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Posts Tagged 'modelling'

Phantom traffic-jams are all too real

Published August 5, 2021 Irish Times Leave a Comment
Tags: modelling

Driving along the motorway on a busy day, you see brake-lights ahead and slow down until the flow grinds to a halt. The traffic stutters forward for five minutes or so until, mysteriously, the way ahead is clear again. But, before long, you arrive at the back of another stagnant queue. Hold-ups like this, with no apparent cause, are known as phantom traffic jams and you may experience several such delays on a journey of a few hours [TM216 or search for “thatsmaths” at irishtimes.com].

Traffic jams can have many causes [Image © Susanneiles.com. JPEG]

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Using Maths to Reduce Aircraft Noise

Published February 6, 2020 Irish Times Leave a Comment
Tags: Fluid Dynamics, modelling

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].

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A Zero-Order Front

Published August 30, 2018 Occasional Leave a Comment
Tags: Fluid Dynamics, Geophysics, modelling

DosTemp18

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.

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Sigmoid Functions: Gudermannian and Gompertz Curves

Published April 28, 2016 Occasional Leave a Comment
Tags: Analysis, modelling

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.

GompertzCurves

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El Niño likely this Winter

Published November 6, 2014 Irish Times Leave a Comment
Tags: Fluid Dynamics, Geophysics, modelling, Physics

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

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

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Sunflowers and Fibonacci: Models of Efficiency

Published June 5, 2014 Irish Times 6 Comments
Tags: Algorithms, Applied Maths, biology, modelling

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’

Clothoids Drive Us Round the Bend

Published April 17, 2014 Irish Times Leave a Comment
Tags: Euler, Geometry, Mechanics, modelling

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

Published January 16, 2014 Irish Times Leave a Comment
Tags: Applied Maths, Hamilton, Mechanics, modelling

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.

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A Simple Growth Function

Published November 28, 2013 Occasional Leave a Comment
Tags: modelling, Statistics

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

Published April 25, 2013 Irish Times Leave a Comment
Tags: biology, modelling

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]

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