Diffusion Attrition Model

In attempting to investigate the attrition of a large target complex (raid) caused by attacking manned or unmanned interceptors, the analogy to the diffusion of electrons or neutrons in suitable media, or similarly, radiation transport in a stellar atmosphere, suggests itself. The interceptors correspond to the diffusing particles while the target complex corresponds to the transporting medium. The particles undergo absorption and elastic scattering in the transport medium, while the interceptors “lock-on” to and destroy targets (absorption), or “break-lock” and possibly seek new targets (scattering) in the target analogue medium. Depletion of the target medium as a result of attrition, which does not usually occur in particulate diffusion, must be taken into account in the target medium analogue. Consideration of the usual interceptor capabilities usually leads to a target medium with “heavy absorption” and “light scattering” properties. The above analogue is used to determine the attrition in target number density in time and space. This is accomplished by finding solutions to the transport equation for the interceptor flux density in the target medium. Solving this integro-differential equation comprises the central effort, since analytical solutions are known exactly only in an isolated number of cases. The transport equation in the interceptor flux and an equation obtained for the target medium density constitute a pair of simultaneous equations. Eliminating the interceptor flux density between these equations yields the sought for expression of time and space history of attrition in the target medium. An illustrative problem is given with an outline of its solution.