The Boundary Layer

In Chapter 1 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I introduce a concept from fluid dynamics called the boundary layer.

The behavior of a sphere moving through a fluid illustrates how flow behavior depends on Reynolds number... At very high Reynolds number, viscosity is small but still plays a role because of the no-slip boundary condition at the sphere surface. A thin layer of fluid, called the boundary layer, sticks to the solid surface, causing a large velocity gradient and therefore significant viscous drag.

Life in Moving Fluids,
by Steven Vogel.

For readers who want to know more about the boundary layer, let me quote the start of Chapter 8 of Steven Vogel’s masterpiece Life in Moving Fluids.

At the interface between a stationary solid and a moving fluid, the velocity of the fluid is zero. This, of course, defines the no-slip condition… The immediate corollary of the no-slip condition is that near every such surface is a gradient in the speed of flow. Entirely within the fluid, speed changes from that of the solid to what we call the “free stream” velocity some distance away. Shearing motion is inescapably associated with a gradient in speed, so in these gradients near surfaces, viscosity, fluids’ antipathy to shear, works its mischief, giving rise to skin friction and consequent power consumption. The gradient region is associated with the term “boundary layer”…

The boundary layer… wasn’t so much discovered as it was invented, in the early part of this century, as a great stroke of genius of Ludwig Prandtl. Recognizing the origin of this notion is crucial. In the basic differential equations for moving fluids, the Navier-Stokes equations, some terms result from the inertia of fluids and some from their viscosity… The Reynolds number gives an indication of the relative importance of inertia and viscosity… At Reynolds numbers below unity, inertia can be ignored and nicely predictive rules nonetheless derived—[such as] Stokes’ law for the drag of a sphere… At high Reynolds number, one might expect to get away with neglecting viscosity… It may sound neat, but it all too commonly gets us in trouble—results diverge from physical reality, drag vanishes, and d’Alembert has his paradox.

Prandtl reconciled practical and theoretical fluid mechanics at high Reynolds numbers by recognizing that viscosity could never be totally ignored. What changes with Reynolds number was where it had to be taken into account; initially it mattered everywhere, but as the Reynolds number increased well above unity, viscosity made a difference only in the gradient regions near surfaces. These regions might be small, and they might get ever smaller… as the Reynolds number increased; but as long as the no-slip condition held, a place had to exist where shear rates were high and viscosity was significant. Prandtl called the place in question… the “boundary layer.” In general, a higher Reynolds number implies a thinner boundary layer but a higher shear rate in that boundary layer.

To learn more about the biological significance of the boundary layer see the Chapter 9 in Life in Moving Fluids, which is all about “Life in Velocity Gradients.”

Boundary Layer Theory,
by Schlichting and Gersten

If you want a more rigorous and mathematical analysis of boundary layers, I recommend Boundary Layer Theory by Hermann Schlichting and his student Klaus Gersten. The eighth edition of this book (2000) is cited in IPMB; a revised and updated ninth edition was published in 2017. Schlichting and Gersten write

At the end of the 19th century, fluid mechanics had split into two different directions which hardly had anything more in common. On one side was the science of theoretical hydrodynamics, emanating from Euler’s equations of motion and which had been developed to great perfection. However this had very little practical importance, since the results of this so-called classical hydrodynamics were in glaring contradiction to everyday experience. This was particularly true in the very important case of pressure loss in tubes and channels, as well as that of the drag experienced by a body moved through a fluid. For this reason, engineers, on the other side, confronted by the practical problems of fluid mechanics, developed their own strongly empirical science, hydraulics. This relied upon a large amount of experimental data and differed greatly from theoretical hydrodynamics in both methods and goals.

It is the great achievement of [German scientist] Ludwig Prandtl [1875–1953] which, at the beginning of this century, set forth the way in which these two diverging directions of fluid mechanics could be unified. He achieved a high degree of correlation between theory and experiment, which, in the first half of this century, has led to unimagined successes in modern fluid mechanics. It was already known then that the great discrepancy between the results in classical hydrodynamics and reality was, in many cases, due to neglecting the viscosity effects in the theory. Now the complete equations of motion of viscous flows (the Navier Stokes equations) had been known for some time. However, due to the great mathematical difficulty of these equations, no approach had been found to the mathematical treatment of viscous flows (except in a few special cases). For technically important fluids such as water and air, the viscosity is very small, and thus the resulting viscous forces are small compared to the remaining forces (gravitational force, pressure force). For this reason it took a long time to see why the viscous forces ignored in the classical theory should have an important effect on the motion of the flow.

In his lecture on “Über Flüssigkeitbewegung bei sehr kleiner Reibung” (On Fluid Motion with Very Small Friction) at the Heidelberg mathematical congress in 1904, L. Prandtl... showed how a theoretical treatment could be used on viscous flows in cases of great practical importance. Using theoretical considerations together with some simple experiments, Prandtl showed that the flow past a body can be divided into two regions: a very thin layer close to the body (boundary layer) where the viscosity is important, and the remaining region outside this layer where the viscosity can be neglected. With the help of this concept, not only was a physically convincing explanation of the importance of the viscosity in the drag problem given, but simultaneously, by hugely reducing the mathematical difficulty, a path was set for the theoretical treatment of viscous flows. Prandtl supported his theoretical work by some very simple experiments in a small, self–built water channel, and in doing this reinitiated the lost connection between theory and practice. The theory of the Prandtl boundary layer or the frictional layer has proved to be exceptionally useful and has given considerable stimulation to research into fluid mechanics since the beginning of this century. Under the influence of a thriving flight technology, the new theory developed quickly and soon became, along with other important advances—airfoil theory and gas dynamics—a keystone of modern fluid mechanics.

