# Tag Info

### Good examples of "two is easy, three is hard" in computational sciences

One example that appears in many areas of physics, and in particular classical mechanics and quantum physics, is the two-body problem. The two-body problem here means the task of calculating the ...
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### Good examples of "two is easy, three is hard" in computational sciences

In one and two dimensions, all roads lead to Rome, but not in three dimensions. Specifically, given a random walk (equally likely to move in any direction) on the integers in one or two dimensions, ...
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### Good examples of "two is easy, three is hard" in computational sciences

A famous example is the boolean satisfiability problem (SAT). 2-SAT is not complicated to solve in polynomial time, but 3-SAT is NP-complete.
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### Good examples of "two is easy, three is hard" in computational sciences

In social choice theory, designing an election scheme with two candidates is easy (majority rules), but designing an election scheme with three or more candidates necessarily involves making trade-...
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Accepted

### Conserving Energy in Physics Simulation with imperfect Numerical Solver

There are a few ways to conserve energy during ODE integration. Method 1: Symplectic Integration The cheapest way that is to use a symplectic integrator. A symplectic integrator solves the ODE on a ...
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### Good examples of "two is easy, three is hard" in computational sciences

Here's one close to the hearts of the contributors at SciComp.SE: The Navier–Stokes existence and smoothness problem The three-dimensional version is of course a famous open problem and the subject ...
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### What language should I use when teaching an undergraduate course in computer programming?

In 2014, I would've said Python. In 2017, I wholeheartedly believe that the language to teach undergraduates is Julia. Teaching is always about a tradeoff. On one hand, you want to choose something ...
• 11.6k
Accepted

### Why should I renormalize physical variables?

This question is very closely related to (and possibly a duplicate of) Is variable scaling essential when solving some PDE problems numerically?. There are still good practical reasons to ...
• 29.8k
Accepted

### Why is leapfrog integration symplectic and RK4 not, if the latter is more accurate?

TL;DR: It depends on what kind of accuracy you need. Energy conservation does not automatically equal accuracy. Suppose, you want to simulate the solar system, and you are using a solver that – to ...
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### Good examples of "two is easy, three is hard" in computational sciences

Simultaneous diagonalization of two matrices $A_1$ and $A_2$: $$U_1^T A_1 V = \Sigma_1,\quad U_2^TA_2V=\Sigma_2$$ is covered by existing generalized singular value decomposition. However, when the ...
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Accepted

### What are the differences between CFD simulations and realistic ocean/atmosphere model simulations?

Atmosphere and ocean have highly-stratified flows in which the Coriolis force is a major source of dynamics. Maintaining geostrophic balance is extremely important and many numerical schemes are ...
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