Martingale

Submitted by Nicholas C. Darnton (inactive) on Friday, 4/17/2009, at 12:10 PM

A nice summary of the martingale (also known as the gambler's ruin) for lay audiences.  This is really mathematics, applied here to the stock market / credit crisis, but it pops up in many other contexts.  In particular, the analysis is identical to first passage calculations that predict the speed of biomolecular motors or the time for a DNA binding protein to locate its binding site, and also to polymer physics descriptions of DNA confinement. 

The article refers to a collaboration between a mathematician, statistician and physicist to decide whether a flipped coin really comes up heads and tails with equal probability.  Many concepts from Physics 16 crop up in course of the collaboration, including projectile motion, angular momentum, air resistance, and experimental uncertainty.

Swimming in goop

Submitted by Nicholas C. Darnton (inactive) on Friday, 4/17/2009, at 12:05 PM

Chemical engineers at the University of Minnesota filled a swimming pool with guar gum (which should be familiar to anyone who reads food labels) to answer the age-old question "Can you swim faster in goop than in water?" 

High Reynolds number hydrodynamics (roughly speaking, the study of large, fast things in water, where Re>1) is considerably more complex than low Reynolds number hydrodynamics (roughly speaking, the study of small, slow things in goop, where Re<1).  Since a swimming human operates in the complicated high Reynolds number regime (at Re ~ 4.5 × 106), there had been controversy about whether people would swim more or less quickly in viscous goop. 

Molasses

Short answer: it makes no difference whatsoever.  But lest you feel disappointed, this research did earn Cussler and Gettelfinger one of the highest-profile prizes in the natural sciences: an Ig Nobel!  Unfortunately, their goop only increased the swimming pool's viscosity by a factor of two, which means that all else being equal (and, in fact, all else was equal because their test subjects swam at exactly the same speed as in water) the Reynolds number was only 2× smaller in the goop.  This is still very far from the simple yet weird physics that occurs at small Reynolds numbers.

Cautionary note: this experiment is sometimes incorrectly compared to swimming in molasses.  This is a dangerously bad analogy.  You can swim in a swimming pool filled with guar gum goop, but you cannot swim in molasses.  In fact, molasses are very dangerous.

Projectile motion in biophysics

Submitted by Nicholas C. Darnton (inactive) on Friday, 2/27/2009, at 11:32 AM
Standard projectile motion
Real biological projectiles

Steven Vogel is a biophysicist who thinks about how principles of physics show up in the design or behavior of biological organisms.  For instance, organisms that jump or throw use projectile motion, which we talk about extensively in Physics 16.

Starting from the standard picture of projectile motion that you have learned, are learning, or will learn  (Figure 1), Vogel points out that the smaller the organism, the worse the approximation of neglecting air resistance becomes.  By the time you get to small seeds and spores, trajectories definitely do not look parabolic (Figure 2).  Extensive information about spore ejection (probably more than you want to know), including 50,000 fps video of the process is available in this article and accompanying materials.

See Steven Vogel, "Living in a physical world II. The bio-ballistics of small projectiles" J. Biosci. 30:167-175 (2005) for full details.

Aristotelian projectiles
Compare this to the lovingly rendered trajectories of cannonballs bombarding a peaceful hillside town, according to Aristotle's theory.  Aristotle gets the cannonball's trajectory completely wrong, but in the high-air-resistance limit (such as for Sordaria in Figure 2) he's not so far off.  Of course, Aristotle really is wrong about the physics, but when you add a lot of air resistance to gravity you happen to end up (coincidentally?) with something similar to Aristotle's prediction.  Lesson: you can safely ignore air resistance if you are a cannonball, but not if you are a spore. 

Gecko-inspired glue

Submitted by Nicholas C. Darnton (inactive) on Thursday, 2/5/2009, at 8:21 PM
Gecko feet excerpt
Stickybot
One of the subdisciplines of biophysics is biomimetics: using principles found in nature to make better man-made structures.  For instance, chemists at Georgia Tech have made artificial gecko feet on silicon wafers; physicists at the University of Manchester previously made gecko tape.  The artificial gecko feet actually adhere more strongly than some real gecko feet.

Update: Robert Full (UC Berkeley) has a "stickybot" that can climb vertical glass surfaces.  This is one biomimetic technology that looks like it's about to become useful.