Introductory Fluid Mechanics L19 p2 — The Boundary Layer Concept.

https://www.youtube.com/watch?v=k37vPSA3E1g

 

E. Bodenschatz — Ludwig Prandtl (1875–1953)

https://www.youtube.com/watch?v=cv952Nhc_vs

Maurice de Broglie and the First Observation of an X-ray Absorption Edge

If you shine x-rays through a material and measure the number absorbed by it, you create an x-ray absorption spectrum. The absorption is related to the cross section; the bigger the cross section, the more the x-rays are absorbed. Figure 15.2 from Intermediate Physics for Medicine and Biology is shown below, where the cross section for carbon is plotted as a function of the x-ray energy. I’ve drawn an oval around what’s the most interesting feature of the plot, the jump in the cross section at an energy of about 0.28 keV. This abrupt rise is known as the K edge, and is an example of an absorption edge. 

A slightly modified version of Figure 15.2 from
Intermediate Physics for Medicine and Biology.

The cross section jumps up when the photon’s energy rises above the binding energy of a K-shell electron [an electron in the innermost energy level]. It’s not a small effect; the cross section increases by more than a factor of ten at the K edge (note that this is a log-log plot). 

When I see such a dramatic effect, I imagine how surprising it must have been for the person who observed it first. Who was the person who discovered the K edge? Maurice de Broglie.

Maurice de Broglie in 1932.

Maurice was the elder brother of the more-famous Louis de Broglie, who Russ Hobbie and I mention when talking about electron waves and the electron microscope. Maurice was born in Paris in 1875. After more than a decade in the French navy, he left the military to study physics. He was interested in x-rays, which were discovered by Wilhelm Röntgen in 1895. In 1913, Maurice published the first observation of an absorption edge (Comptes Rendus, Volume 157, Pages 924–926). When World War I began, he went back to the navy to do research on detecting U-boats (German submarines). After a long career in science, including being awarded the Hughes Medal by the Royal Society of London, he died in 1960 at the age of 85.

Farrel Lytle, an x-ray spectroscopy pioneer, tells Maurice’s story in his review article (Journal of Synchrotron Radiation, Volume 6, Pages 123–134, 1999).

Although Röntgen represents the beginning of X-ray science, the remarkable de Broglie royal family has been significant in both the world of science and the history of France. It has been said that if Maurice did nothing more than convince his younger brother, Louis, to drop his study of history and begin a career in science, he should be memorialized for that alone. But he did considerably more than that. His work in X-ray and atomic physics was innovative and important. Maurice had begun a career as a naval officer, but became interested in the exciting new world of X-rays and physics and resigned his commission. Beginning in the laboratory of Paul Langevin working on the ionization of gases by X-rays, he later built his own laboratory in his personal mansion on rue Châteaubriand. There he became the first in France to work with X-ray diffraction. During these experiments he invented X-ray spectroscopy. The experimental innovation came about when he mounted a single crystal on the cylinder of a recording barometer where the clockwork mechanism rotated it around its vertical axis at 2° h⁻¹. As the crystal rotated, all angles between the incident beam and the diffraction planes (hence, all X-ray energies) were recorded on a photographic plate. In this way he obtained an X-ray line spectrum from the tube with sharp and diffuse lines, bands etc. Two of the absorption bands proved to be the K edges of Ag and Br in the photographic emulsion. This was the first observation of an absorption edge (de Broglie, 1913). It took a few more experiments to reach the correct interpretation of the absorption edges. After the end of the First World War, Maurice gathered a large group of young scientists, all working on X-ray diffraction or X-ray spectroscopy, at the laboratory in his home. Joining him in his work were, among others, Alexandre Dauvillier, Jean Thibaud, Jean-Jacques Trillat, Louis Leprince-Ringuet (all were major contributors to the field of X-ray science) and his young brother, Louis. Maurice’s scientific work and his social position soon made him a major player in the science world.

Apparently it took a while to figure out that the absorption edges belonged to materials in the photographic film and not the x-ray tube or the crystal, but eventually it was all sorted out. A German scientist, Julius Hedwig (1879–1936), independently studied x-ray spectroscopy, and may have observed an x-ray absorption edge before Maurice, but he soon abandoned the work while Maurice pursued it further, becoming the father of x-ray spectroscopy.

Paul Horowitz Discusses The Art of Electronics

The Art of Electronics,
by Horowitz and Hill.

Nine years ago I wrote in this blog about the second edition of Horowtiz and Hill’s textbook The Art of Electronics. At the end of that post I hinted that a new edition of their book was in the works. The third edition of The Art of Electronics appeared in 2015, just in time for Russ Hobbie and me to cite it in the fifth edition of Intermediate Physics for Medicine and Biology.

