Queueing is a bore and waiting to be served is one of life’s unavoidable irritants. Whether we are hanging onto a phone, waiting for response from a web server or seeking a medical procedure, we have little choice but to join the queue and wait. It may surprise readers that there is a well-developed mathematical theory of queues. It covers several stages of the process, from patterns of arrival, through moving gradually towards the front, being served and departing [TM207 or search for “thatsmaths” at irishtimes.com].

## Posts Tagged 'Applied Maths'

### Cornelius Lanczos – Inspired by Hamilton’s Quaternions

Published July 16, 2020 Irish Times ClosedTags: Analysis, Applied Maths, Mechanics, Relativity

In May 1954, Cornelius Lanczos took up a position as senior professor in the School of Theoretical Physics at the Dublin Institute for Advanced Studies (DIAS). The institute had been established in 1940 by Eamon de Valera, with a School of Theoretical Physics and a School of Celtic Studies, reflecting de Valera’s keen interest in mathematics and in the Irish language. Later, a School of Cosmic Physics was added. DIAS remains a significant international centre of research today [TM191 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Cornelius Lanczos – Inspired by Hamilton’s Quaternions’

### Pooling Expertise to Tackle Covid-19

Published June 4, 2020 Irish Times ClosedTags: Applied Maths, Epidemiology

Our lives have been severely restricted in recent months. We are assured that the constraints have been imposed following “the best scientific advice”, but what is the nature of this advice? Among the most important scientific tools used for guidance on the Covid-19 outbreak are mathematical models [TM188; or search for “thatsmaths” at irishtimes.com ].

### Exponential Growth must come to an End

Published April 16, 2020 Irish Times ClosedTags: Analysis, Applied Maths

In its initial stages, the Covid-19 pandemic grew at an exponential rate. What does this mean? The number of infected people in a country is growing exponentially if it increases by a fixed multiple R each day: if N people are infected today, then R times N are infected tomorrow. The size of the growth-rate R determines how rapidly the virus is spreading. An example should make this clear [TM185 or search for “thatsmaths” at irishtimes.com].

### Samuel Haughton and the Twelve Faithless Hangmaids

Published March 12, 2020 Occasional ClosedTags: Applied Maths

In his study of humane methods of hanging, Samuel Haughton (1866) considered the earliest recorded account of execution by hanging (see Haughton’s Drop on this site). In the twenty-second book of the *Odyssey*, Homer described how the twelve faithless handmaids of Penelope “lay by night enfolded in the arms of the suitors” who were vying for Penelope’s hand in marriage. Her son Telemachus, with the help of his comrades, hanged all twelve handmaids on a single rope.

Continue reading ‘Samuel Haughton and the Twelve Faithless Hangmaids’

### Samuel Haughton and the Humane Drop

Published March 5, 2020 Irish Times ClosedTags: Applied Maths, History

Samuel Haughton was born in Co. Carlow in 1821. He entered Trinity College Dublin aged just sixteen and graduated in 1843. He was elected a fellow in 1844 and was appointed professor of geology in 1851. He took up the study of medicine and graduated as a Doctor of Medicine in 1862, aged 40 [TM182 or search for “thatsmaths” at irishtimes.com].

In addition to his expertise in geology and medicine, Haughton was a highly talented applied mathematician. His mathematical investigations included the study of the motion of solid and fluid bodies, solar radiation, climatology, animal mechanics and ocean tides. One of his more bizarre applications of mathematics was to demonstrate a humane method of execution by hanging, by lengthening the drop to ensure instant death.

### Zhukovsky’s Airfoil

Published February 27, 2020 Occasional ClosedTags: Applied Maths, Fluid Dynamics

A simple transformation with remarkable properties was used by Nikolai Zhukovsky around 1910 to study the flow around aircraft wings. It is defined by

and is usually called the *Joukowsky Map*. We begin with a discussion of the theory of fluid flow in two dimensions. Readers familiar with 2D potential flow may skip to the section *Joukowsky Airfoil*.