Chronic acceleration research

Submitted by Nicholas C. Darnton (inactive) on Thursday, 10/16/2008, at 5:47 PM

Ah, the golden years of scientific inquiry. 

To quote from Great Mambo Chicken & the Transhuman Experience by Ed Regis (Addison Wesley, 1990), pp. 54-55:

Mambo chicken
There was the hyper-
g work done on chickens, for example, by Arthur Hamilton ("Milt") Smith in the 1970s.  Milt Smith was a gravity specialist at the University of California at Davis who wanted to find out what would happen to humans if they lived in greater-than-normal g-forces.   Naturally, he experimented on animals, and he decided that the animal that most closely resembled man for this specific purpose was the chicken.  Chickens, after all, had a posture similar to man's: they walked upright on two legs, they had two non-load-bearing limbs (the wings), and so on.  Anyway, Milt Smith and his assistants took a flock of chickens – hundreds of them, in fact – and put them into the two eighteen-foot-long centrifuges in the university's Chronic Acceleration Research Laboratory, as the place was called.

They spun those chickens up to two-and-a-half gs and let them stay there for a good while.   In fact, they left them spinning like that day and night, for three to six months or more at a time.  The hens went around and around, they clucked and they cackled and they laid their eggs, and as far as those chickens were concerned that was what ordinary life was like: a steady pull of two-and-a-half gs.  Some of those chickens spent the larger portion of their lifetimes in that goddamn accelerator.

Well, it was easy to predict what would happen.  Their bones would get stronger and their muscles would get bigger – because they had all that extra gravity to work against.  A total of twenty-three generations of hens was spun around like this and the same thing happened every time. When the accelerator was turned off, out walked ... great Mambo chicken! 

These chronically accelerated fowl were paragons of brute strength and endurance.  They'd lost excess body fat, their hearts were pumping out greater-than-normal volumes of blood, and their extensor muscles were bigger than ever.   In consequence of all this, the high-g chickens had developed a three-fold increase in their ability to do work, as measured by wingbeating exercises and treadmill tests.

I haven't had a chance to track them down, but supposedly these are the references:

Smith, A. H, "Physiological Changes Associated with Long-Term Increases in Acceleration." In "Life Sciences and Space Research XIV", edited by P.H.A. Sneath. Berlin:Akademie-Verlag, 1976.
Smith, A. H., and C. F. Kelly, "Biological Effects of Chronic Acceleration." Naval Research Reviews 18:1 (1965)
Smith, A. H., and C. F. Kelly,  "Influence of Chronic Acceleration upon Growth and Body Composition." Annals of the New York Academy of Sciences 110: 413 (1963)

Dogs can do vector calculus

Submitted by Nicholas C. Darnton (inactive) on Thursday, 10/16/2008, at 5:37 PM
Fetch diagram

Surprising but true: dogs can minimize fetch times by performing vector calculations.  To test this, a dog retrieved a stick by running some distance along shore and then swimming out to the stick; the dog usually chose the shore distance and swimming distance in such a way that it minimized total time-to-fetch. 

I haven't seen any reference to experiments done in moving water, which would reveal whether dogs understand the difference between relative and absolute velocity.  Anyone with a Retriever and transportation to the Connecticut river is encouraged to try it.

Darwin@Home

Submitted by Nicholas C. Darnton (inactive) on Thursday, 10/16/2008, at 10:38 AM
Darwin at Home

Simulated physics and simulated evolution lead to motile 'organisms' in computer code.  Videos on the website are beautiful, but it's unclear how relevant any of this is to real biophysics. 

One of the biggest problems with modeling evolution (or thinking about current organisms from an evolutionary perspective) is that it's unclear exactly where evolution is going.  It's easy to claim that evolution operates through "survival of the fittest", but if you can't define "fittest" that doesn't tell you much.

Many biologists I've talked to believe that extreme selection pressure (such as on bacterial populations) produces organisms that are "optimal" - but no one seems to know exactly what is being optimized.  A physicist is likely to pick something like energy efficiency (the ratio of power generated to power consumed, which is relatively easy to measure if you're looking at propulsion), but it seems that many organisms do not operate in an energy-limited regime and are (presumably as a result) not particularly energy efficient.