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Lanchester's Laws
Lanchester's laws are mathematical formulae for calculating the relative strengths of military forces. The Lanchester equations are differential equations describing the time dependence of two armies' strengths A and B as a function of time, with the function depending only on A and B. In 1915 and 1916, during World War I, M. Osipov and Frederick Lanchester independently devised a series of differential equations to demonstrate the power relationships between opposing forces. Among these are what is known as ''Lanchester's linear law'' (for ancient combat) and ''Lanchester's square law'' (for modern combat with long-range weapons such as firearms). Lanchester's linear law For ancient combat, between phalanxes of soldiers with spears, say, one soldier could only ever fight exactly one other soldier at a time. If each soldier kills, and is killed by, exactly one other, then the number of soldiers remaining at the end of the battle is simply the difference between the larger a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formula
In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a ''chemical formula''. The informal use of the term ''formula'' in science refers to the general construct of a relationship between given quantities. The plural of ''formula'' can be either ''formulas'' (from the most common English plural noun form) or, under the influence of scientific Latin, ''formulae'' (from the original Latin). In mathematics In mathematics, a formula generally refers to an identity which equates one mathematical expression to another, with the most important ones being mathematical theorems. Syntactically, a formula (often referred to as a ''well-formed formula'') is an entity which is constructed using the symbols and formation rules of a given logical language. For example, determining the volume of a sphere requires a significant amount of integral calculus or its geometrical analogue, the method of exhaustion. However, having done t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Battle Of Gettysburg
The Battle of Gettysburg () was fought July 1–3, 1863, in and around the town of Gettysburg, Pennsylvania, by Union and Confederate forces during the American Civil War. In the battle, Union Major General George Meade's Army of the Potomac defeated attacks by Confederate General Robert E. Lee's Army of Northern Virginia, halting Lee's invasion of the North. The battle involved the largest number of casualties of the entire war and is often described as the war's turning point due to the Union's decisive victory and concurrence with the Siege of Vicksburg.Rawley, p. 147; Sauers, p. 827; Gallagher, ''Lee and His Army'', p. 83; McPherson, p. 665; Eicher, p. 550. Gallagher and McPherson cite the combination of Gettysburg and Vicksburg as the turning point. Eicher uses the arguably related expression, " High-water mark of the Confederacy". After his success at Chancellorsville in Virginia in May 1863, Lee led his army through the Shenandoah Valley to begin his second ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Salvo Combat Model
The salvo combat model provides a mathematical representation of anti-ship missile battles between modern warships. It was developed by Wayne Hughes at the U.S. Naval Postgraduate School in Monterey, California, and published in 1995. The salvo model describes the basic elements of modern missile combat in a very simple manner. This is similar to how Lanchester's square law provides a simple model of modern gun combat. Model parameters Basic form Suppose that two naval forces, Red and Blue, are engaging each other in combat. The battle begins with Red firing a salvo of missiles at Blue. The Blue ships try to shoot down those incoming missiles. Simultaneously, Blue launches a salvo that Red tries to intercept. This exchange of missile fire can be modeled as follows. Let symbol ''A'' represent the number of combat units (warships or other weapon platforms) in the Red force at the beginning of the battle. Each one has ''offensive firepower α'', which is the number of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lewis Fry Richardson
Lewis Fry Richardson, FRS (11 October 1881 – 30 September 1953) was an English mathematician, physicist, meteorologist, psychologist, and pacifist who pioneered modern mathematical techniques of weather forecasting, and the application of similar techniques to studying the causes of wars and how to prevent them. He is also noted for his pioneering work concerning fractals and a method for solving a system of linear equations known as modified Richardson iteration. Early life Lewis Fry Richardson was the youngest of seven children born to Catherine Fry (1838–1919) and David Richardson (1835–1913). They were a prosperous Quaker family, David Richardson operating a successful tanning and leather-manufacturing business. At age 12 he was sent to a Quaker boarding school, Bootham School in York, where he received an education in science, which stimulated an active interest in natural history. In 1898 he went on to Durham College of Science (a college of Durham University) whe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Petrie Multiplier
The Petrie multiplier is a thought experiment or mathematical model invented by British computer scientist Karen Petrie, and first described by Ian Gent in 2013. The multiplier "shows that if the percentage of men and women in the room who make questionable remarks to the other sex is equal, then the average number of sexist remarks experienced by members of one party scales by the square of the proportion of one party to the other. Mathematical formulation Gent defined the multiplier in the following terms: The Petrie multiplier corresponds to Lanchester's square law in battle and predator–prey dynamics. Expanded model The model assumes that men and women are equally sexist. Further, each sexist remark made by a man is assumed to randomly target one of the women and vice versa. A more complex analysis published in the Journal of Physics A modeled heterogeneous levels of sexism by assuming each person to make sexist remarks according to an independent Poisson process, mai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maneuver Warfare
Maneuver warfare, or manoeuvre warfare, is a military strategy which seeks to shatter the enemy's overall cohesion and will to fight. Background Maneuver warfare, the use of initiative, originality and the unexpected, combined with a ruthless determination to succeed, seeks to avoid opponents' strengths while exploiting their weaknesses and attacking their critical vulnerabilities and is the conceptual opposite of attrition warfare. Rather than seeking victory by applying superior force and mass to achieve physical destruction, maneuver uses preemption, deception, dislocation, and disruption to destroy the enemy's will and ability to fight. Historically, maneuver warfare was stressed by small militaries, the more cohesive, better trained, or more technologically advanced than attrition warfare counterparts. The term "tactical maneuver" is used by maneuver warfare theorists to refer to movement by forces to gain "advantageous position relative to the enemy," as opposed to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lotka–Volterra Equations
The Lotka–Volterra equations, also known as the predator–prey equations, are a pair of first-order nonlinear differential equations, frequently used to describe the dynamics of biological systems in which two species interact, one as a predator and the other as prey. The populations change through time according to the pair of equations: \begin \frac &= \alpha x - \beta x y, \\ \frac &= \delta x y - \gamma y, \end where * is the number of prey (for example, rabbits); * is the number of some predator (for example, foxes); *\tfrac and \tfrac represent the instantaneous growth rates of the two populations; * represents time; *, , , are positive real parameters describing the interaction of the two species. The Lotka–Volterra system of equations is an example of a Kolmogorov model, which is a more general framework that can model the dynamics of ecological systems with predator–prey interactions, competition, disease, and mutualism. History The Lotka–Volterra predat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Attrition Warfare
Attrition warfare is a military strategy consisting of belligerent attempts to win a war by wearing down the enemy to the point of collapse through continuous losses in personnel and materiel. The word ''attrition'' comes from the Latin root , meaning "to rub against", similar to the "grinding down" of the opponent's forces in attrition warfare. Strategic considerations Attrition warfare represents an attempt to grind down an opponent's ability to make war by destroying their military resources by any means including guerrilla warfare, people's war, scorched earth and all kind of battles apart from a decisive battle. Attrition warfare does not include all kinds of Blitzkrieg or using concentration of force and a decisive battle to win. The side that reinforces their army at a higher speed will normally win the war. Clausewitz called it the exhaustion of the adversary. A side that perceives itself to be at a marked disadvantage may deliberately seek out attrition warfare to neutr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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