### Joseph Fourier and the Greenhouse Effect

Published March 21, 2019 Irish Times ClosedTags: Applied Maths, Fourier analysis, Geophysics

Jean-Baptiste Joseph Fourier, French mathematician and physicist, was born in Auxerre 251 years ago today. He is best known for the mathematical techniques that he developed in his analytical theory of heat transfer. Over the past two centuries, his methods have evolved into a major subject, harmonic analysis, with widespread applications in number theory, signal processing, quantum mechanics, weather prediction and a broad range of other fields [TM159 or search for “thatsmaths” at irishtimes.com].

### The Kill-zone: How to Dodge a Sniper’s Bullet

Published March 14, 2019 Occasional ClosedTags: Applied Maths, Mechanics

Under mild simplifying assumptions, a projectile follows a parabolic trajectory. This results from Newton’s law of motion. Thus, for a fixed energy, there is an accessible region around the firing point comprising all the points that can be reached. We will derive a mathematical description for this *kill-zone *(the term kill-zone, used for dramatic effect, is the region embracing all the points that can be reached by a sniper’s bullet, given a fixed muzzle velocity).

Family of trajectories with fixed initial speed and varying launch angles. Two particular trajectories are shown in black. Continue reading ‘The Kill-zone: How to Dodge a Sniper’s Bullet’

### Euler and the Fountains of Sanssouci

Published September 7, 2017 Irish Times ClosedTags: Applied Maths, Euler, Fluid Dynamics

When Frederick the Great was crowned King of Prussia in 1740 he immediately revived the Berlin Academy of Sciences and invited scholars from throughout Europe to Berlin. The most luminous of these was Leonhard Euler, who arrived at the academy in 1741. Euler was an outstanding genius, brilliant in both mathematics and physics. Yet, a myth persists that he failed spectacularly to solve a problem posed by Frederick. Euler is reputed to have bungled his mathematical analysis. In truth, there was much bungling, but the responsibility lay elsewhere. [TM122 or search for “thatsmaths” at irishtimes.com].

### Inertial Oscillations and Phugoid Flight

Published July 13, 2017 Occasional ClosedTags: Applied Maths, Fluid Dynamics, Geophysics

The English aviation pioneer Frederick Lanchester (1868–1946) introduced many important contributions to aerodynamics. He analysed the motion of an aircraft under various consitions of lift and drag. He introduced the term **“phugoid”** to describe aircraft motion in which the aircraft alternately climbs and descends, varying about straight and level flight. This is one of the basic modes of aircraft dynamics, and is clearly illustrated by the flight of gliders.

### Wavelets: Mathematical Microscopes

Published May 25, 2017 Occasional ClosedTags: Applied Maths, Wave Motion

In the last post, we saw how Yves Meyer won the Abel Prize for his work with wavelets. Wavelets make it easy to analyse, compress and transmit information of all sorts, to eliminate noise and to perform numerical calculations. Let us take a look at how they came to be invented.

### Yves Meyer wins 2017 Abel Prize

Published May 18, 2017 Irish Times ClosedTags: Applied Maths, Wave Motion

On 23 May King Harald V of Norway will present the Abel Prize to French mathematician Yves Meyer. Each year, the prize is awarded to a laureate for “outstanding work in the field of mathematics”. Comparable to a Nobel Prize, the award is named after the exceptional Norwegian, Niels Henrik Abel who, in a short life from 1802 to 1829, made dramatic advances in mathematics. Meyer was chosen for his development of the mathematical theory of *wavelets*. [See TM115 or search for “thatsmaths” at irishtimes.com].

Towering over O’Connell Street in Dublin, the Spire of Light, at 120 metres, is about three times the height of its predecessor [TM109 or search for “thatsmaths” at irishtimes.com]. The Spire was erected in 2003, filling the void left by the destruction in 1966 of Nelson’s Pillar. The needle-like structure is a slender cone of stainless steel, the diameter tapering from 3 metres at the base to 15 cm at its apex. The illumination from the top section shines like a beacon throughout the city.