Recently, I stumbled upon a delightful YouTube video of an interview with Paul Horowitz, explaining how The Art of Electronics began. I’ll keep this post brief, so you’ll have time to watch the video. The host is Limor Fried, who goes by the moniker Ladyada in honor of computer programing pioneer Ada Lovelace. Fried owns the electronics company Adafruit Industries, which is a cross between a business and an educational organization. Notice that during the interview Fried wears a “transistor man” tee shirt; I remember reading about transistor man in The Art of Electronics when I was designing a circuit in John Wikswo’s lab during graduate school.

Enjoy the video, and make The Art of Electronics your go-to book for designing circuits; or, just read it for fun.

Ladyada interview with Paul Horowitz, author of The Art of Electronics.
  https://www.youtube.com/watch?v=iCI3B5eT9NA

 

Meet Limor “Ladyada” Fried at Adafruit Industries.
  https://www.youtube.com/watch?v=SpYMgScKRwk

Thomas Young, Biological Physicist

The Last Man Who Knew Everything,
by Andrew Robinson.

Almost ten years ago in this blog, I speculated about who was the greatest biological physicist of all time, and suggested that it was the German scientist Hermann von Helmholtz. Today, I present another candidate for GOAT: the English physicist and physician Thomas Young. Young’s life is described in Andrew Robinson’s biography The Last Man Who Knew Everything.

Young (1773–1829) went to medical school and was a practicing physician. How did he learn enough math and physics to become a biological physicist? In Young’s case, it was easy. He was a child prodigy and a polymath who learned more through private study than in a classroom. As an adolescent he was studying optics and building telescopes and microscopes. As a teenager he taught himself calculus. By the age of 17 was reading Newton’s Principia. By 21 he was a Fellow of the Royal Society.

Some of his most significant contributions to biological physics were his investigations into physiological optics, including accommodation and astigmatism. In Intermediate Physics for Medicine and Biology, Russ Hobbie and I state that the “ability of the lens to change shape and provide additional converging power is called accommodation.” Robinson describes Young’s experiments that proved the changing shape of the lens of the eye is the mechanism for accommodation. For instance, he was able to rule out a mechanism based on changes in the length of the eyeball by making careful and somewhat gruesome measurements on his own eye as he changed his focus. He showed that patients whose lens had been removed, perhaps because of a cataract, could no longer adjust their focus. He also was one of the first to identify astigmatism, which Russ and I describe as “images of objects oriented at different angles… form at different distances from the lens.”

Young’s name is mentioned in IPMB once, when analyzing the wave nature of light: “Thomas Young performed some interference experiments that could be explained only by assuming that light is a wave.” The Last Man Who Knew Everything describes Young’s initial experiment, where he split a beam of light by letting it pass on each side of a thin card, with the beams recombining to form an interference pattern on a screen. Young presents his famous double-slit experiment in his book A Course of Lectures on Natural Philosophy and the Mechanical Arts. Robinson debates if Young actually performed the double-slit experiment or if for him it was just a thought experiment. In any case, Young’s hypothesis about interference fringes was correct. I’ve performed Young’s double-slit experiment many times in front of introductory physics classes. It establishes that light is a wave and allows students to measure its wavelength. Interference underlies an important technique in medical and biological physics described in IPMB: Optical Coherence Tomography. 

A green laser passing through two slits 0.1 mm apart produces an interference pattern.
Photo by Graham Beards, published in Wikipedia.

Young also studied color vision based on the idea that the retina can detect three primary colors. This work was rediscovered and further developed by Helmholtz fifty years later. Young was also one of the first to suggest that light is a transverse wave and therefore can be polarized.

In Chapter 1 of IPMB, Russ and I define the Young’s modulus, which relates stress to strain in elasticity and plays a key role in biomechanics. Young also studied capillary action and surface tension, two critical phenomena in biology.

Was Young a better biological physicist than Helmholtz? Probably not. Was Young a better scientist? It’s a close call, but I would say yes (Helmholtz had nothing as influential as the double slit experiment). Was Young a better scholar? Almost certainly. In addition to his scientific contributions, he had an extensive knowledge of languages and helped decipher the Rosetta Stone that allowed us to understand Egyptian hieroglyphics. He really was a man who knew everything.

Radiofrequency Radiation and Cancer, by David Robert Grimes

Grimes DR (2021)
Radiofrequency Radiation and Cancer,
JAMA Oncology, 8:456–461.

In my book Are Electromagnetic Fields Making Me Ill? I discussed the danger of cell phone radiation. Recently David Robert Grimes wrote his own review about this topic—Radiofrequency Radiation and Cancer—which appeared in JAMA Oncology (Volume 8, Pages 456–461, 2021). Below is his abstract.

Importance Concerns over radiofrequency radiation (RFR) and carcinogenesis have long existed, and the advent of 5G mobile technology has seen a deluge of claims asserting that the new standard and RFR in general may be carcinogenic. For clinicians and researchers in the field, it is critical to address patient concerns on the topic and to be familiar with the existent evidence base.

