Random Ramblings to 24 April 2010

Cascading failure
A failure of a system where one component's failure causes a chain-reaction failure of other components. A system bearing a load is susceptible to this type of failure, where an overloaded component shifts its load to other components upon its individual failure. In an electrical grid, a cascading failure occurs when a transformer's failure requires the other transformers to bear the electrical load, increasing the chance that one of those transformers will also fail due to overloading.

Where the components are fully interconnected and handle a fixed load, the per-component load trend is a rectangular hyperbola. This signifies that the per-component load increases at an increasing rate as components fail. As a result, the chance of any individual component's failing also increases at an increasing rate.

A graph illustrating a cascading failure in a World of Warcraft boss encounter. The trend is a rectangular hyperbola.

Coriolis effect
The apparent curving of an object moving in a straight line, according to a rotating observer. It explains the rotation of cyclones as anti-clockwise in the Northern Hemisphere and clockwise in the Southern Hemisphere. It also partially explains the direction that draining water rotates, although factors such as turbulence in the water have a greater effect.

The effect of the Coriolis effect on a ball rolling on a rotating surface.

Economic profit
The profit on an economic activity, considering opportunity cost. While a firm will not pursue an activity that incurs an accounting loss, it will also not want to pursue it if there are 'greener pastures' available to them. As a result, when the accounting profit is positive, the economic profit can still be negative (they can incur an economic loss) if the opportunity cost exceeds accounting profit. Where accounting profit equals opportunity cost, the firm will generate normal profit (which will occur when every firm in the market maximises their individual profits). The formula for economic profit is:

Economic profit = Revenues - Expenses - Opportunity cost ; or
Economic profit = Accounting profit - Opportunity cost

Euler's number
The base a of the function y = a^x where the gradient at x = 0 is 1. By convention, it is designated the pronumeral e, and to 9 decimal places, e = 2.718281828. This mathematical constant is important in situations involving exponential growth and decay, such as compound interest and biological growth, since this trend is considered natural.

For y = a^x , a = e where ^dy/_dx = 1 at x = 0 .

Keratin
A tough protein commonly used by organisms as protection. In humans, it is found in the nails and hair. When burnt (e.g. using a hair straightener on hair), it produces a foul odour.

Phycocyanin
A pigment used by cyanobacteria (blue-green algae), in conjunction with chlorophyll, in photosynthesis. It absorbs red and orange light and appears cyan (the additive secondary colour of blue and green). As a food colouring, it is known as Lina Blue.

Rhombus
A quadrilateral with all four sides of equal length. It is a square when there is one right angle between two adjacent sides (which implies that all of the other three angles are right angles). It is more commonly known as a diamond.

The set of raid target icons in World of Warcraft. The rhombus is purple.

Whiplash
In medicine, an injury involving a sudden distortion of the neck. Where serious, damage to the spinal cord can occur, potentially leading to quadriplegia. It is most commonly suffered by occupants of a car in a rear-end collision (where there are no headrests), although a baby can also suffer from it when their body is shaken while being held.