Posts Tagged 'modelling'

Using Maths to Reduce Aircraft Noise

If you have ever tried to sleep under a flight-path near an airport, you will know how serious the problem of aircraft noise can be. Aircraft noise is amongst the loudest sounds produced by human activities. The noise is over a broad range of frequencies, extending well beyond the range of hearing. The problem of aviation noise has become more severe as aircraft engines have become more powerful  [TM180 or search for “thatsmaths” at irishtimes.com].

Engine inlet of a CFM56-3 turbofan engine on a Boeing 737-400 [image Wikimedia Commons].

A Zero-Order Front

Sharp gradients known as fronts form in the atmosphere when variations in the wind field bring warm and cold air into close proximity. Much of our interesting weather is associated with the fronts that form in extratropical depressions.

Below, we describe a simple mechanistic model of frontogenesis, the process by which fronts are formed.

Sigmoid Functions: Gudermannian and Gompertz Curves

The Gudermannian is named after Christoph Gudermann (1798–1852). The Gompertz function is named after Benjamin Gompertz (1779–1865). These are two amongst several sigmoid functions. Sigmoid functions find applications in many areas, including population dynamics, artificial neural networks, cartography, control systems and probability theory. We will look at several examples in this class of functions.

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.

Sunflowers and Fibonacci: Models of Efficiency

The article in this week’s That’s Maths column in The Irish Times ( TM046 ) is about the maths behind the efficient packing of sunflowers and many other plants

Strolling along Baggot Street in Dublin recently, I noticed a plaque at the entrance to the Ibec head office. It showed a circular pattern of dots, reminiscent of the head of a sunflower. According to the Ibec website, “The spiral motif brings dynamism … and hints at Ibec’s member-centric ethos.” Wonderful! In fact, the pattern in the logo is vastly more interesting than this. Continue reading ‘Sunflowers and Fibonacci: Models of Efficiency’

The Future of Society: Prosperity or Collapse?

The article in this week’s That’s Maths column in the Irish Times ( TM045 ) is about a mathematical model to simulate the future of society.

Our extravagant lifestyle is draining the Earth’s natural resources. Population is climbing and climate change looms ever larger. Is the collapse of society imminent?

The historical precedents are ominous. Many civilizations have ended abruptly with drastic population reductions and centuries of oblivion. The fall of the Roman, Han, Mayan and Gupta Empires show that advanced and sophisticated civilisations can be fragile and impermanent. There are many causes, but over-consumption of resources and inequalities within society are primary.

Clothoids Drive Us Round the Bend

The article in this week’s That’s Maths column in the Irish Times ( TM043 ) is about the mathematical curves called clothoids, used in the design of motorways.

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Robots & Biology

The article in this week’s That’s Maths column in the Irish Times ( TM037 ) is about connections between robotics and biological systems via mechanics.

The application of mathematics in biology is a flourishing research field. Most living organisms are far too complex to be modelled in their entirety, but great progress is under way in simulating individual organs and modelling specific functions such as blood-flow and locomotion.

A Simple Growth Function

Three Styles of Growth

Early models of population growth represented the number of people as an exponential function of time,

$\displaystyle N(t) = N_0 \exp(t/\tau)$

where ${\tau}$ is the e-folding time. For every period of length ${\tau}$, the population increases by a factor ${e\approx 2.7}$. Exponential growth was assumed by Thomas Malthus (1798), and he predicted that the population would exhaust the food supply within a half-century. Continue reading ‘A Simple Growth Function’

Spots and Stripes

How do leopards get their spots? Mathematics gives us a better answer than the one offered by Rudyard Kipling in Just So Stories. This is the topic of That’s Maths this week ( TM019 ).

African Leopard (Panthera pardus pardus). [Image from Wikimedia Commons]