All Questions
9
questions
2
votes
0
answers
98
views
Heat from a geothermal well: your take?
Imagine digging a cylinder-shaped (vertical) bore-well of depth $L$ and diameter $r$ ($L\gg r$). The (infinitely thin) cylinder-wall is made watertight and we split the well in half using a kind of ...
- 2,455
2
votes
2
answers
252
views
Probability density for velocity in mechanical energy
To be sure my basic physics isn't rusty...
Consider a 2-D bowled shaped classical potential well within which a classical particle of mass m is rolling.
In this system the conservation of energy ...
- 6,343
2
votes
2
answers
1k
views
Prove $v = \sqrt{\frac{2gRh}{R + h}}$ from Given (below)
Given:
$$F = \frac{mgR^2}{(x + R)^2}$$
$m = \text{mass}$
$g = \text{Acceleration due to gravity}$
$x = x(t)$ is the object's distance above the surface at time $t$.
I believe this is the ...
- 141
0
votes
1
answer
112
views
How to show something does not vary with time?
Consider a glider flying at velocity $\bf u$ (giving $u = |\bf u| $ on its speedometer) at an angle $θ ∈ (−π, π]$ to the horizon.
Positive angle $θ ∈ (0, π/2)$ coincides with the glider’s nose ...
- 145
1
vote
0
answers
80
views
Heat problem with an internal source of heat for which the maximum principle doesn't hold.
Heat problem with an internal source of heat for which the maximum principle doesn't hold. The problem is the following and honestly I don't know how to solve it...
$$u_{t}=u_{tt}+2(t+1)+x(1-x) , 0&...
- 3,766
0
votes
0
answers
51
views
partial differential equation applicational problem
As a Maths student with not much knowledge in physics, I dont understand how the "string" can be "cut" into half at x=L/2. Also, how many initial conditions(data) does this question have apart from yt(...
- 259
2
votes
0
answers
286
views
Basis representation for non-negative, compact support, reasonably smooth spectral function
I was wondering if anyone has ideas on representing a non-negative, compact support (from x=-1 to 1 on the real axis) spectral function as a superposition of basis elements. Ideally, the basis ...
- 21
8
votes
2
answers
475
views
What is the simplest mathematical concept that does not map to a physical phenomenon?
One of my colleagues argues that everything in math proves something in the physical world. For instance, he claims that the existence of math to describe fractals proves the infinite divisibility of ...
- 191
3
votes
3
answers
6k
views
Converting realtive humidity and temperature to an absolute value
I'm a software developer (although math isn't my strong point). I've developed a device to monitor/control my clothes dryer by monitoring the intake air's humidity & temperature, and the exhaust's ...
- 141