Stahl67" bmp

186

WALTER R. STAHL

a very restricted modeling situation. Mannikins are also in use for cloth-ing design, anthropometry, analysis of cabin and cockpit instrument arrangement, etc.

In a sense synthetic furs, leathers, and clothing represent physical analogs of the mammalian skin, as defined by pertinent thermal dimen-sional constants. Thermal analog models of various kinds are in use. Detailed simulations of heat balance in very cold climates and after exposure to nuclear-heat radiation flashes have been madę. Rutkin and Barish (1964) present eąuations and data on local tissue freezing of brain tumors which can be analyzed in terms of known thermal dimen-sionless numbers.

V. Numerical and Kinetic Models

Typical examples of this class of models are Computer simulations of Chemical transport and migration in body compartments, multiple simultaneous enzyme reactions, gene redistributions during natural selection, disease or rumor spread in a community, and celi birth and death in the bonę marrow. Typically, the eąuations governing such models contain very few physical dimensional constants and tend to be homogeneous in some simple dimensionality, e.g., rates of changes of molecules or species with time. Cybernetic and psychological models of a numerical naturę are considered in a subseąuent section.

A. Numerical Kinetics Simulation

A large number of reports are available on numerical “compartment models.” These consist of several reservoirs of substances, usually Solutions, into which theie is intake and outfłow, and between which there is kinetic transport. The governing eąuations are usually of the form

dNt/dt = k_a -f- kijNj + /w*A* T . • . T^- k<_zN_z    (3)

in which the change of ąuantity (or of concentration) of substance N, is a linear function of ąuantities Nj,N_k, . . . N_z (or concentrations) of all other substances and the interaction coefficients may be positive or negative. In morę complex cases nonlinear terms of the form kujNiNj or k_ijkNjN_k may occur and complicate analysis. The terms in such eąuations should be homogeneous. If divided by each other, they yield dimensionless invariants representing ratios of rates of species formation due to various causes; complex physical dimensionless numbers are not expected to arise in such eąuations.

A comprehensive discussion of compartment models of this type and