### Marvellous Merchiston’s Logarithms

Published November 17, 2016 Irish Times ClosedTags: Applied Maths, History, Numerical Analysis

Log tables, invaluable in science, industry and commerce for 350 years, have been consigned to the scrap heap. But logarithms remain at the core of science, as a wide range of physical phenomena follow logarithmic laws [TM103 or search for “thatsmaths” at irishtimes.com].

### Thank Heaven for Turbulence

Published October 20, 2016 Irish Times ClosedTags: Applied Maths, Fluid Dynamics

The chaotic flow of water cascading down a mountainside is known as turbulence. It is complex, irregular and unpredictable, but we should count our blessings that it exists. Without turbulence, we would gasp for breath, struggling to absorb oxygen or be asphyxiated by the noxious fumes belching from motorcars, since pollutants would not be dispersed through the atmosphere [TM101, or search for “thatsmaths” at irishtimes.com].

### Modelling Rogue Waves

Published May 5, 2016 Irish Times ClosedTags: Applied Maths, Fluid Dynamics, Wave Motion

There are many eyewitness accounts by mariners of gigantic waves – almost vertical walls of water towering over ocean-going ships – that appear from nowhere and do great damage, sometimes destroying large vessels completely. Oceanographers, who have had no way of explaining these ‘rogue waves’, have in the past been dismissive of these reports [TM090, or search for “thatsmaths” at irishtimes.com].

### Richardson’s Fantastic Forecast Factory

Published January 7, 2016 Irish Times ClosedTags: Applied Maths, Computer Science, Fluid Dynamics

Modern weather forecasts are made by calculating solutions of the mathematical equations that express the fundamental physical principles governing the atmosphere [TM083, or search for “thatsmaths” at irishtimes.com]

The solutions are generated by complex simulation models with millions of lines of code, implemented on powerful computer equipment. The meteorologist uses the computer predictions to produce localised forecasts and guidance for specialised applications.

### The Flight of a Golf Ball

Published December 3, 2015 Irish Times ClosedTags: Applied Maths, Fluid Dynamics

Golf balls fly further today, thanks to new materials and mathematical design. They are a triumph of chemical engineering and aerodynamics. They are also big business, and close to a billion balls are sold every year. [TM081: search for “thatsmaths” at Irish Times ].

### Mathematics Solving Crimes

Published November 19, 2015 Irish Times ClosedTags: Applied Maths, Geometry, Statistics

What use is maths? Why should we learn it? A forensic scientist could answer that virtually all the mathematics we learn at school is used to solve crimes. Forensic science considers physical evidence relating to criminal activity and practitioners need competence in mathematics as well as in the physical, chemical and biological sciences [TM080: search for “thatsmaths” at irishtimes.com ].

Trigonometry, the measurement of triangles, is used in the analysis of blood spatter. The shape indicates the direction from which the blood has come. The most probable scenario resulting in blood spatter on walls and floor can be reconstructed using trigonometric analysis. Such analysis can also determine whether the blood originated from a single source or from multiple sources.

### Game Theory & Nash Equilibrium

Published June 11, 2015 Occasional ClosedTags: Algorithms, Applied Maths, Computer Science, Games

Game theory deals with mathematical models of situations involving conflict, cooperation and competition. Such situations are central in the social and behavioural sciences. Game Theory is a framework for making rational decisions in many fields: economics, political science, psychology, computer science and biology. It is also used in industry, for decisions on manufacturing, distribution, consumption, pricing, salaries, etc.

During the Cold War, Game Theory was the basis for many decisions concerning nuclear strategy that affected the well-being of the entire human race.

### Modelling the Markets

Published May 7, 2015 Irish Times ClosedTags: Algorithms, Applied Maths, Computer Science

Mathematics now plays a fundamental role in modelling market movements [see this week’s That’s Maths column (TM067) or search for “thatsmaths” at irishtimes.com].

### For Good Comms, Leaky Cables are Best

Published April 16, 2015 Irish Times ClosedTags: Applied Maths, History, Wave Motion

A counter-intuitive result of Oliver Heaviside showed how telegraph cables should be designed [see this week’s *That’s Maths* column (TM066) or search for “thatsmaths” at irishtimes.com].

