Can I replace the Sun with a non-nuclear equivalent?

D

Dmyt

The Scientocratic Hivemind has killed the Fire Deity at the cost of erasing the Earth's sun. For the sake of the lifeforms of this Earth before it goes away, it refines the Deity's corpse into a Sun replacement. Now, the eternally burning corpse is big and dense enough to have the same gravity as the Sun and it radiates an equivalent amount of heat and light. Essentially, the Fire Deity's corpse is a literal ball of fire and light that gains its energy from some supernatural source, unlike a regular star derived through nuclear processes. Everything else characteristic of a normal star isn't present in the corpse Sun.

From the perspective of the Earth and solar system, would this corpse Sun be an adequate replacement? In other words, does our actual Sun have some other intrinsic quality(which the corpse Sun doesn't have) that's necessary to maintain the integrity of the solar system?
 

Unreplied Threads

What common proverb does this string refer to?

What common proverb is referenced by this three-character string?

ᚷᛖᚨ

Chromatic number of distance graphs on the integers with restricted prime divisors

  • MistressMadeline
  • Mathematics
  • Replies: 0
Let $P$ be a finite set of prime numbers. Define the distance graph $G(P, n)$ on the vertex set $V = \{1, 2, ..., n\}$ where two vertices $a$ and $b$ are connected by an edge if and only if $|a-b|$ is a product of primes in $P$. Denote the chromatic number of $G(P, n)$ by $\chi(G(P, n))$.

Can we find a function $f(k)$ such that $$ \chi(G(P, n)) \leq f(k) $$ for all $n$ and all sets $P$ with $|P| = k$?

Minimal bipartite graph density in the log-edge-density version

A graphon is a bounded measurable symmetric function $W:[0,1]^2\to [0,1]$. Let $\mathcal{W}$ denote the set of all graphons. For any $p\in [0,1]$, let $\mathcal{W}_p$ denote the set of all graphons $W$ such that $\int W=p$. For any graphon $W$ and any bipartite graph $H$ with bipartition $(A,B)$ where $|A|=v_1,\ |B|=v_2$, the density of $H$ in $W$ is defined as: $$t(H,W)=\int_{[0,1]^{v(H)}}\prod_{ij\in E(H)}W(x_i,y_j)\prod_{i\in A} dx_i \prod_{i\in B} dy_j .$$ Define $h(H,W)=\log_{\int W}t(H,W).$ For any $p\in (0,1)$ does the following hold? $$\max_{W\in\mathcal{W}}h(H,W)=\max_{W\in\mathcal{W}_p}h(H,W).$$

Positivity for the mild solution of a heat equation on the torus

Consider the following linear parabolic equation in one spatial dimension for $u=u(x,t)$ on the one-dimensional torus $\mathbb{T}^1,$ meaning $x \in \mathbb{T}^1$ and $t \in (0, T]:$ $$ \partial_t u- a \cdot\partial_{x}^2u +g(x,t)\cdot u= f(x,t),$$ with the constant $a > 0,$ and the given functions $g,f \geq 0,$ subjected to the strictly positive initial condition $u_0(x) \in C^1(\mathbb{T}^1).$ Let $f,g \in L^{\infty}((0, T); L^1(\mathbb{T}^1)).$

I need a well-posedness result (existence, uniqueness and positivity of the solution in the mild sense) for this equation on the torus.

A mild formulation is given by (representing the flat torus by $[0,1]$ and periodic boundary conditions): $$ u(x,t) = \int_{0}^{1} G(x-y,t) u_0(y) \, \mathrm{d}y + \int_{0}^{t} \int_{0}^{1} G(x-y,t-s) (f - g \cdot u)(y,s) \, \mathrm{d}y\mathrm{d}s, $$ where $G = G(x,t) > 0$ is the heat kernel on the one-dimensional torus. The existence of a local solution $u \in L^{\infty}(\mathbb{T}^1 \times (0,T))$ would follow from a Picard-Iteration, at least for small enough times. Since the right-hand side of the mild formulation would define a contraction from $L^{\infty}(\mathbb{T}^1 \times (0,T))$ to $L^{\infty}(\mathbb{T}^1 \times (0,T)).$ (I supposed semigroup arguments would fail here since $g$ depends on time.)

But how can I show positivity for the local solution? (The problem is I don't have enough regularity for the solution to use a maximum principle.)

Would be very grateful for help!

Subspaces of $\ell_\infty^3$

  • A beginner mathmatician
  • Mathematics
  • Replies: 0

Soldering Iron - How long to heat the pad and component leads?

  • Dr Negative
  • Physics
  • Replies: 0
I'm fairly new to soldering and am curious as to how long it's supposed to take to heat the component contacts and copper pads on a PCB to get to solder-melting temperature.

I'm using a YIHUA 939D+ III EVO Digital Soldering Iron Station set for 350 Celsius which I bought new just a few months ago; the tip is clean and tinned, and it's placed so it's touching both the pad and the component, but it seems to take much too long to actually heat anything. Usually around 45-60 seconds if I'm lucky.

I'm really stumped here as to whether this is normal, I just suck at soldering, or the iron is defective. (I have a feeling it's that I suck, though.)

Models have a weird dotted-like texture when viewing in Material Preview & Rendered, how do I fix this issue?

  • Vin Solo2000
  • Technology
  • Replies: 0
I recently got Blender v4.2.1 and already I'm starting to have a render issue when viewing in Material Preview and Rendered on EEVEE Render engine but when I go into Cycles Engine, it looks normal only in Rendered viewport. I decided to check if it was something with the nodes I use by loading a new General and turns out it has nothing to do with the nodes I use as the white dot texture issue still persisted, even for a model that doesn't have nodes. And it's definitely not any textures I give models as the cube doesn't have any textures added either.

Is there a way I could fix this issue so I could see the renders without any weird texture bug?

Render Comparison
Top