Observations This review considers potential biophysical mechanisms of cancer induction, elucidating mechanisms of electromagnetically induced DNA damage and placing RFR in appropriate context on the electromagnetic spectrum. The existent epidemiological evidence in humans and laboratory animals to date on the topic is also reviewed and discussed.

Conclusions and Relevance The evidence from these combined strands strongly indicates that claims of an RFR–cancer link are not supported by the current evidence base. Much of the research to date, however, has been undermined by methodological shortcomings, and there is a need for higher-quality future research endeavors. Finally, the role of fringe science and unsubstantiated claims in patient and public perception on this topic is highly relevant and must be carefully considered.

Many of Grimes’s conclusions are similar to those in Are Electromagnetic Fields Making Me Ill? and in Intermediate Physics for Medicine and Biology. I was particularly interested in the last few paragraphs of his discussion, where he examines the public perception of cell phone radiation health risks.

Public perception is also an important consideration, especially in the context of addressing patient fears. Given the combined biophysical and epidemiological evidence base to date against the proposition that RFR is carcinogenic, it might seem surprising that this belief is so widely evangelized and propagated relentlessly. A major and unedifying part of the reason for this is the noxious influence of fringe science on confounding public understanding; the BioInitiative Report, a nonscholarly [non-peer reviewed] work that insists that RFR causes many harms from cancer to autism, has been widely circulated since 2007. Despite its popularity, it has been repeatedly debunked by health bodies worldwide, and the attempts to treat its unsubstantiated assertions as equivalent to the weight of peer-reviewed weight of scientific evidence are archetypical false balance.

Tellingly perhaps, the recent misinformation propagated around 5G is not even new—the same grave claims were made about prior mobile technologies for decades and were equally unsupported. Their renaissance now is underpinned by disinformation perpetuated across social media and a microcosm of a greater problem with online disinformation. There is, for example, a thriving online market for dubious devices that promise to protect consumers from RFR, furthering a likely misguided perception of harm. Cancer is an emotive topic, which undoubtedly increases the virulence of misguided assertions. It is accordingly important to be cognizant of the fact that while the issue may be strictly academic to researchers, it is a source of anxiety and apprehension to patients and the general public, and there is an onus on scientists to both convey the scientific consensus and to ensure that future work is conducted to a high standard.

The International Agency for Research on Cancer designation of RFR as a group 2B agent (a possible carcinogen) in 2011 is also frequently misunderstood as implying evidence of harm. However, such an interpretation is incorrect, as reiterated in the most recent International Agency for Research on Cancer communication in 2020, which stated that “despite considerable research efforts, no mechanism relevant for carcinogenesis has been consistently identified to date. In the past 5 years, epidemiological research on mobile phone use and tumours occurring in the head has slowed down compared with the previous decade. Most new and previous case-control studies do not indicate an association between mobile phone use and risk of glioma, meningioma, acoustic neuroma, pituitary tumours, or salivary gland tumours.”

It is worthwhile too to acknowledge a potentially political dimension to the propagation of falsehoods on 5G in particular; a New York Times investigation found that Russian state forces were complicit in spreading falsehoods, with the European Commission finding the fingerprints of both Russian and Chinese health disinformation rising with the advent of COVID-19, including false claims linking cancer to RFR. All of this undermines collective understanding and makes it imperative that scientists be at the vanguard of communicating the evidence to prevent detrimental misconceptions [my italics].

Grimes has taken much criticism for his article, all of which, in my opinion, is undeserved. See, for example, this website containing an attack titled “Why did JAMA Oncology publish a paper written by a Telecom industry spokesperson?” by Joel Moskowitz (JAMA Oncology did no such thing). Several groups called for JAMA Oncology to retract Grimes’s article, but the journal refused (I’m proud of them). My advice for Grimes is to just be happy that people are paying attention to his work. Are Electromagnetic Fields Making Me Ill?, which covers much of the same ground and comes to similar conclusions, has not been similarly criticized, apparently because the critics are either unaware of it or don’t think it’s important enough to bother with.

Grimes is an Irish scientist and science writer who won the 2014 John Maddox Prize for standing up for science and was elected a fellow of the Committee for Skeptical Inquiry. If you want to read more by him, I suggest his excellent book Good Thinking: Why Flawed Logic Puts Us All at Risk and How Critical Thinking Can Save the World.

Michael Joy (1940–2020)

This week I belatedly learned that Mike Joy died. This was sad news indeed. Joy was a Canadian electrical engineer who measured current density in the body using magnetic resonance imaging. In Chapter 8 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I include a homework problem in which the magnetic field throughout the body is known and the student’s task is to determine the current density.

Section 8.6 

Problem 24. The differential form of Ampere’s law, Eq. 8.24, provides a relationship between the current density j and the magnetic field B that allows you to measure biological current with magnetic resonance imaging (see, for example, Scott et al. (1991)). Suppose you use MRI and find the distribution of magnetic field to be 

B_x = C(yz² − yx²) 

B_y = C(xz² − xy²) 

B_z = C4xyz 

where C is a constant with the units of T m⁻³. Determine the current density. Assume the current varies slowly enough that the displacement current can be neglected.

