Friday, September 28, 2018

Steven Strogatz Lectures on Youtube

Nonlinear Dynaics and Chaos, by Steven Strogatz
Nonlinear Dynamics and Chaos.
Previously (here, here, and here), I’ve written about Steven Strogatz, Professor of Applied Mathematics at Cornell University. Strogatz wrote one of my favorite textbooks: Nonlinear Dynamics and Chaos. Russ Hobbie and I cite it in Chapter 10 of Intermediate Physics for Medicine and Biology.

Nowadays students rarely read textbooks; they prefer watching videos. Well, I have good news. Strogatz taught a course based on his book, and his lectures are posted on YouTube. You can learn chaos straight from the horse’s mouth. You better get started: there are over 24 hours of video (all embedded below).

The second edition of Nonlinear Dynaics and Chaos, by Steven Strogatz
The 2nd Edition of Nonlinear Dynamics and Chaos.
Strogatz is an enormously successful mathematician. According to Google Scholar, his 1998 article with Duncan Watts—“Collective Dynamics of ‘Small-World’ Networks” (Nature, Volume 393, Pages 440-442)—has been cited over 35,000 times! His textbook has over ten thousand citations. (To put this in perspective, IPMB has 392.) He won the Lewis Thomas Prize for Writing about Science, tweets at @stevenstrogatz, and is buddies with M*A*S*H star and science communicator Alan Alda. In IPMB, Russ and I cite the first edition of Nonlinear Dynamics and Chaos, but Strogatz published a second edition in 2015.


1. Introduction and Overview

2. One Dimensional Systems

3. Overdamped Bead on a Rotating Hoop

4. Model of Insect Outbreak

5. Two Dimensional Nonlinear Systems

6. Two Dimensional Nonlinear Systems Fixed Points

7. Conservative Systems

8. Index Theory and Introduction to Limit Cycles

9. Testing for Closed Orbits

10. Van der Pol Oscillator

11. Averaging Theory for Weakly Nonlinear Oscillators

12. Bifurcations in Two Dimensional Systems

13. Hopf Bifurcations in Aeroelastic Instabilities and Chemical Oscillators

14. Global Bifurcations of Cycles

 15. Chaotic Waterwheel

16. Waterwheel Equations and Lorenz Equations

17. Chaos in the Lorenz Equations

18. Strange Attractor for the Lorenz Equations

19. One Dimensional Maps

20. Universal Aspects of Period Doubling

21. Feigenbaum’s Renormalization Analysis of Period Doubling

22. Renormalization: Function Space and a Hands-on Calculation

23. Fractals and the Geometry of Strange Attractors

24. Henon Map

25. Using Chaos to Send Secret Messages

Friday, September 21, 2018

Quick Calculus

In Intermediate Physics for Medicine and Biology, Russ Hobbie and I assume the reader knows calculus. Some readers, however, have weak or rusty math skills. Is there an easy way to learn what is needed?

Quick Calculus is a self-teaching guide written by Daniel Klepner and Norman Ramsey
Quick Calculus.
Yes! Quick Calculus is a self-teaching guide written by Daniel Klepner and Norman Ramsey. Their preface states:
Before you plunge into Quick Calculus, perhaps we ought to tell you what it is supposed to do. Quick Calculus should teach you the elementary techniques of differential and integral calculus with a minimum of wasted effort on your part; it is designed for you to study by yourself. Since the best way for anyone to learn calculus is to work problems, we have included many problems in this book. You will always see the solution to your problem as soon as you have finished it, and what you do next will depend on your answer. A correct answer generally sends you to new material, while an incorrect answer sends you to further explanations and perhaps another problem.
The book covers nearly all the calculus needed in IPMB.
  • Chapter One reviews functions and graphs, emphasizing trigonometry, exponentials, and logarithms.
  • Chapter Two discusses differentiation—including the product rule and the chain rule—and maximum/minimum problems.
  • Chapter Three analyzes integration, both definite and indefinite, and covers techniques such as change of variable, integration by parts, and multiple integrals.
  • Chapter Four summarizes all the results in a few pages.
Math Book useful for Intermediate Physics for Medicine and Biology
Math Books Useful for IPMB.
The only calculus in IPMB that Quick Calculus doesn’t teach is vector calculus; for that you should consult Div, Grad, Curl and All That. Used Math covers more ground than Quick Calculus, but it’s a handbook rather than a self-teaching guide.

Quick Calculus has several virtues. It is clearly written, it emphasizes understanding math visually with lots of plots, and it focuses on utilitarian techniques without distracting rigor. If you want to understand math at a fundamental level, you should take a real calculus class. If you want to brush up on what's needed to get through IPMB, use Quick Calculus.

One disadvantage is that Quick Calculus is old. The second edition—the most recent one I am aware of—was published in 1985. It might be difficult to purchase, although Amazon seems to have copies for sale. The authors make quaint comments about “readers who have an electronic calculator,” as opposed to slide rules I suppose. I also found several typos, which might frustrate readers using the book for self-study.

