It’s especially exciting because it’s the **Feature article** in the Focus Issue, From Chemical Oscillations to Applications of Nonlinear Dynamics: Dedicated to Richard J. Field on the Occasion of his 80th Birthday.

After many months of email exchanges and virtual meetings, I met Bob Mazo for the first time in person this January (see blog entry ‘50 years later‘). Together with Dick Field, the sole living scientist of the Field-Kőrös-Noyes (FKN) mechanism, developed in the early 1970s we revisited the exciting start of a new field in physical chemistry. The FKN mechanism was the first complete reaction scheme to describe the behavior of the Belousov-Zhabotinsky (BZ) reaction, a nonlinear chemical reaction-diffusion system (more here). Shortly after, they developed a mathematical three-variable model to describe the BZ reaction’s nonlinear behavior – the Oregonator model. The name was a response to the Brusselator model, developed by Ilya Prigogine in Brussels in the 1950s and 1960s. For his work on non-equilibrium thermodynamics and dissipative structures, Ilya Prigogine was awarded the Nobel Prize in Chemistry in 1977.

**Fun fact: The total author age is 225, the average author age is 75!** This will be difficult to beat.

Michelle and I began studying the architecture of **daylighting** terrestrial buildings for energy efficiency as part of her senior thesis, but due to our mutual interests, we gravitated to **extraterrestrial** possibilities. After my return from a yearlong sabbatical, Ariel eagerly continued the work for her senior thesis. Despite a **pandemic** keeping us a planet apart and meeting via **video conference** at simultaneously very early and very late hours, we completed the project, one of the most beautiful in my 33 years at **Wooster**. During one of our early morning, late evening sessions, we mathematically derived the conditions for reversals for the important special case of zero **obliquity** or tilt.

In the first figure below, exoplanet **spin-orbit ratio** \rho increases rightward, **orbital eccentricity** e increases upward, and **time** t increases outward. Red rods represent planetary observers, and coils represent apparent position and angle of their suns for 8 orbits. Yellow and cyan indicate apparent clockwise and counterclockwise motion, which signify reversals in coils with both colors. Our own solar system’s **Mercury** (Me) is just inside the reversal region. Red-white-blue background colors represent the product of the differences of the planet’s spin angular speed and its extreme orbital angular speeds at **apoapsis** and **periapsis**; red means no apparent solar reversals, blue means reversals, and the saturation indicates the reversal magnitude.

On Mercury, **one (solar) day lasts two years,** and once a year an equatorial observer witnesses a brief solar reversal, as in the second figure below, surely a special day for any future inhabitants. For a civilization inhabiting such a planet, we expect “reversal day” to be culturally significant.

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The** Event Horizon Telescope** team combined signals from radio telescopes that span Earth to reconstruct the image using** Very Long Baseline Interferometry**. Famously, not even light can escape a black hole, but EHT can see the glow of compressed and ionized gas or **plasma** in its orbiting **accretion disk** and the “shadow” of its **event horizon**. A conventional false-color black-orange-white palette makes visible the averaged radio-wave data.

The giant **Taylor Bowl** slide rule used to be used to teach the slide rule but today is the **trophy** for the annual Taylor Hall bowling tournament between the **Physics** and **Math Clubs**.

and

\log \frac{x}{y} = \log x - \log y.Slide rules feature logarithmic scales that slide past each other. For **straight** slide rules, logarithms of the numbers are proportional to their distances along them. To multiply 2\times 3 = 6, as below, slide the upper (blue) scale from 1 to 2 along the lower (red) scale, add the distance from 1 to 3 along the upper (blue) scale, and read the product from the lower (red) scale.

For **circular** slide rules, logarithms of the numbers are proportional to their distances around them. To multiply 3\times 7 = 21, as below, rotate the outer (blue) scale from 1 to 3 around the inner (red) scale, add the distance from 1 to 7 around the outer (blue) scale, and read the product from the inner (red) scale. Circular slide rules eliminate **off-scale** calculations because they naturally **wrap around**, with each wrap multiplying (or dividing) the numbers by 10.

The test image below shows a long exposure of a faint star. The radial lines are **diffraction spikes**. Confine light in one direction and it spreads in the perpendicular direction. Here, the six large spikes are from Webb’s 18 hexagonal mirror-segment edges and the one horizontal spike is from the vertical **strut** supporting **the secondary mirror, **which is visible in the Webb **selfie**. (The remaining two secondary mirror struts are parallel to mirror edges and their diffraction patterns combine with the mirror edge patterns.)

Due to Webb’s unprecedented **resolution** and **sensitivity**, many **galaxies** are also visible in this alignment image, whetting the appetite of Earth-bound astronomers!

Even as a child, the expedition seemed remote in time, but **Frank Hurley** meticulously documented it, and the cover image of Lansing’s book is an actual **photograph** of the Endurance trapped in the ice. Today, almost exactly 100 years after Shackleton’s death, news broke that a team of scientists and adventurers have found Endurance 3008 meters beneath the surface of the **Weddell Sea**. Protected by cold waters and the **Antarctic Treaty**, the wreck is upright, well preserved, and will not be disturbed.

In the accompanying animation, a star (red) and planet (cyan) orbit their common center of mass (cross). The inward force to pull a moving mass (orange) into a circular orbit of fixed period increases proportionally with distance, but at the distance of L_2, the *combined* gravitational pulls of the star and planet are sufficient. Shifting the mass upward increases its distances from the star and planet, which decreases their pull. Shifting the mass inward compensates for this radially (orange), but perpendicularly a force component (yellow) now pulls the moving mass into a circle about L_2 in a reference frame rotating with the planet (and the mass bobs up and down sinusoidally along its orbit in an inertial frame fixed to the distant stars.)

In 1971/1972 he helped developing the key model to describe chemical reaction-diffusion systems. But, as he stated, he was “only the catalyst” and only accepted to be recognized in the acknowledgments. The now called FKN mechanics, named after the three authors Dick Field, Endre Kőrös, and Dick Noyes, was the first model to describe the necessary reactions to create temporal, spatial, and spatiotemporal patterns in the nonlinear chemical Belousov-Zhabotinsky reaction. It had been published between 1972 and 1974 in a series called *Oscillations in chemical systems* I, II, III, IV, and V.

I am honored to write a manuscript with him, now at age 91, and the sole survivor of the original FKN papers, Dick Field, for a special edition in Chaos this year to celebrate Dick Field’s 80th birthday last October. During our meeting, Dick Field joined us via Skype from Missoula, Montana. It was a wonderful time travel back five decades while they were exchanging anecdotes and talked about nearly forgotten stories.

At the end of our meeting he joked that people in 50 years will know pretty much exactly which year our selfie had been taken…

]]>**Gas generator** engines tap off and burn a little **propellant** to drive a **turbine**, which turns a **centrifugal pump**, which rapidly pushes the **fuel **and** oxidizer **to the **combustion chamber**, after the **cryogenic** fuel first circulates around the **rocket nozzle** to cool it. The combustion generates supersonic **exhaust **out the **converging-diverging** nozzle that pushes the rocket. (The nozzle pushes the exhaust, and the exhaust pushes the nozzle).

The **Merlin** is an **open-cycle** engine because the **fuel-rich** flow of its gas generator is dumped overboard and not fully burned in the combustion chamber. The **Raptor** is a **closed-cycle **and **full-flow staged-combustion** engine as *all* of its propellants flow through the **pre-burners** (aka gas generators) to fully burn in the combustion chamber in the **optimal ratio **and exhaust out the nozzle for maximum efficiency.