To solve this homework problem, calculate the curl of the magnetic field to get, within a proportionality constant, the current density. By the way, the problem doesn’t ask you to do this, but you might want to verify that the divergence of B is zero as it must be according to Maxwell’s equations, and that the divergence of j is zero (conservation of current).

Scott et al. (1991)
IEEE Trans Med Imaging
10:362–374.

The article we cite in IPMB is a beautiful paper by Greig Scott, Robin Armstrong, Mark Henkelman, and Joy. At that time Scott was Joy’s graduate student at the University of Toronto.

Scott GC, Joy MLG, Armstrong RL, Henkelman RM (1991) Measurement of nonuniform current density by magnetic resonance. IEEE Transactions on Medical Imaging Volume 10, Pages 362–374.

Using MRI to measure current density was one of those ideas I wish I’d thought of, but I didn’t. When Peter Basser and I wrote a paper analyzing an alternative (and less successful) method to detect action currents using MRI, we cited four of Joy’s articles in our very first sentence! I first met Joy when we co-chaired a session at the 2009 IEEE Engineering in Medicine and Biology Society Conference in Minneapolis. I had the honor of being the external examiner for one of Joy’s graduate students, Nahla Elsaid, at her 2016 dissertation defense. Joy was a delightful guy, and a joy to work with. I’ll miss him.

Below is Joy’s obituary.

MICHAEL LAWRENCE GRAHAME JOY (July 31, 1940–July 5, 2020) was born in Toronto and died at Drynoch Farm in Caledon, on his own terms, in his own time. He was predeceased by his wife Jane (née Andras) and will be dearly missed by his wife Carol Fanning, his son Rob, his daughters Gwen and Ellen, their partners, his grandchildren (Asha, Nel, Tallulah, Freya, Kelvin, and Skyler) and generations of nieces, nephews, cousins, former students, friends and colleagues.

Mike was professor emeritus at the University of Toronto; Institute of Biomaterials & Biomedical Engineering; Department of Electrical & Computer Engineering. He was a pioneer in the development of Magnetic Resonance and Electric Current Density Imaging and earned numerous significant grants, awards and citations.

Mike, (Muncle Ike, Zeepa) was truly a unique individual. He was a man of many interests who always had time for the numerous children who would follow him like shadows as he puttered on his latest amazing project. He could turn the most mundane chore into both an adventure and a learning experience. He imparted his love of nature, enquiry and adventure on his young assistants, whether tinkering on his jet boat Feeble, constructing a zip line, building model rockets, fishing, or going on long walks where “getting lost” was all part of the fun.

Mike enjoyed being surrounded by those he loved. His birthday parties at the Bay were the highlight of the summer while the Christmas tree parties at the Farm kicked off the festive season. Whether at summer picnics, Church, dinners, gatherings, bridge games, visiting family at Nares Inlet or summer afternoons on the side porch, he was always at the center of things with his distinctive laugh and quick sense of humour.

Mike left his imprint on so many. His was a life well lived and well loved. In lieu of flowers, please consider a donation to the Georgian Bay Land Trust, one of the many conservation projects Mike supported.

Drawdown

Drawdown,
Edited by Paul Hawken.

This blog is about physics applied to medicine and biology, but if we don’t solve the climate crisis there’s no use developing fancier ways to do medical imaging or radiation therapy; we’ll all be dead. So today I’m going to tell you about a book I just read, titled Drawdown: The Most Comprehensive Plan Ever Proposed to Reverse Global Warming. It’s the book I’ve been looking for. It analyzes all the different ways we can address global warming, and ranks them by impact and importance. Here’s how the editor Paul Hawken begins Drawdown.

The genesis of Project Drawdown was curiosity, not fear. In 2001 I began asking experts in climate and environmental fields a question: Do we know what we need to do in order to arrest and reverse global warming? I thought they could provide a shopping list. I wanted to know the most effective solutions that were already in place, and the impact they could have if scaled. I also wanted to know the price tag. My contacts replied that such an inventory did not exist, but all agreed it would be a great checklist to have, though creating one was not within their individual expertise. After several years, I stopped asking because it was not within my expertise either.

Then came 2013. Several articles were published that were so alarming that one began to hear whispers of the unthinkable: It was game over. But was that true, or might it possibly be game on? Where did we actually stand? It was then that I decided to create Project Drawdown. In atmospheric terms drawdown is that point in time at which greenhouse gases peak and begin to decline on a year-to-year basis. I decided that the goal of the project would be to identify, measure, and model one hundred substantive solutions to determine how much we could accomplish within three decades towards that end.

Many solutions are presented in Drawdown, but here I count down the top ten, ranked according to their total atmospheric carbon dioxide reduction, with a brief quote from Drawdown accompanying each.

10. Rooftop Solar

As households adopt rooftop solar… they transform generation [of electricity] and its ownership, shifting away from utility monopolies and making power production their own.

9. Silvopasture

Silvopasture is… the integration of trees and pasture or forage into a single system for raising livestock… Trees create cooler microclimates and more protective environments, and can moderate water availability. Therein lies the climatic win-win of silvopasture: As it averts further greenhouse emissions from one of the world’s most polluting sectors, it also protects against changes that are now inevitable.

