percolation

physicists-unlock-another-clue-to-brewing-the-perfect-espresso

Physicists unlock another clue to brewing the perfect espresso

espresso, fluid dynamics, percolation, Physics, Science / /

The team initially tried to use a simple home coffee machine for their experiments but eventually partnered with Coffeelab, a major roaster in Poland, and CoffeeMachineSale, the largest global distributor of roasting gear. This brought industrial-grade equipment and much professional coffee expertise to the project: state-of-the-art grinders, for instance, and a cafe-grade espresso machine, tricked out with a pressure sensor, flow meter, and a set of scales. The entire setup was connected to laboratory laptops via a microchip and controlled with custom software that allowed the scientists to precisely monitor pressure, mass, and water flowing through the coffee.

The scientists measured the total dissolved solids to determine the rate at which coffee is dissolved, comparing brews without a channel to those with artificially induced channels. They found that, indeed, channeling adversely affected extraction yields. However, channeling does not have an impact on the rate at which water flows through the espresso puck.

“That is mostly due to the structural rearrangement of coffee grounds under pressure,” Lisicki said. “When the dry coffee puck is hit with water under high pressure—as high as 10 times the atmospheric pressure, so roughly the pressure 100 meters below the sea surface—it compacts and swells up. So even though water can find a preferential path, there is still significant resistance limiting the flow.”

The team is now factoring their results into numerical and theoretical models of porous bed extraction. They are also compiling an atlas of the different kinds of espresso pucks based on micro-CT imaging of the coffee.

“What we have found can help the coffee industry brew with more knowledge,” said Myck. “Many people follow procedures based on unconfirmed intuitions or claims which prove to have confirmation. What’s more, we have really interesting data regarding pressure-induced flow in coffee, the results of which have been a surprise to us as well. Our approach may let us finally understand the magic that happens inside your coffee machine.”

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why-solving-crosswords-is-like-a-phase-transition

Why solving crosswords is like a phase transition

mathematics, networks, percolation, phase transitions, Physics, Science, statistical physics / /

There’s also the more recent concept of “explosive percolation,” whereby connectivity emerges not in a slow, continuous process but quite suddenly, simply by replacing the random node connections with predetermined criteria—say, choosing to connect whichever pair of nodes has the fewest pre-existing connections to other nodes. This introduces bias into the system and suppresses the growth of large dominant clusters. Instead, many large unconnected clusters grow until the critical threshold is reached. At that point, even adding just one or two more connections will trigger one global violent merger (instant uber-connectivity).

Puzzling over percolation

One might not immediately think of crossword puzzles as a network, although there have been a couple of relevant prior mathematical studies. For instance, John McSweeney of the Rose-Hulman Institute of Technology in Indiana employed a random graph network model for crossword puzzles in 2016. He factored in how a puzzle’s solvability is affected by the interactions between the structure of the puzzle’s cells (squares) and word difficulty, i.e., the fraction of letters you need to know in a given word in order to figure out what it is.

Answers represented nodes while answer crossings represented edges, and McSweeney assigned a random distribution of word difficulty levels to the clues. “This randomness in the clue difficulties is ultimately responsible for the wide variability in the solvability of a puzzle, which many solvers know well—a solver, presented with two puzzles of ostensibly equal difficulty, may solve one readily and be stumped by the other,” he wrote at the time. At some point, there has to be a phase transition, in which solving the easiest words enables the puzzler to solve the more difficult words until the critical threshold is reached and the puzzler can fill in many solutions in rapid succession—a dynamic process that resembles, say, the spread of diseases in social groups.

In this sample realization, sites with black sites are shown in black; empty sites are white; and occupied sites contain symbols and letters.

In this sample realization, black sites are shown in black; empty sites are white; and occupied sites contain symbols and letters. Credit: Alexander K. Hartmann, 2024

Hartmann’s new model incorporates elements of several nonstandard percolation models, including how much the solver benefits from partial knowledge of the answers. Letters correspond to sites (white squares) while words are segments of those sites, bordered by black squares. There is an a priori probability of being able to solve a given word if no letters are known. If some words are solved, the puzzler gains partial knowledge of neighboring unsolved words, which increases the probability of those words being solved as well.

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