Gerald Houghton

Cubic Cell Model for Self‐Diffusion in Liquids

A cubic cell model for viscous flow and self‐diffusion in liquids has been developed such that a linear Langevin equation for condensed systems can be deduced directly from the corresponding Navier‐Stokes equation, the molecular friction coefficient being then related to the viscosity and cell size. On restricting interactions to nearest neighbors in cubic symmetry involving an arbitrary choice of the number of nearest molecules and linking the friction coefficient and diffusivity by stochastic considerations, an expression has been produced that predicts self‐diffusion coefficients from viscosity and density data with an average deviation of 9%.

A lumped-film model for gas-liquid partition chromatography: Part I. Numerical methods of solution

Summary The differential equations of non-ideal gas-liquid partition chromatography have been derived and simplified by introducing the concept of a lumped liquid film.The resulting equations have been solved numerically by finite difference methods using an IBM-704 digital computer. The stability and convergence of the computer solutions is discussed and the computer program is used to simulate the actual behavior of a typical column under various operating conditions. The system chosen for study was the elution of a slug of isobutylene with argon as the carrier gas and dinonyl phthalate as the stationary phase.

The additivity of rate and diffusion phenomena in continuous chromatography

Abstract By considering a finite rate of exchange between the mobile and stationary phases as a perturbation on equilibrium theory, it has been possible to arrive at conditions for the additivity and diffusion phenomena in continuous chromatography. The resulting diffusion equation and its solution for a pulse input provide an alternative method to the plate theory for the treatment of experimental chromatography data.

A lumped-film model for gas-liquid partition chromatography: Part II. Experimental evaluation of analytical solutions

Summary The differential equations governing gas-liquid partition chromatography have been simplified by using the assumptions of linear solubility and no pressure drop and introducing the concept of a lumped liquid film. Analytical solutions of the equations have been obtained for the cases with and without longitudinal dispersion. The solutions show that a finite rate of mass transfer into the liquid phase can affect both the shape of the elution curve and the retention time. A simple equation has been obtained relating the apparent retention time to the column variables and the depth of penetration into the liquid film. Experimental data on the elution of a pure isobutylene slug with helium using a stationary phase of dinonyl phthalate on fireback has shown the average fractional depth of penetration to be in the range 0.6–0.9 under normal operating conditions. It was found that the peneration model correlatates the retention time at various temperatures remarkably well, provided the slug size and the amount of stationary phase are held constant.

Optimal models for social change

By assigning coordinates to the environmental function space comprising all physical and mental stimuli, mathematical interpretations can be based on such terms as adaptability, and reactivity which relate to individuals interacting with their environment within a society. These psychometric concepts are incorporated into a framework of functional analysis, which permits the optimization of social change by maximizing the satisfaction integral through the use of variational or dynamic programming methods in conjunction with some optimal social policy. The approach provides a mathematical connection between psychology and sociology, and further demonstrates that existing forms of government are simulated by differential equations belonging to the same general class. The synthesis of new classes of functional equations describing social progress is visualized as a legitimate objective for abstract mathematical sociology.

Academic learning, a variational model

By assigning coordinates to the information space comprising all knowledge, rigorous mathematical interpretations can be placed on such terms as academic ability, memory and creativity such that these psychometric concepts can be incorporated into a framework of functional analysis which then permits the optimization of long-term academic learning processes through the location of the teaching trajectories in information space which will maximize the knowledge accumulated in a generalized educational system composed of a complex of subject-pupil-teacher interactions. The concepts of discrete and continuous information spaces are discussed in connection with subject-subject, subjectpupil and pupil-pupil interactions, and the advantages of using variational versus dynamic programming methods of optimizing alternative educational systems are evaluated.

The origin of lift forces in fluttering flight

A two-dimensional nonlinear integro-differential equation with time-varying coefficients describing the behavior of the fluttering wing-body systems typical of natural flight mechanisms has been deduced from the Navier-Stokes equation which generalizes local pressure and velocity distributions in the externally oscillating air field. The resulting equation for the wing forces is combined with an analogous expression for the forces of gravitation and acceleration associated with the body. The air acceleration force, not previously considered in bio-physical models of insect and bird flight, is shown to arise from a formal analysis of unsteady or time-varying contributions to the velocity field, while the square form of the conventional steady state aerodynamic forces is derived from the intertial terms in the Navier-Stokes equation with the aid of the approximations of Newtonian impact theory. Previous calculations (Houghton, 1964) have indicated that the contribution to gravitational stability of air acceleration and aerodynamic life are roughly in the ratio of 3:1.