On counts of Bernoulli strings and connections to rank orders and random permutations

A method and apparatus for achieving adiabatic heat ignition of combustible material, particularly explosive compositions which involves entrapping a quantity of gas in a chamber which is in communication with the combustible material and suddenly compressing the gas to the extent that the temperature thereof is increased adiabatically to the ignition temperature of the combustible material. The apparatus is particularly adaptable for use as an adiabatic ignition device for detonating cord and shaped charges of perforating guns for completion of wells. A quantity of high explosive within an explosive barrel is in detonating proximity with the detonating cord. A cylinder forms an air chamber which is in communication with the explosive composition and is provided with a piston for compression of the gas. One or more shear pins or other locking devices are provided to secure the piston in immovable relation with the cylinder. A force is caused to act on the piston which force is typically induced by fluid pressure within the well which acts on the piston and which may also be induced. As this force reaches a predetermined magnitude, or by means of a weight bar dropped or lowered on wireline from the surface, the piston will be released and the force will drive the piston into the cylinder, compressing the gas sufficiently to raise the temperature of the gas adiabatically to the ignition temperature of the explosive composition.