Diffuvisity Induced Segregation

It takes only a small difference in size or shape for particles to spontaneously demix. The famous "Brazil Nut Effect" is one common example.

There are perhaps sociological analogs, where racial, income-based, or religious clustering arises from small differences. A Google or Google-Scholar search for "auto-segregation" or  "self-segregation" brings out many of these examples.

It was with much interest that I read "Binary Mixtures of Particles with Different Diffusivities Demix" (paywalled). The abstract reads:

The influence of size differences, shape, mass, and persistent motion on phase separation in binary mixtures has been intensively studied. Here we focus on the exclusive role of diffusivity differences in binary mixtures of equal-sized particles. We find an effective attraction between the less diffusive particles, which are essentially caged in the surrounding species with the higher diffusion constant. This effect leads to phase separation for systems above a critical size: A single close-packed cluster made up of the less diffusive species emerges. Experiments for testing our predictions are outlined.

There is a non-paywalled video that shows the demixing process in the supplemental materials section.

Here is a decent commentary:

Soluble substances normally become evenly distributed throughout the solvent medium, thanks to passive molecular diffusion. The rate at which this occurs depends on the diffusion constant of the molecule concerned, whose magnitude increases with the temperature. In mixtures that have attained thermal equilibrium, particles of equal size normally exhibit the same diffusion constant. "We were interested in what happens when particles of equal size differ in their diffusion constants," says Simon Weber, first author on the new paper.

Advice from a scientist

I found this article via this blog that I follow.

The advice is commonsensical, which, ironically, makes it a must-read.

Some of my favorite excerpts:

Now for the matter of drive. You observe that most great scientists have tremendous drive. I worked for ten years with John Tukey at Bell Labs. He had tremendous drive. One day about three or four years after I joined, I discovered that John Tukey was slightly younger than I was. John was a genius and I clearly was not. Well I went storming into Bode's office and said, ``How can anybody my age know as much as John Tukey does?'' He leaned back in his chair, put his hands behind his head, grinned slightly, and said, ``You would be surprised Hamming, how much you would know if you worked as hard as he did that many years.'' I simply slunk out of the office!

My own PhD advisor, Ron Larson, is this (Tukey) type of person. Towards the end of my PhD, I realized that I had to do something he wasn't interested in. Barring luck, it is hard to directly compete with him. He is smarter, and works longer hours.

Another quote from the speech:

What Bode was saying was this: ``Knowledge and productivity are like compound interest.'' Given two people of approximately the same ability and one person who works ten percent more than the other, the latter will more than twice outproduce the former. The more you know, the more you learn; the more you learn, the more you can do; the more you can do, the more the opportunity - it is very much like compound interest. I don't want to give you a rate, but it is a very high rate. Given two people with exactly the same ability, the one person who manages day in and day out to get in one more hour of thinking will be tremendously more productive over a lifetime.

There's another trait on the side which I want to talk about; that trait is ambiguity. It took me a while to discover its importance. Most people like to believe something is or is not true. Great scientists tolerate ambiguity very well. They believe the theory enough to go ahead; they doubt it enough to notice the errors and faults so they can step forward and create the new replacement theory. If you believe too much you'll never notice the flaws; if you doubt too much you won't get started. It requires a lovely balance. But most great scientists are well aware of why their theories are true and they are also well aware of some slight misfits which don't quite fit and they don't forget it.

Does the human skin sense temperature?

The answer is no, if you are in a hurry. But if you have time, let me pose a puzzle:

"Your body temperature is about 37C or 98F depending on which side of the Atlantic you are. If you are like most people it "feels" quite uncomfortable when the temperature outside is 37C. When asked most people say they like 20-27C (or 65-80F). "

Why?

The basic point is that our body is constantly producing heat. In fact, most of the food we eat is eventually converted to heat. This should explain why the average daily intake of an adult is approximately 2500 calories, while only about 300 of those are consumed by jogging for 30 minutes.

For heat to flow, it needs a temperature difference. Thus, the 10-12 celcius difference that a 25 celcius environment provides, enables us to efficiently dissipate the heat we constantly generate. This leads us to the answer.

Our skin senses heat flow (flux), not temperature.

There are several manifestations which illustrate this point:

• When you sleep, you feel colder because your body processes have slowed down, producing less heat.
• When it is hot your body sweats. Sweat vaporizes, and in doing so takes away a lot of heat from your body (aka latent heat of vaporization).
• When it is windy you feel colder because heat is being convected away from your body faster (the wind chill effect).
  

Notice, how the outside temperature is only one of the factors which governs how "hot" or "cold" we feel. The mere fact that other things, such as level of activity, humidity, convection, perspiration affect that feeling suggests that we don't sense outside temperature.

Feynman Lectures

I found a this link via Simoleon Sense. It is really a fabulous resource, and I highly recommend it, even if your interest in physics is only marginal.

From the blog:

Apparently, Bill Gates has purchased the rights (to many of the Feynman lectures) and posted them for free on his Microsoft Research Labs “Project Tuva”. I can’t recommend these enough, Feynman had the ability of teaching science in a simple, insightful, and eloquent manner.

Often all it taken to enliven a dull subject is a spectacular teacher, and few can doubt Feynman's charisma. What Warren Buffet is to investing, Feynman is to general physics. They serve their specialties with a hearty dose of common-sense and humor.

The only problem with these lectures is that it requires SilverLight!

Without hot air

I've been recently doing some preliminary studies using a Bayesian formulation to tackle a hard inverse problem that had been sitting on my back-burner for a little too long. I'll have more to say about this, since this work is turning out quite nicely at the moment, and I have a really smart undergrad working on it.

One of the useful things about Bayesian methods is that they have an built-in Occam's razor, which naturally prefers simple models over more complex models. I was looking at some work done by David Mackay as part of his PhD thesis in 1991, when out of boredom I just googled his name to find out what he was up to now.

One thing I found was this fabulous resource. So far I have only read the 10-page synopsis and skimmed through the rest of the introduction, and wish I knew about it before. As it turns out, I taught undergrad thermodynamics three years in a row, and initially struggled with what I should assign for the first homework. These days I make them do a survey on recent topics relating to the energy crisis we face. While there are a tons of resources, and a plethora of information, it is nice to have some of that distilled into knowledge and wisdom, which is what this book (freely available as pdf) does.