A sample from Quick Calculus
A sample from Quick Calculus.
The format is unusual. The text is divided into approximately half-page “frames,” and the reader is guided from one frame to the next. Someone should put this book online, because it would lend itself to an interactive online format. Rather than explain how the book is organized, I’ve taken Section 1.17 of IPMB and rewritten it in the style of Quick Calculus (see below). In my opinion, if all of Intermediate Physics for Medicine and Biology were organized like this it would be tedious. What do you think?

Friday, September 14, 2018

Gulliver was a Bad Biologist

Gulliver's Travels
Gulliver’s Travels by Jonathan Swift.
Most of my reading is nonfiction, but recently I read Jonathan Swift’s Gulliver’s Travels. The story describes Englishman Lemuel Gulliver’s journeys to exotic lands, including Lilliput inhabited by tiny people, and Brobdingnag where giants live. Swift was a delightful and funny writer, but Florence Moog claims “Gulliver was a Bad Biologist” (Scientific American, Volume 179, November 1948, Pages 52–55). The problem is scaling, which Russ Hobbie and I discuss in Chapter 2 of Intermediate Physics for Medicine and Biology. The properties of animals change as they get bigger or smaller; you can’t just scale people up or down and expect them to function correctly. As Moog writes “for a student of comparative biology Gulliver’s book may serve as an unpremeditated textbook on biological absurdities.”

Gulliver was a Bad Biologist
“Gulliver was a Bad Biologist,” by Florence Moog.
Moog’s first example was the 60-foot tall Brobdingnagians. She notes that because their mass increases as the cube of their height, supporting their body would “necessitate a truly ponderous skeleton” (A point I’ve discussed before in this blog when contemplating elephants). The giants would need thick stubby legs and fat bones.

Gulliver's Travels Title Page
Title Page of Gulliver’s Travels.
Moog then considers the six-inch-tall Lilliputians. “If the Brobdingnagians were too big to exist, the mouse-sized Lilliputians were too small to be human.” She explains that smaller animals have a higher specific metabolic rate (that is, rate per unit mass) than larger animals. “Gulliver … failed to realize that the creatures of his invention would have spent the larger part of their time stuffing themselves with food.”

Why was I reading Gulliver’s Travels? Blame Neil deGrasse Tyson. The Public Broadcasting System is sponsoring the Great American Read this summer, where we vote for our favorite of one hundred famous books. In their Launch Special, various celebrities select their personal favorite, and Tyson—one of the few scientists featured on the special—chose Gulliver. Apparently he hasn’t studied Chapter 2 of IPMB. Regular readers of this blog know that I am a fan of Isaac Asimov, and I have been voting for his Foundation Series twice a day (once using the Firefox browser, and once using Safari) all summer.

Neil deGrasse Tyson likes Gulliver's Travels
Neil deGrasse Tyson discussing Gulliver’s Travels.
Maybe Tyson has a point. Moog concludes that “after all, we must not be too hard on Gulliver for failing to understand the biological conditions that made him a man—and an implausible liar. His talents … were in the psychological realm.” His satirical story provides great insight into human behavior.

Friday, September 7, 2018

Microwave Weapons are Prime Suspect in Ills of U.S. Embassy Workers

Last Saturday, The New York Times published an article by Pulitzer Prize-winning science writer William Broad with the headline “Microwave Weapons are Prime Suspect in Ills of U.S. Embassy Workers.”
Doctors and scientists say microwave strikes may have caused sonic delusions and very real brain damage among embassy staff and family members.
The article has made quite a splash; I even heard about it on the news.

This topic is relevant to Intermediate Physics for Medicine and Biology, so I
-->ll address it in this post. I hesitate, however, because the science is uncertain and the topic of electromagnetic effects on health is fraught with conspiracy theories and voodoo science. Yet, the issue has more than academic importance; U.S.-Cuban relations suffered because of these unexplained health effects. So, reluctantly, I wade in.
I begin with a report from last March in the prestigious Journal of the American Medical Association (JAMA) by Swanson et al. about “Neurological Manifestations Among US Government Personnel Reporting Directional Audible and Sensory Phenomena in Havana, Cuba” (Volume 319, Pages 1125–1133).
  • Question: Are there neurological manifestations associated with reports of audible and sensory phenomena among US government personnel in Havana, Cuba? 
  • Findings: In this case series of 21 individuals exposed to directional audible and sensory phenomena, a constellation of acute and persistent signs and symptoms were identified, in the absence of an associated history of blunt head trauma. Following exposure, patients experienced cognitive, vestibular, and oculomotor dysfunction, along with auditory symptoms, sleep abnormalities, and headache. 
  • Meaning: The unique circumstances of these patients and the consistency of the clinical manifestations raised concern for a novel mechanism of a possible acquired brain injury from a directional exposure of undetermined etiology.
The articles claim of cognitive dysfunction has been hotly debated. A post in the blog Neuroskeptic was….er….skeptical. It concludes
Overall … the JAMA paper is pretty weak. Clearly, something has happened to make these 21 people experience so many unpleasant symptoms, but at present I don’t think we can rule out the possibility that the cause is psychological in nature.
Last weeks New York Times article was triggered by the recently proposed hypothesis that microwaves are responsible for these health issues. Russ Hobbie and I discuss the biological effects of electric and magnetic fields in Section 9.10 of IPMB. We focus on the potential of microwaves to induce tumors, and conclude that nonthermal mechanisms are implausible. In other words, radiofrequency fields can heat tissue—just like in your microwave oven—but they don’t cause cancer. The hypothesis touted in the Times article, however, is a thermal mechanism: a thermoelastic pressure wave sensed as sound by part of the inner ear called the cochlea.

