac{1 \cdot (\vec{x}/|\vec{x}|)} {|\vec{x}|^2} [/math] [math](2)~~F_x = \frac{1 \cdot (x/|x|)}{x^2}[/math] where [imath]\vec{F} \equiv F_x \hat{x} [/imath]

cessna : You are much better off describing (in as much detail as possible) your application, and allowing the solutions to evolve out of discussion. You seem to think that you know all there is to know about the required parameters for optimal heat-sink design - and maybe you do. But let me warn you that this is not a trivial problem. The specific heat is not the only parameter. I speak from a little bit of experience in heat-sink design. Another important parameter (besides the heat capacity) is often the thermal conductivity - especially if the power dissipated by the device (being heat-sunk) is highly time-varying. Then there's geometric and other considerations. Yes, copper is often used for heat-sinking, thanks to its excellent thermal conductivity and not terrible heat capacity. Aluminum is also very popular, due to its high specific heat capacity, good thermal conductivity and high strength-to-weight ratio. In general, the specific heat capacity of a metal goes inversely with its molar mass - thanks to Dulong and Petit. Hence, the lighter metals like Mg, Al, Be, B, Li, etc. have a high specific heat capacity.

That would be a much better guess !

Okay, I'm just impatient to see the "real stuff" - the calculation that says ends with "E(at some point inside) = ..."

I think this belonged in the previous section, but I'd like to comment on it before I forget. Just because some particular explanation is flawed does not mean a statement is incorrect. Why go to all these lengths of proving that different proofs are flawed ? That does NOTHING to prove that the property in question is untrue. The ONLY WAY to disprove the theorem is to calculate the field inside and show that it has a non-zero value somewhere. But I have no idea if your intention is to dispove the theorem, or just show that different arguments are possibly flawed...or just discuss related stuff. Which is it ? And what result are you going to arrive at finally ? Are you going to calculate the field inside a sphere and show us how big it is - in other words are you going to show us the magnitude of the error (say as a fraction of the field at the surface) ?

That is incorrect.

No doubt, you mean it "represents the probability of being found within a certain interval of space at a certain time". The probability of being found at a certain location is always zero (unless you can show me a system that has discrete position eigenvalues).

Guessing this is late enough that giving away answers now doesn't result in "cheating", so here's my guesses : (i) 500 (ii) 4725

Why should a lack of expansion of the universe imply no relative motion between two galaxies ?

This statement, however, is priceless ! Just pulling your leg ...

That makes absolutely no sense...to me. Would you please explain this statement using well-defined terminology, or else by defining your jargon ("exponential level") in terms of accepted terminology ?

If the heat capacity of the panels is comparable to the heat capacity of the enclosed gas, then this (former) number will determine the time constant for temperature change. And of course, heat capacity =mC (proportional to mass).

Why do you want to eliminate the square root ? I can't imagine that the square root causes a problem with the plotting ! Nevertheless, you know you can exliminate the sqrt by collecting terms and squareing - only you'll end up with something that has 16 terms ! You could, alternatively, use the parametric form : [math]x = (R + rcos \theta) cos \phi [/math] [math]y = (R + rcos \theta) sin \phi [/math] [math]z = r sin \phi [/math]

double-post; deleted

Just a clarification - the "sphere theorem" says there's no field inside the spherical shell, right ?

If section (1) is now complete, I'd like to point out that the curve provided for the potential energy of the solid sphere is incorrect. You might want to fix that before you continue. Also, in the future, it might be useful to make it clear at the end of each post, whether or not you have completed a section with that post.

That explains the low conductivity value...but raises another problem. You'll now need the mass of the box as well. Or, more accurately, the mass of the vacuum insulation panels. Final, question : what kind of accuracy do you want the answer to ? A rough, analytical approach will probably get you within 20% but if you want to do much better (<5% error), it may take more carefully setup PDEs or an FEM calculation.

And also, are you certain about the total surface area ? That makes the side of the cube about 25 mm. But the wall thickness is 20 mm, so that's not possible either. <gotta go now...will get back to this later, if need be>

1. The specific heat capacity of the material of the walls 2. Is the box airtight ? 3. Is the inside just air or is the box filled with something ? 4. Are you ABSOLUTELY certain about the value of K (=0.00375W/m.K) for the walls ? That number looks way too small - much smaller than for wood (about 10 times) or plastic or even styrofoam (which is essentially air). Heck, it's a better insulator than air !

Okay, that's better. So 5 of the walls have thickness t1 and the 6th has thibkness t2. Correct ? As for the heat flow question, this is still not well-defined. Let me make a guess at one possible interpretation, and you can correct it from there. Now, I guess the box is sitting in an atmosphere of uniform temperature T2, that does not change with time. The initial temperature of the air inside the box is T0. Assuming the air inside the box is essentially isothermal, you want to find the heat flow into the box as a function of time, and hence the temperature of the inside as a function of time. There are no other sources or sinks (of heat). Am I even close ?

Maybe a good way to think of something mechanical is in terms of mechanical energy - namely, kinetic energy and the forms of potential energy that are considered "mechanical" - gravitational and elastic. So, if a device deals with these forms of energy (macroscopically, of course), it is a mechanical device. So, in that context, I would not call a lens "mechanical".

You have not defined your problem sufficiently. Can you throw in a drawing of what you want ? If you want to make a cube, all its sides must be equal (by definition), so I don't understand what these widths are, and why one is different. And what quantity are you calculating by taking the average ? Yes, you calculated the average of 6 numbers but what does this average represent in your box ? Also, it is impossible to have a cuboid where 5 faces have a certain width and one face has a different width. But you could build a distorted box that comes "close" to this. And as for heat flow, surely you don't expect us to tell you how to calculate the heat flow into the box, when you've told us absolutely nothing about the heating mechanism or any physical conditions associated with the box and/or the heating scheme ?

MetaFrizzics, do you have references to stuff that actually got published in peer reviewed journals ? People are going to be much less likely to take the effort to read through stuff if there is no guarantee that it's been through peer review. And since you insist on pushing your non-mainstream ideas, would you please go through at least the basic minimum of : (i) citing experiments that show the superiority of these models over accepted models (such as GR, SR, the Std Model, etc.) (ii) showing mathematically, the differences in some key results from those predicted by the mainstream formulation, and estimate the numerical order of these differences, and (iii) state the postulates upon which your model is built. What I'm saying is this : Instead of making completely unsubstantiated claims like you did in the OP, or resorting to rhetoric (the Oktoberfest comment), or making half-baked statements (Pauli Spin Matrices for a diatomic gas), please at least do a thorough job and give your model a chance.

Different densities, that's all. Different ratios of bone tissue to muscle tissue to fat, I guess.

What part didn't you get ? Let's look at PG's solution #2 again : First join BD (at least mentally). Since AD is a diameter, <ABD is a right angle ("angle in a semicircle is a right angle") Hence triangles ACB and BCD are similar (all angles are equal) So, AC/BC = BC/CD (corresponding sides are in the same ratio) Thus, AC*CD = BC^2 But from Pythagoras, BC^2 = AB^2 - AC^2 ... ...plug in and complete...