RIPE: Rheology

I just came back from a workshop, and one of the things I "re-learnt" was the need to communicate research in plain english (RIPE) to a broad audience. I am going to try to do a pitch on some aspect of my research hopefully on a monthly basis.

Here is the first installment. It is an attempt to introduce my field of rheology to an audience with a high-school level science background.

You probably know that there are three states of matter: solid, liquid and gas (there are a few more exotic ones too).

Take water for example. At room temperature it is a liquid. You can drink it, splash it, swim in it etc. Put some water in a freezer and cool it below melting temperature, and you get cold solid ice-cubes. You can use them to chill your soda, preserve food in an ice-box, or as cold-compress to heal a bruise. Instead of cooling water, you could heat it until it e-“vapor”-ates into steam, which, as it turns out, is the life-blood of the chemical industry.

Okay. So you know your solids, liquids and gases.

So let me ask you this: Is toothpaste solid or liquid?

It holds its shape like a solid, but you can easily “deform” it like a liquid.

How about shaving gel? Mayonnaise, silly-putty, jam?

It turns out that a wide class of materials that you encounter frequently in the food and cosmetic industry, defy this simple binary classification into solids or liquids. The size of this class of materials – unimaginatively dubbed “complex fluids” - is actually even larger.

For instance, most synthetic polymers or plastics that you see around you are processed in the molten state and are called polymer melts (I single them out because I have been studying them for over a decade now, and often feel that they don’t get the attention they deserve).

Polymer melts are also complex fluids.

The study of how such complex fluids respond to deformation is called rheology.

Let me restate the statement above in plain English.

When you try to deform or strain matter, it gets “stressed out”. Different materials, like people, react to stress differently.

Solids usually resist strain by opposing the forces that try to deform or disfigure it. Solids are like people who really don’t like to be pushed around!

Fluids (liquids and gases), on the other hand, go with the flow. Like Zen monks, they don’t resist. They bend, assimilate the imposed force, dissipate its energy, and return to a state of calm.

Complex fluids are like children with “solid” and “liquid” parents. They inherit traits like elasticity from their “solid” parent, and viscosity from their “liquid” parent. It is therefore no surprise that they are very frequently called “viscoelastic fluids”.

Studying the rheology of viscoelastic fluids like polymer melts, helps us devise better methods of processing them.

Octave/Matlab: Loop through Files in a Directory

Looping through files that match a certain pattern is an easy and routine operation for a BASH shell for example:

One can mimic this feature from within an Octave or Matlab program by using the command "glob". Here's how:

Academic Career Advice

Radhika Nagpal dishes out some very sensible advice that is not dished out as often as it should be.

In 2004 when I came to Harvard as a junior faculty, I wrote it on my desk. This-is-a-7-year-postdoc.
I type it in every day. For all seven+ years I have been at Harvard. No joke. 

It is an incredibly liberating point of view. If I’m not here for tenure, then there are a bunch of things I do not need to do. For example, I don’t need to spend my seventh year travelling doing the tenure talk circuit (I did not do this), or make sure I invite and get to know personally exactly 18 folks who might be my letter writers, or be on organizing committees so everyone important knows me well, or try to get nominated for awards as fast and as young as possible (I just turned 42). Frankly most of this is not possible to actually do!

Orthogonal Polynomials: Mathematica Script

A family of polynomials \[\{ \phi_{0}, \phi_1, ..., \phi_{n} \}\] (the subscript indicates the degree) are orthogonal with respect to a weighting function \(w(x)\), over an interval \([a,b]\), if \[\langle\phi_n, \phi_m\rangle = \int_{a}^{b} w(x) \phi_{n}(x) \phi_{m}(x) dx = \delta_{nm} c(n)\]
In other words, given a \(w(x)\) and an interval \([a, b]\) an orthogonal sequence of polynomials can be found via Gram-Schmidt orthogonalization of monomials.

This is done by a straightforward Mathematica script (link at the end). A possible use is:

P = OrthoPoly[Exp[-x], 0, 10, 3] // FullSimplify

This spits out the first three members of the family of orthogonal polynomials with \(w(x)=\exp(-x)\), over the interval [0,10].

One can use the zeros of these polynomials to obtain corresponding Gauss quadrature points. For example:

Solve[P[[3]] == 0, x] // N

yields {{x -> 0.180784}, {x -> 0.752396}}.

The code is available here.

GeoGebra Worksheet

GeoGebra makes building JavaScript or HTML5 applets a piece of cake.

I recently wrote a quick program to dynamically "analyze" the effect of additional monthly prepayments on a loan, on the amortization schedule. The formulae are available on this wikipedia page.

Here is a link to the GeoGebra worksheet on GeoGebraTube. You can download the file, or merely play with it in (either JavaScript or HTML5).

How thick is a human hair?

The quick answer seems to be between 20 to 200 microns.

If you want to find out how thick your hair is, using only a laser pointer and measuing tape, check out these two cool YouTube videos.

They make for very interesting summer afternoon projects for kids!

Links

1. Keith Devlin has some interesting thoughts on the use of video games to facilitate math learning. In particular why we should be wary of "Benny's Rules". He also has an interesting response to "Math Wars" that I linked to earlier.

2. Empirical Zeal tries to explain the visually fascinating phenomenon of "gravity defying chain of metal beads". This effect is very well-known in my field of polymer rheology and there are nice YouTube videos highlighting some of these features here, here and here.

3. Happy Birthday from SpikedMath

Podcasts on my iPod

I've been a big fan of listening to podcasts on my iPod Touch for three years now. Here's are the some of the podcasts I subscribe to:

• RadioLab: As of this moment, my favorite podcast. Jad and Robert explore scientific ideas under a theme. Powerful narratives,  ingenious use of sound effects, and seeped in humor.
• This American Life: Ira Glass regales us with stories or "acts" under a theme. Similar in spirit to Radiolab, although the topics are more "human interest" than science.
• EconTalk: Russ Roberts chats up one guest each week on topics loosely related to economics. I love the question and answer format.
• The Reality Check: A bunch of college friends talking science. Each person leads a story, while the others ask questions, and make snarky quips.
• Way With Words: Martha and Grant do with language what Tom and Ray Magliozzi do with cars (in CarTalk). Entertaining and educational!
• Rationally Speaking: Another skeptical take on issues and ideas in a chat-based format.
• Commonwealth Club and Big Ideas: Talks on interesting topics by smart and/or famous people. Most of the talks are more in-depth than TED talks.
• NPR StoryCorps: Extraordinary stories of ordinary people archived for posterity.
• Selected Shorts: Actors read famous short stories. In some ways, my only reliable source of fiction these days.
• Stuff To Blow Your Mind: Another discussion-based science program.

The links above are to their webpages. Links to the podcasts may be different.