Hearing induced by microwaves has been studied for years, and is known as the “Frey effect” after Allen Frey, who first reported it. A 2007 article in the journal Health Physics by James Lin and Zhangwei Wang (Volume 92, Pages 621-628) describes this phenomenon.
Hearing of Microwave Pulses by Humans and Animals: Effects, Mechanism, and Thresholds

The hearing of microwave pulses is a unique exception to the airborne or bone-conducted sound energy normally encountered in human auditory perception. The hearing apparatus commonly responds to airborne or bone-conducted acoustic or sound pressure waves in the audible frequency range. But the hearing of microwave pulses involves electromagnetic waves whose frequency ranges from hundreds of MHz to tens of GHz. Since electromagnetic waves (e.g., light) are seen but not heard, the report of auditory perception of microwave pulses was at once astonishing and intriguing. Moreover, it stood in sharp contrast to the responses associated with continuous-wave microwave radiation. Experimental and theoretical studies have shown that the microwave auditory phenomenon does not arise from an interaction of microwave pulses directly with the auditory nerves or neurons along the auditory neurophysiological pathways of the central nervous system. Instead, the microwave pulse, upon absorption by soft tissues in the head, launches a thermoelastic wave of acoustic pressure that travels by bone conduction to the inner ear. There, it activates the cochlear receptors via the same process involved for normal hearing. Aside from tissue heating, microwave auditory effect is the most widely accepted biological effect of microwave radiation with a known mechanism of interaction: the thermoelastic theory. The phenomenon, mechanism, power requirement, pressure amplitude, and auditory thresholds of microwave hearing are discussed in this paper. A specific emphasis is placed on human exposures to wireless communication fields and magnetic resonance imaging (MRI) coils.
Their introduction gives some useful numbers.
The microwave auditory phenomenon or microwave hearing effect pertains to the hearing of short-pulse, modulated microwave energy at high peak power by humans and laboratory animals (Frey 1961, 1962; Guy et al.1975a, b; Lin 1978, 1980, 2004). The effect can arise, for example, at an incident energy density threshold of 400 mJ m-2 for a single, 10-µs-wide pulse of 2,450 MHz microwave energy, incident on the head of a human subject (Guy et al. 1975a, b; Lin 1978). It has been shown to occur at a specific absorption rate (SAR) threshold of 1.6 kW kg-1 for a single 10-µs-wide pulse of 2,450 MHz microwave energy. A single microwave pulse can be perceived as an acoustic click or knocking sound, and a train of microwave pulses to the head can be sensed as an audible tune, with a pitch corresponding to the pulse repetition rate (Lin 1978).
The temperature increase caused by such a microwave pulse is rapid (microseconds) and tiny (microdegrees Celsius), and the associated pressure is small (tenths of a Pascal, or equivalently millionths of an atmosphere). People can hear these sounds because the cochlea is so sensitive.

One reason that microwaves might be a more plausible mechanism than sound waves for the apparent embassy attacks is acoustic impedance, discussed in Chapter 13 of IPMB. Air and water have very different impedances. When a sound wave impinges on a person, most of the acoustic energy is lost by reflection, and little (perhaps one part in a thousand) enters the fluid-filled body. Animals have evolved elaborate structures in the middle ear to mitigate this acoustic mismatch. However, a pressure wave caused by microwave heating originates inside the ear. No energy is lost by sound reflecting from the air-tissue interface.

I am no expert on thermoeleastic effects, but it seems plausible that they could be responsible for the perception of sound by embassy workers in Cuba. By modifying the shape and frequency of the microwave pulses, you might even induce sounds more distinct than vague clicks. However, I don’t know how you get from little noises to brain damage and cognitive dysfunction. My brain isn’t damaged by listening to clicky sounds. Either there is more to this that I don’t understand, or—as neuroskeptic speculates—the rest of the cause is “psychological in nature.”

Right now, our country could use a hard-nosed scientist or engineer expert in the bioeffects of microwave radiation to look into this problem. Where have you gone John Moulder and Ken Foster? We need you!