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Although abstract in character, mathematics has concrete origins: the greatest advances have been inspired by the natural world. Recently, a new result in linear algebra was discovered by three physicists trying to understand the behaviour of neutrinos [TM176 or search for “thatsmaths” at irishtimes.com].
Neutrino trails in a bubble chamber [image from Physics World]
Continue reading ‘A New Mathematical Discovery from Neutrino Physics’
The Wilberforce Spring (often called the Wilberforce pendulum) is a simple mechanical device that illustrates the conversion of energy between two forms. It comprises a weight attached to a spring that is free to stretch up and down and to twist about its axis.
Wilberforce spring [image from Wikipedia Commons].}
However, due to a mechanical coupling between the stretching and torsion, there is a link between stretching and twisting motions, and the energy is gradually converted from vertical oscillations to axial motion about the vertical. This motion is, in turn, converted back to vertical oscillations, and the cycle continues indefinitely, in the absence of damping.
The conversion is dependent upon a resonance condition being satisfied: the frequencies of the stretching and twisting modes must be very close in value. This is usually achieved by having small adjustable weights mounted on the pendulum.
There are several videos of a Wilberforce springs in action on YouTube. For example, see here.
Continue reading ‘The curious behaviour of the Wilberforce Spring.’
Next Tuesday, the 30th of August, is the 200th anniversary of the birth of George Gabriel Stokes. This extended blog post is to mark that occasion. See also an article in The Irish Times.
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:
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
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.
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.
