30 | May | 2022 | Physics Town

A First Course in String Theory

Verify that for $\displaystyle{d=3}$ equation (3.74) coincides with (3.67).

~~~

Eq. (3.67):

$\displaystyle{E(r) = \frac{q}{4 \pi r^2}}$

Eq. (3.74):

$\displaystyle{E(r) = \frac{\Gamma\left( \frac{d}{2} \right)}{2 \pi^{\frac{d}{2}}} \frac{q}{r^{d-1}}}$

When $\displaystyle{d=3}$ ,

$\displaystyle{\begin{aligned} E(r) &= \frac{\Gamma\left( \frac{3}{2} \right)}{2 \pi^{\frac{3}{2}}} \frac{q}{r^{2}} \\ \\ &= \frac{\sqrt{\pi}}{2} \frac{1}{2 \pi \pi^{\frac{1}{2}}} \frac{q}{r^{2}} \\ \\ &= \frac{1}{4 \pi} \frac{q}{r^{2}} \\ \\ \end{aligned} }$

— Me@2022-05-30 01:15:00 PM

If a flight-simulator could transport you from A to B then it would be a flight-emulator.

An emulator can replace the original for real use.

A Virtual PC emulates a PC.

A simulator is a model for study and analysis.

An emulator will always have to operate close to real-time. For a simulator that is not always the case. A geological simulation could do 1000 years/second or more.

— edited Dec 26, 2018 at 17:37

— answered Oct 18, 2009 at 11:25

— Henk Holterman

Virtual PC does not emulate, it virtualizes. QEmu, on the other hand, does emulate. In both cases, the name should be a hint. – Jörg W Mittag Oct 18, 2009 at 12:36

— Stack Overflow

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