Allen Hjelmfelt’s research while affiliated with Stanford University and other places

Oscillations in light emission and species concentrations, are measured as periodic perturbations are simultaneously applied to the input rates of acetaldehyde and oxygen in the gas-phase combustion of acetaldehyde in a continuous-flow stirred tank reactor for conditions where the autonomous reaction itself is oscillatory. The experimental results are compared with the predictions of a five-variable thermokinetic model. We measure periodic responses in the fundamental entrainment band (ratio of frequency of perturbation to frequency of response equal to unity) for four different values of phase shift between the acetaldehyde and oxygen perturbation wave forms as we vary the frequency and amplitude of the external periodic perturbations. Outside of the entrainment bands we find quasiperiodic response. We determine the phases of the light emission and six species concentrations, as measured with a mass spectrometer, with respect to the periodic perturbation, the variation of these phases across the fundamental entrainment band for different values of reactant phase shift and for different amplitudes of perturbation, and the effects of the phase shift between the two input perturbations on the light emission response of the system for different frequencies of perturbation. Both the experiments and calculations predict a widening of the entrainment band with an increase in perturbation amplitude, and the same variation in bandwidths for the four values of reactant phase shift studied. The experiments and calculations also predict the same general trends in light phase and species phases (difference between the light emission and species concentrations with respect to the perturbing wave form) as the band is traversed for different amplitudes of perturbation and for different values of reactant phase shift.

Experiments are reported on the electrochemical displacement of the nonlinear minimum bromate reaction from stationary states far from equilibrium and from equilibrium. We measure the CeIV/CeIII electrode potential V at a given displacement effected by an imposed current clamp, I. The variation of the excess power (V - Vs)I, where Vs is the electrode potential at a stationary state, versus the imposed current is of the same form as the time derivative of an excess work, related in prior theoretical analyses to the thermodynamics of systems far from equilibrium.

We review our work on the computational functions of the kinetics of chemical networks. We examine spatially homogeneous networks which are based on prototypical reactions occurring in living cells and show the construction of logic gates and sequential and parallel networks. This work motivates the study of an important biochemical pathway, glycolysis, and we demonstrate that the switch that controls the flux in the direction of glycolysis or gluconeogenesis may be described as a fuzzy AND operator. We also study a spatially inhomogeneous network which shares features of theoretical and biological neural networks.

Experiments on pattern recognition are: performed with a network of eight open, bistable, mass-coupled chemical reactors. A programming rule is used to determine the network connectivity in order to store sets of stationary patterns of reactors with low or high concentrations. Experiments show that these stored patterns can be recalled from similar initial patterns. To our knowledge, this is the first chemical implementation of a type of neural network computing device. The experiments on this small network agree with simulations and support the predictions of the performance-of large:networks.

We present experiments which test for a nonequilibrium component to the electromotive force (emf) for a half-reaction involving species generated by a nonlinear reaction in a nonequilibrium steady state. The existence of this effect has been predicted by Keizer. The minimal bromate oscillatory reaction is run in a continuous flow stirred tank reactor under conditions which result in bistability. The reaction forms Ce(IV) from Ce(III) in a nonequilibrium steady state. This redox couple generates a voltage at a Pt electrode, relative to a reference electrode. Knowing the concentrations of the cerium species, this potential can be compared with that given by those concentrations of Ce(III) and Ce(IV) under equilibrium conditions, the Nernst equation. In the nonequilibrium stationary state we find deviations. We search for the source of these deviations. We do not find evidence for such explanations as mixed potentials but are unable to entirely rule them out. In the absence of such effects, the results are consistent with the existence of a non-Nernstian component of the emf for nonlinear systems in nonequilibrium steady states. 17 refs., 2 figs., 1 tab.

We stabilize the unstable steady state of a spatially inhomogeneous optically bistable ZnSe interference filter and measure the average intensity of the light transmitted and reflected by the filter. We also image the spatial structures which are the stable and unstable steady states by spatially resolving the transmitted light. We further measure relaxations from the unstable branch to the two stable branches. Relaxations to the low-temperature branch occur homogeneously while relaxations to the high-temperature branch occur by the propagation of a front. The results are in agreement with calculated predictions of a deterministic model of this system. A comparison is also made to nonlinear reaction-diffusion systems.

We study a neural network composed of excitable FitzHugh neurons that interact by diffusive type connections. Patterns of neural activity may be stored by a Hebbian rule. The stored patterns are recalled and given by the transient activity of the neurons after the network has been perturbed by related patterns and relaxes back to its steady state. Periodic perturbations of the network are repeated requests for computations and result in simple periodic, complex periodic, and chaotic responses and corresponding computational performances.

A feedback method is used to stabilize unstable stationary states in experiments with the chlorite-iodide reaction. The unstable stationary states occur in oscillatory and excitable regions of constraint space. Stabilization of unstable steady states provides information about these states and may be of practical importance. An analytical study of a model mechanism of this reaction is consistent with the experiments. This feedback method does not create new stationary states but stabilizes unstable stationary states present in the autonomous system. Unlike ''thermostat'' type methods, knowledge of the exact location of the unstable stationary states of the autonomous system is not required to implement this feedback method.

Schloegl's criterion for equistability of two stable stationary states of an inhomogeneous chemical kinetic system is valid only for single-variable cases dependent along a single spatial coordinate. We test the thermodynamic theory, developed in the preceding article for multivariable systems, in one dimension by comparison with calculations based on the deterministic reaction-diffusion equation for a cubic Schloegl model (single variable). This reaction-diffusion system is equivalent to a coupled multivariable system. The prediction of the thermodynamic theory of equistability approaches Schloegl's result as the length of the system increases. We also test the theory for an optically bistable (ZnSe) system which has been studied experimentally; in this system, temperature is the variable, and there is transport by thermal conduction. Again, we find that the prediction of the multivariable thermodynamic theory approaches the result from the deterministic kinetic equation as the length of the system increases. Further, the single-variable thermodynamic theory of relative stability of homogeneous steady states agrees with experiments and with the prediction of the deterministic equation.

We simulate a pattern recognition device constructed from mass-coupled chemical reactors. Each reactor is an open system containing a bistable (iodate-arsenous acid) reaction. We store arbitrary patterns of high and low iodide concentrations in the network using a Hebb type rule. When the network is initialized with a pattern which is similar to a stored pattern, errors in the initial pattern are corrected and the similar stored pattern is recalled. When the network is initialized with a pattern which is not similar to a stored pattern, the network evolves to a homogeneous state which signals nonrecognition. The network is a programmable parallel computational device.