Tuesday, February 16, 2016

Janus Words

“Life after xyz is all downhill.”

Does that mean things get easier as in riding a bike downhill? Or does it mean things deteriorate and head south, perhaps like a stock chart?

Words like these that have somewhat opposite connotation, are amusing and frustrating in equal parts. Here are some interesting collections of such words.

I was at a conference last month, and in the polymer simulation talks I went to, I noticed that the word “explicit” could mean a calculation was easy or hard depending on the noun it modified.

In explicit solvent simulations of proteins or surfactants in water, for example, we explicitly resolve all the water molecules. Typically, the number of water molecules is very large, and this drives up the computational cost. This makes “explicit solvent” calculations more time consuming, than implicit solvent simulations, which model the effect of the solvent indirectly.

The reward for the extra effort is generally greater accuracy.

In the numerical solution of a differential equation (like Newton’s law), an explicit method, marches in time by using quantities that are known from the past. The canonical example is Euler’s famous method. In contrast, implicit methods, involve solving systems of equations at each time step, since the future value of a quantity is not expressed purely in terms of quantities known from the past. Implicit methods are typically more demanding to set up and execute than explicit methods of comparable accuracy.

The reward for the extra work is generally enhanced numerical stability.

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