8. Solar Farms

Any scenario for reversing global warming includes a massive ramp-up of solar power by mid-century. It simply makes sense: the sun shines every day, providing a virtually unlimited, clean, and free fuel at a price that never changes. Small, distributed clusters of rooftop panels are the most conspicuous evidence of the renewables revolution powered by solar photovoltaics (PV). The other, less obvious iteration of the PV phenomenon is large-scale arrays of hundreds, thousands, or in some cases millions of panels [solar farms] that achieve generating capacity in the tens or hundreds of megawatts.

7. Family Planning

Increased adoption of reproductive healthcare and family planning is an essential component to achieve the United Nations’ 2015 medium global population projection of 9.7 billion people by 2050. If investment in family planning, particularly in low-income countries, does not materialize, the world’s population could come closer to the high projection, adding another 1 billion people to the planet.

6. Educating Girls

Girls education, it turns out, has a dramatic bearing on global warming. Women with more years of education have fewer, healthier children and actively manage their reproductive health… Synchronizing investments in girls’ education with those in family planning would be complementary and mutually reinforcing. Education is grounded in the belief that every life bubbles with innate potential. When it comes to climate change, nurturing the promise of each girl can shape the future for all.

5. Tropical Forests

In recent decades, tropical forests... have suffered extensive clearing, fragmentation, degradation, and depletion of flora and fauna… One of the dominant storylines of the nineteenth and twentieth centuries was the vast loss of forestland. Its restoration and re-wilding could be the twenty-first-century story.

4. Plant-Rich Diet

Eat food. Not too much. Mostly plants.

3. Reduced Food Waste

Whether on the farm, near the fork, or somewhere in between, efforts to reduce food waste can address emissions and ease pressure on resources of all kinds, while enabling society more effectively to supply future food demand.

2. Wind Turbines

Ongoing cost reduction will soon make wind energy the least expensive source of installed electricity capacity, perhaps within a decade.

1. Refrigerant Management

As temperatures rise, so does reliance on air conditioners. The use of refrigerators, in kitchens of all sizes and throughout “cold chains” of food production and supply, is seeing similar expansion. As technologies for cooling proliferate, evolution in refrigerants and their management is imperative.

While reading Intermediate Physics for Medicine and Biology, let’s turn up the thermostat a bit during warm days. Between chapters, let’s ditch the hamburger and eat a salad instead (and if you can’t finish it, save the rest for leftovers). Let’s make sure girls in particular are encouraged to read IPMB (or whatever else that will help with their education). And let’s write our congressional representatives and encourage them to support solar and wind energy sources.

If you don’t have the time to read Drawdown, or don’t have easy access to it, then visit the website drawdown.org or watch the videos below, which summarize the plan to reverse global warming.

Climate Solutions 101. Unit 1, Setting the Stage

https://www.youtube.com/watch?v=qT_O2F5zgXc&list=PLwYnpej4pQF7UPnt0nkZEa8sxR9TmWR1B&index=1

Climate Solutions 101. Unit 2, Stopping Climate Change 

https://www.youtube.com/watch?v=bkDherHOymo&list=PLwYnpej4pQF7UPnt0nkZEa8sxR9TmWR1B&index=2

Climate Solutions 101. Unit 3, Reducing Sources 

https://www.youtube.com/watch?v=EiE2DbUOmgc&list=PLwYnpej4pQF7UPnt0nkZEa8sxR9TmWR1B&index=3 

Climate Solutions 101. Unit 4, Supporting Sinks and Improving Society

https://www.youtube.com/watch?v=n_ysjDqZlDw&list=PLwYnpej4pQF7UPnt0nkZEa8sxR9TmWR1B&index=4 

Climate Solutions 101. Unit 5, Putting It All Together

https://www.youtube.com/watch?v=t3tZi7aTym8&list=PLwYnpej4pQF7UPnt0nkZEa8sxR9TmWR1B&index=5

Climate Solutions 101. Unit 6, Making It Happen

 https://www.youtube.com/watch?v=xmt1oOUis0E&list=PLwYnpej4pQF7UPnt0nkZEa8sxR9TmWR1B&index=6

An Immense World

“Earth teems with sights and textures, sounds and vibrations, smells and tastes, electric and magnetic fields. But every animal can only tap into a small fraction of reality’s fullness. Each is enclosed within its own unique sensory bubble, perceiving but a tiny sliver of our immense world.”

An Immense World,
by Ed Yong.

Those three sentences sum up Ed Yong’s new book An Immense World: How Animal Senses Reveal the Hidden Realms Around Us. Yong is a science writer for The Atlantic who won a Pulitzer Prize for his reporting about the COVID-19 pandemic. I’ve mentioned Yong in this blog before when quoting advice from his chapter in the book Science Blogging: “you have to have something worth writing about, and you have to write it well.” In An Immense World, Yong does both.

An Immense World sometimes overlaps with Intermediate Physics for Medicine and Biology. For example, both books discuss vision. Yong points out the human eye has better visual acuity than most other animals. He writes “we assume that if we can see it, they [other animals] can, and that if it’s eye-catching to us, it’s grabbing their attention… That’s not the case.” Throughout his book, Yong returns to this idea of how sensory perception differs among animals, and how misleading it can be for us to interpret animal perceptions from our own point of view.

