Why would a perfectly incompressible ball on a rough surface stop rolling?

We know that the force that opposes the rolling of an object exists due to the deformation of the body's surface at the point of contact which creates a decelerating torque on the body. What if the object is perfectly rigid such that it doesn't deform even a little? In ....

Gianna Gianna: 2 hours ago


About the prime divisors of values of polynomials

Let $P$ be a polynomial having integer coefficients (and degree $\geq 3$), and let $\mathscr P_P$ be the set of prime numbers dividing some value $P(n)$ with $n \in \mathbb Z$. Is it true that $\sum_{p \in \mathscr P_P} \frac1 p$ diverges? The case of polynomials with degree $2$ can ....

Nova Nova: 2 hours ago


How to avoid disrupting the narrative in a scientific paper when you have done too much work

I have been working on a project for almost a year now. This project involves the implementation of a computational method to calculate material properties and the application to different material systems. I have also done original modifications to the method during the course of the implementation. At the moment ....

Violet Violet: 2 hours ago


Very basic question about empty universe

I'm trying to understand the empty universe model. My first textbook (which doesn't cover the empty universe) gives the Friedmann equation as $$\left^{2}=\frac{8\pi G}{3}\rho-\frac{kc^{2}}{R^{2}}$$ Am I right in thinking all I need do is put $\rho=0$ so $$\frac{dR}{dt}=\pm c$$ for $k=-1$ and then say $$R=\pm ct$$ for an expanding or ....

Amelia Amelia: 2 hours ago

Earth Science

Heating and cooling a non-magnetic iron ore causes it to become magnetic?

I'm a potter. I find what I think are iron concretions in a deep red local clay. I fired these iron concretions to cone 6 (about 2100F) and when I removed it from the kiln (room temp) they were then magnetic. I tested for magnetism before and after firing just ....

Luke Luke: 2 hours ago


Unit conversion of Molar Conductivity

I know this might be a silly question but I am confused with different answers of internet. My question is: Molar conductivity is given as: Molar conductivity = $\frac{\kappa}{M}$. S.I. unit of : $\kappa$ is $\pu{Sm}^{-1}$ & $M$ is in $\mathrm{mol \, m^{-3}}$. Thus, Molar conductivity in S.I. is $\mathrm{S ....

Carson Carson: 2 hours ago


How many nested stable (1 Mio years) orbits are theoretically possible?

If we look at our solar system we have the sun which has planet orbits and planets have moon orbits. If we look at the possible size difference from hypergiants to small asteroids why shouldn't it be possible to nest orbits to an astounding degree: supergiant orbit a hypergiant, star ....

Austin Austin: 2 hours ago

Computer Science

Numerically computing the advection equation

I am trying to write a program to compute the advection equation. $$u_t +u_x = 0$$ I use the spectral method for the spatial derivative $u_x$ and the leapfrog method for the time derivative $u_t$. That will give the an equation for the next time step: $$u_{j}^{k+1} = u_{j}^{k-1} - ....

Benjamin Benjamin: 2 hours ago

Wolfram Mathematica

Problem with Get'ting files with << as opposed to Get

When trying to import some files into my Mathematica notebook, I wanted to use ToString to specify the file path. Consider the following MWE, where we export some expression to the directory of the notebook, and immediately import it back: In:= Export]<>"output.txt", 2020]; import1 = Import]<>"output.txt"] Out= "2020" This works ....

Micah Micah: 2 hours ago