Month: September 2022

STASIS. "Why does the bubble not grow over time, if the pressure inside is larger than the pressure outside? We have to take another pressure into account: The pressure from the soap film itself, towards the centre of the bubble. As a result of surface tension the soap film will minimize its surface area by making the bubble as small as possible. Hence the bubble does not grow because there is a balance between the pressure inside the bubble and the pressure from the soap film plus the air pressure from the outside." https://lnkd.in/dVnXykS View in LinkedIn

SOAP BUBBLES INFORM EINSTEIN. "The structure of the equations obeyed by minimal surfaces or soap bubbles is eerily similar to that of Einstein's equations, the centerpiece of his general theory of relativity. Results from the theory of minimal surfaces give information that is important for analyzing solutions to Einstein's equations, and vice versa." https://lnkd.in/dJxmSGq View in LinkedIn

SINGULARITIES. "A singularity is the point at which any given mathematical object -- such as an equation or surface -- breaks down and "explodes", no longer defined. According to a new study, identifying a type of curve in a film of soap can help predict where singularities are likely to occur in other films of soap -- which, in turn, could help researchers understand real-world natural singularities." https://lnkd.in/dX6zRsR View in LinkedIn

THE SYSTOLE. "In geometry, the systole refers to the shortest closed curve around the surface of a 3D object. The researchers found that the systole's properties can determine where on the surface the singularity will occur. If the systole loops around the wire frame, for instance, the singularity will occur at the wire frame -- as in the Mobius strip -- but if it does not, then the singularity will occur at the surface's bulk." https://lnkd.in/dX6zRsR View in LinkedIn

DOUBLE BUBBLE PROBLEM. "In the mathematical theory of minimal surfaces, the double bubble conjecture states that the shape that encloses and separates two given volumes and has the minimum possible surface area is a standard double bubble — three spherical surfaces meeting at angles of 2π/3 on a common circle. It is now a theorem, as a proof of it was published in 2002." https://lnkd.in/dnPcbKg View in LinkedIn

DOUBLE BUBBLE PROBLEM. "In the mathematical theory of minimal surfaces, the double bubble conjecture states that the shape that encloses and separates two given volumes and has the minimum possible surface area is a standard double bubble — three spherical surfaces meeting at angles of 2π/3 on a common circle. It is now a theorem, as a proof of it was published in 2002." https://lnkd.in/dnPcbKg View in LinkedIn

DOUBLE BUBBLE PROBLEM. "In the mathematical theory of minimal surfaces, the double bubble conjecture states that the shape that encloses and separates two given volumes and has the minimum possible surface area is a standard double bubble — three spherical surfaces meeting at angles of 2π/3 on a common circle." https://lnkd.in/dnPcbKg View in LinkedIn

MULTIPLE BUBBLE PROBLEMS. "Over the past few decades, mathematicians have become increasingly interested in “multiple bubble problems.” These problems ask which figure among all those that separately contain a given number of volumes has the least surface area." http://jur.byu.edu/?p=3684 View in LinkedIn

HEXAGONAL BUBBLES. "When two bubbles meet, they will merge walls to minimize their surface area. If bubbles that are the same size meet, then the wall that separates them will be flat. If bubbles that are different sizes meet, then the smaller bubble will bulge into the large bubble. If bubbles that are different sizes meet, then the smaller bubble will bulge into the large bubble. Bubbles meet to form walls at an angle of 120°. If enough bubbles meet, the cells will form hexagons." https://lnkd.in/d7g3Avs View in LinkedIn

FOAMS. "Physical effects drive these interfaces around, and the complexity has to do with the fact that the mechanics occur on a wide range of time and space scales ... It's challenging to build numerical models that allow you to couple these wildly different scales together so that they talk to each other in a way that's accurate and physically reasonable." https://lnkd.in/dGWCSXR View in LinkedIn