Posts Tagged 'Applied Maths'

Marvellous Merchiston’s Logarithms

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].

Android app RealCalc with natural and common log buttons indicated.

Thank Heaven for Turbulence

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].

Turbulent flow behind a cylindrical obstacle [image from “An Album of Fluid Motion”, Milton Van Dyke, 1982].

Modelling Rogue Waves

Rogue wave [image from BBC Horizons, 2002]

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

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

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 ].

Simulation of flow around the dimples of a golf ball. Image from http://www.bioe.umd.edu/~balaras/html/topics.shtml

Mathematics Solving Crimes

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

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.

Theory of Games and Economic Behavior.
Centre: John von Neumann. Right: Oskar Morgenstern.

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.