The basic gist of how Monte Carlo simulations work is that you randomly select inputs, perform calculations on the randomly-selected inputs, and collect the outputs. This process is repeated several times (perhaps thousands, tens of thousands, or even more! As with any statistical sample, the more, the better), and in the end, all the outputs are gathered together and analyzed. To randomly select inputs, you’ll need to specify boundaries for which inputs can be selected from. A statistical model can help with this, such as a Gaussian distribution, which is a fancy term for the familiar “bell curve.” As for the aggregated outputs, statistical analysis would make sense in order to make sense of thousands of data sets. Basically, statistics is a useful tool that compliments the Monte Carlo technique. Also, generally computers are used to perform a Monte Carlo simulation due to the large number of repetitive calculations required.

This is what a bell curve looks like.

Monte Carlo simulations can be used in space sciences. For example, if one wants to analyze the risk of failure of a spacecraft in orbit, one can perform a Monte Carlo simulation with random inputs for how the spacecraft begins its orbit (speed, physical orientation, etc.), since that state cannot be predetermined accurately and instead can be modeled statistically. Then, the laws of orbital mechanics can be applied to the inputs to produce outputs that can be analyzed later. A more simple example of where the Monte Carlo method is used is the classic game of Battleship. Initially, a player would randomly guess locations for where a battleship is located. After the player scores a hit, the player would follow an algorithm (guess points that are in line with the hit) to sink the battleship (the outcome).

(Image from Wikipedia)

From the article:

In computer-animated movies, sound can be added after the fact from recordings or by Foley artists. But as virtual worlds grow increasingly interactive and immersive, the researchers point out, sounds will need to be generated automatically to fit events that can’t be predicted in advance. Recordings can be cued in, but can be repetitive and not always well matched to what’s happening.

“We have no way to efficiently compute the sounds of water splashing, paper crumpling, hands clapping, wind in trees or a wine glass dropped onto the floor,” the researchers said in their research proposal.

Along with fluid sounds, the research also will simulate sounds made by objects in contact, like a bin of Legos; the noisy vibrations of thin shells, like trash cans or cymbals; and the sounds of brittle fracture, like breaking glass and the clattering of the resulting debris.

Faucet Simulation

The article explains that the calculations for the simulations are based on physics – how particles in a model would vibrate and thus emit sound waves if the model existed in real life. Specifically for water, the sounds that we hear when water is poured into a container come from tiny bubbles in the water that are repeatedly contracted and expanded. This is essentially a vibratory motion, and these vibrations create the sounds that we hear from water.

What does this mean for our everyday lives? It has the potential to greatly enhance the quality and increase the scope of computer-animated movies, software, and simulations, to name a few things.

By the way, foley artistry is pretty cool!

(Image from the Cornell Chronicle.)

Experiments are performed in a real-world context, while simulations are run under the most ideal conditions. Now, we all know that things in real life are not perfect, but simulations assume these “perfect” conditions. For example, the temperature distribution in a solid object is almost never perfectly uniform (meaning the temperature is the same at all points inside the object) in reality, but in order to simplify a problem in heat transfer, an assumption of uniform temperature distribution is made. Simulations often make simplifications and assumptions like these.

It is fairly difficult to perform large-scale tests in a space environment.

Experiments are usually performed in order to collect data that is representative of a real-life system, and analyze the data afterwards. For example, someone who is interested in seeing how well various insulations work on a pipe can use each of the different insulations in normal everyday use of the pipe, collect data on how well the pipe was insulated for each insulation, and interpret the results. This is what an experiment can be like. Experiments are arguably more accurate than simulations in the sense that they are performed under real-world conditions, and we as people who live in this world usually care about how things work in the real world, not in an idealized perfect setting.

After these descriptions of what experiments and simulations are and how they differ, when are simulations helpful? In settings that are difficult to access in real life, such as outer space. Spacecraft missions are often rehearsed in simulations of a space setting because it is rather difficult to run an experiment of such a large scale in outer space.

Hopefully this sheds a bit of light on what I think the main differences are between experiments and simulations. Have a great day!