B. Hasslacher

~e show that a class of deterministic lattice gases with discrete Boolean elements simulates the Navier-Stokes equation, and can be used to design simple, massively parallel computing machines.

A technique introduced by Symanzik is used to derive a series of equations obeyed order by order in perturbation theory by the structure functions ${W}_{1}$ and $\ensuremath{\nu}{W}_{2}$ entering the cross section for inelastic electron scattering. These equations relate the ${q}^{2}$, $\ensuremath{\nu}$, and coupling-constant dependence of ${W}_{1}$ and $\ensuremath{\nu}{W}_{2}$ in a manner reminiscent of the renormalization-group results of Gell-Mann and Low. The equations are used to compute the leading logarithmic contribution to $\ensuremath{\nu}{W}_{2}$ in a theory of fermions coupled to pseudoscalar particles and a theory of fermions coupled to vector particles.

Reactive lattice gas automata simulations show that Turing structure can form on a mesoscopic scale and are stable to molecular fluctuations in this domain. Calculations on the Sel'kov model suggest that Turing instabilities can give rise to global spatial symmetry breaking in ATP concentration within the cell cytoplasm with a mesoscopic Turing scale well within typical cell dimensions. This leads to a new mechanism for the global breaking of energy distribution in the cell. It also leads to reappraisal of the importance of the Turing effect on extended biochemical spatial structures and energy transport available to cell morphogenesis.