## Posts Tagged 'Physics'

### Symplectic Geometry

For many decades, a search has been under way to find a theory of everything, that accounts for all the fundamental physical forces, including gravity. The dictum “physics is geometry” is a guiding principle of modern theoretical physics. Einstein’s General Theory of Relativity, which emerged just one hundred years ago, is a crowning example of this synergy. He showed how matter distorts the geometry of space and this geometry determines the motion of matter. The central idea is encapsulated in an epigram of John A Wheeler:

$\displaystyle \mbox{Matter tells space how to curve. Space tells matter how to move.}$

### Plateau’s Problem and Double Bubbles

Bubbles floating in the air strive to achieve a spherical form. Large bubbles may oscillate widely about this ideal whereas small bubbles quickly achieve their equilibrium shape. The sphere is optimal: it encloses maximum volume for any surface of a given area. This was stated by Archimedes, but he did not have the mathematical techniques required to prove it. It was only in the late 1800s that a formal proof of optimality was completed by Hermann Schwarz [Schwarz, 1884].

Computer-generated double bubble

### El Niño likely this Winter

This week’s That’s Maths column in The Irish Times (TM056 or search for “thatsmaths” at irishtimes.com) is about El Niño and the ENSO phenomenon.

In 1997-98, abnormally high ocean temperatures off South America caused a collapse of the anchovy fisheries. Anchovies are a vital link in the food-chain and shortages can bring great hardship. Weather extremes associated with the event caused 2000 deaths and 33 million dollars in damage to property. One commentator wrote that the warming event had “more energy than a million Hiroshima bombs”.

Patterns of Pacific Ocean sea surface temperature during El Niño and La Niña episodes. Image courtesy of Climate.gov.

### Light Weight (*)

Does light have weight? Newton thought that light was influenced by gravity and, using his laws of motion, we can calculate how gravity bends a light beam. The effect is observable during a total eclipse of the sun: photographs of the sky are compared with the same region when the sun is elsewhere and a radial displacement of the star images is found. But the amount predicted by Newton’s laws is only half the observed value.

### How Big was the Bomb?

By a brilliant application of dimensional analysis, G.I.Taylor estimated the explosive energy of the first atomic blast, the Trinity Test (see this week’s That’s Maths column in The Irish Times, TM053, or search for “thatsmaths” at irishtimes.com).

US army soldiers watching the first test of an atomic weapon, the Trinity Test.

### “Come See the Spinning Globe”

That’s Maths in The Irish Times this week (TM050, or Search for “thatsmaths” at irishtimes.com) is about how a simple pendulum can demonstrate the rotation of the Earth.

Reconstruction of Foucault’s demonstration. Original experiment in 1851. [Illustration (1902) from the cover of WIlliam Tobin’s book [1].]

Continue reading ‘“Come See the Spinning Globe”’

### Rollercoaster Loops

We all know the feeling when a car takes a corner too fast and we are thrown outward by the centrifugal force. This effect is deliberately exploited, and accentuated, in designing rollercoasters: rapid twists and turns, surges and plunges thrill the willing riders.

Many modern rollercoasters have vertical loops that take the trains through 360 degree turns with the riders upside-down at the apex. These loops are never circular, for reasons we will explain.