The secret to good digital animation is physics

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This article is a little different from the fare you’re used to getting from me: it’s for SIAM News, which is the magazine for members of the Society for Industrial and Applied Mathematics (SIAM). The audience for this magazine, in other words, is professional mathematicians and related researchers working in a wide variety of fields. While the article contains equations, I wrote it to be understandable even if you skip over the math.

The Serious Mathematics of Digital Animation

For SIAM News:

While computer simulations have a wide range of uses, their goals are generally similar: find the simplest model that recreates the properties of the system under investigation. For scientific systems, this involves matching observed or experimental phenomena as precisely as necessary.

But what about movie simulations? Should they match the processes they replicate so closely? Computer-generated imagery (CGI) is a common feature in both animated and live-action films. For these CGI systems, creating visuals that look right is an important task. However, Joseph Teran of the University of California, Los Angeles believes that starting from physical models is still a good idea.

During his invited address at the 2018 SIAM Annual Meeting, held in Portland, Ore., this July, Teran pointed out that beginning with a mathematical system is often easier than drawing from real life. Many movies model a system’s various forces and internal structures with partial differential equations (PDEs) for this reason. While solving these equations to produce CGI is computationally expensive, such methods have become powerful tools for creating realistic visual cinematic effects.

[Read the rest at SIAM News]

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The knotty problem of DNA tangling

[ This blog is dedicated to tracking my most recent publications. Subscribe to the feed to keep up with all the science stories I write! ]

This article is a little different from the fare you’re used to getting from me: it’s for SIAM News, which is the magazine for members of the Society for Industrial and Applied Mathematics (SIAM). The audience for this magazine, in other words, is professional mathematicians and related researchers working in a wide variety of fields. While the article contains equations, I wrote it to be understandable even if you skip over the math.

I will also have you know, I only included one of the many knot-theory puns I came up with while writing the piece. Professionalism, people. Professionalism.

Untangling DNA with Knot Theory

For SIAM News:

Long before there were sailors, nature learned to tie—and untie—knots. Certain DNA types, proteins, magnetic fields, fluid vortices, and other diverse phenomena can manifest in the form of loops, which sometimes end up tangled. But knots, kinks, and tangles are often undesirable for the system in which they occur; for instance, knotted DNA can kill its cell. In such cases, nature finds ways to restore order.

Mariel Vazquez of the University of California, Davis, uses topology to understand the knotting and unknotting of real-world molecules. Specifically, she and her colleagues employ topological concepts from knot theory to demonstrate that cells detangle DNA with optimal efficiency.

During her talk at the 2018 SIAM Annual Meeting, held in Portland, Ore., this July, Vazquez emphasized her work’s multidisciplinary nature; although she focuses on DNA, her research has applications beyond molecular biology.

[Read the rest at SIAM News]

Emmy Noether and her wonderful theorem

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Mathematician to know: Emmy Noether

Noether’s theorem is a thread woven into the fabric of the science

For Symmetry Magazine:

We are able to understand the world because it is predictable. If we drop a rubber ball, it falls down rather than flying up. But more specifically: if we drop the same ball from the same height over and over again, we know it will hit the ground with the same speed every time (within vagaries of air currents). That repeatability is a huge part of what makes physics effective.

The repeatability of the ball experiment is an example of what physicists call “the law of conservation of energy.” An equivalent way to put it is to say the force of gravity doesn’t change in strength from moment to moment.

The connection between those ways of thinking is a simple example of a deep principle called Noether’s theorem: Wherever a symmetry of nature exists, there is a conservation law attached to it, and vice versa. The theorem is named for arguably the greatest 20th century mathematician: Emmy Noether.

So who was the mathematician behind Noether’s theorem? [Read the rest at Symmetry…]