Like IPMB, An Immense World examines color vision. Yong speculates about what a bee would think of the color red, if bees could think like humans.

Imagine what a bee might say. They are trichromats, with opsins that are most sensitive to green, blue, and ultraviolet. If bees were scientists, they might marvel at the color we know as red, which they cannot see and which they might call “ultrayellow” [I would have thought “infrayellow”]. They might assert at first that other creatures can’t see ultrayellow, and then later wonder why so many do. They might ask if it is special. They might photograph roses through ultrayellow cameras and rhapsodize about how different they look. They might wonder whether the large bipedal animals that see this color exchange secret messages through their flushed cheeks. They might eventually realize that it is just another color, special mainly in its absence from their vision.

Both An Immense World and IPMB also analyze hearing. Yong says

Human hearing typically bottoms out at around 20 Hz. Below those frequencies, sounds are known as infrasound, and they’re mostly inaudible to us unless they’re very loud. Infrasounds can travel over incredibly long distances, especially in water. Knowing that fin whales also produce infrasound, [scientist Roger] Payne calculated, to his shock, that their calls could conceivably travel for 13,000 miles. No ocean is that wide.…

Like infrasound, the term ultrasound… refers to sound waves with frequencies higher than 20 kHz, which marks the upper limit of the average human ear. It seems special—ultra, even—because we can’t hear it. But the vast majority of mammals actually hear very well into that range, and it’s likely that the ancestors of our group did, too. Even our closest relatives, chimpanzees, can hear close to 30 kHz. A dog can hear 45 kHz; a cat, 85 kHz; a mouse, 100 kHz; and a bottlenose dolphin, 150 kHz. For all of these creatures, ultrasound is just sound.

In IPMB, Russ Hobbie and I introduce the decibel scale for measuring sound intensity, or how loud a sound is. Yong uses this concept when discussing bats.

The sonar call of the big brown bat can leave its mouth at 138 decibels—roughly as loud as a siren or jet engine. Even the so-called whispering bats, which are meant to be quiet, will emit 110-decibel shrieks, comparable to chainsaws and leaf blowers. These are among the loudest sounds of any land animal, and it’s a huge mercy that they’re too high-pitched for us to hear.

Yong examines senses that Russ and I never consider, such as smell, taste, surface vibrations, contact, and flow. He wonders about the relative value of nociception [a reflex action to avoid a noxious stimulus] and the sensation of pain [a subjective feeling created by the brain].

The evolutionary benefit of nociception is abundantly clear. It’s an alarm system that allows animals to detect things that might harm or kill them, and take steps to protect themselves. But the origin of pain, on top of that, is less obvious. What is the adaptive value of suffering?

On the continuum ranging from life’s unity to diversity, Yong excels at celebrating the diverse, while Russ and I focus on how physics reveals unifying principles. I’m sometimes frustrated that Yong doesn’t delve into the physics of these topics more, but I am in awe of how he highlights so many strange and wonderful animals. There’s a saying that “nothing in biology makes sense except in light of evolution.” That’s true for An Immense World, which is a survey of how the evolution of sensory perception shapes they way animals interact, mate, hunt their prey, and avoid their predators.

Two chapters of An Immense World I found especially interesting were about sensing electric and magnetic fields. When discussing the black ghost knifefish’s ability to sense electric fields, Yong writes

Just as sighted people create images of the world from patterns of light shining onto their retinas, an electric fish creates electric images of its surroundings from patterns of voltage dancing across its skin. Conductors shine brightly upon it. Insulators cast electric shadows.

Then he notes that

Fish use electric fields not just to sense their environment but also to communicate. They court mates, claim territory, and settle fights with electric signals in the same way other animals might use colors or songs.

Even bees can detect electric fields. For instance, the 100 V/m electric field that exists at the earth’s surface can be sensed by bees.

Although flowers are negatively charged, they grow into the positively charged air. Their very presence greatly strengthens the electric fields around them, and this effect is especially pronounced at points and edges, like leaf tips, petal rims, stigmas, and anthers. Based on its shape and size, every flower is surrounded by its own distinctive electric field. As [scientist Daniel] Robert pondered these fields, “suddenly the question came: Do bees know about this?” he recalls. “And the answer was yes.”

The chapter on sensing magnetic fields is different from the others, because we don’t yet know how animals sense these fields.

Magnetoreception research has been polluted by fierce rivalries and confusing errors, and the sense itself is famously difficult both to study and to comprehend. There are open questions about all the senses, but at least with vision, smell, or even electroreception, researchers know roughly how they work and which sense organs are involved. Neither is true for magnetoreception. It remains the sense that we know least about, even though its existence was confirmed decades ago.

Yong lists three possible mechanisms for magnetoreception: 1) magnetite, 2) electromagnetic induction, and 3) magnetic effects on radical pairs. Russ and I discuss the first two in IPMB. I get the impression that the third is Yong’s favorite, but I remain skeptical. In my book Are Electromagnetic Fields Making Me Ill? I say that “they jury is still out” on the radical pair hypothesis.

