Cybernetic models, developed earlier by the authors, have been evaluated experimentally for growth of Klebsiella oxytoca in batch cultures using mixed substrates from glucose, xylose, arabinose, lactose, and fructose. Based entirely on information procured single substrates, models accurately predict without further parameter fitting, diauxic automatically predicting order which are consumed. Even triauxic a mixture lactose is predicted model based substrate data. Growth glucose-fructose...

Abstract The internal regulatory processes, which underlie a variety of behavior in microbial growth on multiple substrates, are viewed as manifestation an invariant strategy to optimize some goal the cells. A goal‐seeking or cybernetic model is proposed here, with optimization obased short‐term perspective response environment. parameters determined from data single substrates. predicts entire range substrates simultaneous utilization all sugars sequential pronounced diauxic lags. It shown...

Abstract Mathematical models for microbial growth in batch and continuous cultures are formulated. The have been referred to as distributed since the population a culture is looked upon protoplasmic mass uniformly throughout culture. Growth regarded increase this by conversion of medium components into biological metabolic products. Two sets presented. first arise from introducing additional considerations model proposed Monod account stationary phase decline These unstructured, they do not...

Abstract Experimental measurements of transient drop size distributions in a stirred liquid‐liquid dispersion (with low dispersed phase fraction) have been used concomitantly with population balance theory to recover the transition probability droplet breakage, based on similarity concept. The data remarkably uphold proposed hypothesis, and estimated function displays same qualitative trend as model due Narsimhan et al. (1979).

Abstract Photographic measurements of transient drop‐size distributions from stirred liquid‐liquid systems low dispersed phase fraction in a batch vessel confirm consistency with similarity behavior population balance established earlier by Narsimhan et al. (1980). Moreover, breakage functions are presented generalized dimensionless form accounting for dependence on physical properties the system and power input through stirring. This information is essential predicting systems. Experimental...

Abstract A simulation procedure is presented in this work which can analyze the behavior of any dispersed phase system consisting particles whose random specified terms probability functions. The distinguishes itself from its predecessors being free arbitrary discretization time or other parameter along evolves, and ability to predict randomly behaving small populations. Where population balance equations, describe particulate systems, cannot be readily solved, technique herein represents an...

Abstract A cybernetic framework is presented which views microbial response in multiple substrate environments as a judicious investment of cellular resources synthesizing different key proteins according to an optimal regulatory strategy. mathematical model developed within the for diauxic growth Klebsiella pneumoniae on mixture D ‐glucose and ‐xylose. The “bang–bang” policy describes well experimental observations obtained using fermenter coupled Apple II microcomputer. Striking variations...

Abstract An analytical solution is obtained to the extended Graetz problem with prescribed wall flux, based on a selfadjoint formalism resulting from decomposition of convective diffusion equation into pair first‐order partial differential equations. The simple, computationally efficient and in striking contrast incomplete numerical efforts past.

Abstract Flux balance analysis (FBA) in combination with the decomposition of metabolic networks into elementary modes has provided a route to modeling cellular metabolism. It is dependent, however, on availability external fluxes such as substrate uptake or growth rate before estimates can become available intracellular fluxes. The framework classically does not allow regulation formulation dynamic models except through measurement cybernetic approach Ramkrishna and coworkers provides for...