### You Can Do Maths

Published March 19, 2015 Irish Times ClosedTags: Applied Maths, Arithmetic, Education, Maps, Social attitudes

Bragging about mathematical ineptitude is not cool. There is nothing admirable about ignorance and incompetence. Moreover, everyone thinks mathematically all the time, even if they are not aware of it. Can we all do maths? Yes, we can! [See this week’s *That’s Maths* column (TM064) or search for “thatsmaths” at irishtimes.com].

### Earth’s Shape and Spin Won’t Make You Thin

Published November 20, 2014 Irish Times ClosedTags: Applied Maths, Geometry

Using a simple pendulum we can determine the shape of the Earth. That amazing story is told in this week’s *That’s Maths* column in *The Irish Times* (**TM057** or search for “thatsmaths” at www.irishtimes.com ).

Continue reading ‘Earth’s Shape and Spin Won’t Make You Thin’

### Light Weight (*)

Published October 30, 2014 Occasional ClosedTags: Applied Maths, Astronomy, Mechanics, Physics

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?

Published September 18, 2014 Irish Times ClosedTags: Applied Maths, Fluid Dynamics, Physics, Wave Motion

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).

### Sunflowers and Fibonacci: Models of Efficiency

Published June 5, 2014 Irish Times ClosedTags: 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’

Next week’s post will be about a model of the future of civilization! It is based on the classical predator-prey model, which is reviewed here.

### Rollercoaster Loops

Published April 10, 2014 Occasional ClosedTags: Applied Maths, Mechanics, Physics

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.

Continue reading ‘Rollercoaster Loops’

### Robots & Biology

Published January 16, 2014 Irish Times ClosedTags: 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.

### White Holes in the Kitchen Sink

Published January 9, 2014 Occasional ClosedTags: Applied Maths, Fluid Dynamics, Mechanics, Physics, Wave Motion

A tidal bore is a wall of water about a metre high travelling rapidly upstream as the tide floods in. It occurs where the tidal range is large and the estuary is funnel-shaped (see previous post on this blog). The nearest river to Ireland where bores can be regularly seen is the Severn, where favourable conditions for these hydraulic jumps occur a few times each year.

But you do not have to leave home to observe hydraulic jumps. Continue reading ‘White Holes in the Kitchen Sink’

### Interesting Bores

Published January 2, 2014 Irish Times ClosedTags: Applied Maths, Fluid Dynamics, Geophysics, Mechanics, Wave Motion

This week’s *That’s Maths* column in the* Irish Times* ( TM036 ) is about bores. But don’t be put off: they are very interesting.

### The Simpler the Better

Published October 3, 2013 Irish Times ClosedTags: Algorithms, Applied Maths, Computer Science

This week’s* That’s Maths* in *The Irish Times* ( TM030 ) is about Linear Programming (LP) and about how it saves millions of Euros every day through optimising efficiency.

A Berkeley graduate student, George Dantzig, was late for class. He scribbled down two problems written on the blackboard and handed in solutions a few days later. But the problems on the board were not homework assignments; they were two famous unsolved problems in statistics. The solutions earned Dantzig his Ph.D.

Continue reading ‘The Simpler the Better’

The topic of the *That’s Maths* column ( TM026 ) in the* Irish Times* this week is the surprising and delightful way in which mathematics developed for its own sake turns out to be eminently suited for solving practical problems.

Recently, I kayaked with two friends on the River Shannon, which flows southward through the centre of Ireland. Starting at Dowra, Co. Cavan, we found it easy paddling until we reached Lough Allen, when the going became very tough. It was an uphill struggle.

*Could we really be going uphill while heading downstream?* That seems bizarre but, in a certain sense, it is possible.

### Ducks & Drakes & Kelvin Wakes

Published May 18, 2013 Irish Times ClosedTags: Applied Maths, History, Wave Motion

The theme of this week’s *That’s Maths* column in the* **Irish Times* ( TM021 ) is Kelvin Wakes, the beautiful wave patterns generated as a duck or swan swims through calm, deep water or in the wake of a ship or boat.

Continue reading ‘Ducks & Drakes & Kelvin Wakes’