If you want to read a beautifully written book that explores how much of the physics in Intermediate Physics for Medicine and Biology can be used by species throughout the animal kingdom to sense their environment, I recommend An Immense World. You’ll love it.

 Umwelt: The hidden sensory world of animals. By Ed Yong.

https://www.youtube.com/watch?v=Pzsjw-i6PNc

 

 Ed Yong on An Immense World

https://www.youtube.com/watch?v=bQS0Ioch05E

Numerical Integration

A homework problem in Chapter 14 of Intermediate Physics for Medicine and Biology states

Problem 28. Integrate Eq. 14.33 over all wavelengths to obtain the Stefan-Boltzmann law, Eq. 14.34. You will need the integral

Equation 14.33 is Planck’s blackbody radiation law and Eq. 14.34 specifies that the total power emitted by a blackbody.

Suppose Russ Hobbie and I had not given you that integral. What would you do? Previously in this blog I explained how the integral can be evaluated analytically and perhaps you’re skilled enough to perform that analysis yourself. But it’s complicated, and I doubt most scientists could do it. If you couldn’t, what then?

You could integrate numerically. Your goal is to find the area under the curve shown below.

Unfortunately x ranges from zero to infinity (the plot shows the function up to only x = 10). You can’t extend x all the way to infinity in a numerical calculation, so you must either truncate the definite integral at some large value of x or use a trick.

A good trick is to make a change of variable, such as

When x equals zero, t is also zero; when x equals infinity, t is one. The integral becomes

Although this integral looks messier than the original one, it’s actually easier to evaluate because the range of t is finite: zero to one. The integrand now looks like this: 

 

The colored stars in these two plots are to guide the reader’s eye to corresponding points. The blue star at t = 1 is not shown in the first plot because it corresponds to x = ∞.

We can evaluate this integral using the trapezoid rule. We divide the range of t into N subregions, each extending over a length of Δt = 1/N. Ordinarily, we have to be careful dealing with the two endpoints at t = 0 and 1, but in this case the function we are integrating goes to zero at the endpoints and therefore contributes nothing to the sum. The approximation is shown below for N = 4, 8, and 16. 

 

The area of the purple rectangles approximates the area under the red curve This approximation gets better as N gets bigger. In the limit as N goes to ∞, you get the integral.

I performed the calculation using the software Octave (a free version of Matlab). The program is:

N=8; 

dt=1/N; 

s=0; 

for i=1:N-1 

     t=i*dt; 

     s=s+dt*t^3/((exp(t/(1-t))-1)*(1-t)^5); 

     endfor

I found the results shown below. The error is the difference between the numerical integration and the exact result (π⁴/15 = 6.4939…), divided by the exact result, and expressed as a percent difference.

N	I	% error
2	1.1640	–82
4	6.2823	–3.26
8	6.6911	3.04
16	6.5055	0.178
32	6.4940	0.000282
64	6.4939	0.00000235
128	6.4939	0.00000000174

These results show that you can evaluate the integral accurately without too much effort. You could even imagine doing this by hand if you didn’t have access to a computer—using, say, N = 16—and getting an answer accurate to better than two parts per thousand.

For many purposes, a numerical solution such as this one is adequate. However, 6.4939… doesn’t look as pretty as π⁴/15. I wonder how many people could calculate 6.4939 and then say “Hey, I know that number; It’s π⁴/15”!

Transcranial Magnetic Stimulation

When I was at the National Institutes of Health in the early 1990s, I worked on transcranial magnetic stimulation of the brain. In Chapter 8 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I describe this technique.

8.7 Magnetic Stimulation 

Since a changing magnetic field generates an induced electric field, it is possible to stimulate nerve or muscle cells without using electrodes. The advantage is that for a given induced current deep within the brain, the currents in the scalp that are induced by the magnetic field are far less than the currents that would be required for electrical stimulation. Therefore transcranial magnetic stimulation (TMS) is relatively painless...

One of the earliest investigations was reported by Barker, Jalinous and Freeston (1985). They used a solenoid in which the magnetic field changed by 2 T in 110 μs to apply a stimulus to different points on a subject’s arm and skull. The stimulus made a subject’s finger twitch after the delay required for the nerve impulse to travel to the muscle.

The story of how Tony Barker invented transcranial magnetic stimulation is fascinating. You can hear about it in the video below, where John Rothwell—another early magnetic stimulation researcher—reminisces with Barker about his invention. The most interesting part of the video is when Barker describes a crucial trip he made from Sheffield (he worked at the Royal Hallamshire Hospital in Sheffield, England) to London (The National Hospital, Queen’s Square), so he could demonstrate his device to leading neurophysiologist Pat Merton. Rothwell, also at Queen’s Square, had his brain stimulated that day, and the next day he wrote Barker asking to get a stimulator of his own. Barker’s 1985 paper in The Lancet (cited in IPMB) was the first publication about magnetic stimulation of the brain. As Barker says, “like all the best papers it was one page long.”

The 15-minute video is well worth your time. I’ll stop writing so you can listen. Enjoy!

Anthony Barker reminiscing with John Rothwell about the invention of transcranial magnetic stimulation.

https://www.youtube.com/watch?v=1DI3EC2pQ44