A hybrid neuroal network algorithm for on-line state inference that accounts for differences in inoculum of Cephalosporium acremonium in fed-batch fermentors

One serious difficulty in modeling a fermentative process is the forecasting of the duration of the lag phase. The usual approach to model biochemical reactors relies on first-principles, unstructured mathematical models. These models are not able to take into account changes in the process response caused by different incubation times or by repeated fed batches. Toover come this problem, we have proposed a hybrid neural network algorithm. Feedforward neural networks were used to estimate rates of cell growth, substrate consumption, and product formation from on-line measurements during cephalosporin C production. These rates were included in the mass balance equations to estimate key process variables: concentrations of cells, substrate, and product. Data from fed-batch fermentation runs in a stirred aerated bioreactor employing the microorganism Cephalosporium acremonium ATCC 48272 were used. On-line measurements strongly related to the mass and activity of the cells used. They include carbon dioxide and oxygen concentrations in the exhausted gas. Good results were obtained using this approach.     

Nonlinear diffusion under a time dependent external force: q-maximum entropy solutions

Nonlinear diffusion equations provide useful models for a number of interesting phenomena, such as diffusion processes in porous media. We study here a family of nonlinear Fokker-Planck equations endowed both with a power-law nonlinear diffusion term and a drift term with a time dependent force linear in the spatial variable. We show that these partial differential equations exhibit exact time dependent particular solutions of the Tsallis maximum entropy (q-MaxEnt) form. These results constitute generalizations of previous ones recently discussed in the literature [C. Tsallis, D.J. Bukman, Phys. Rev. E 54, R2197 (1996)], concerning q-MaxEnt solutions to nonlinear Fokker-Planck equations with linear, time independent drift forces. We also show that the present formalism can be used to generate approximate q-MaxEnt solutions for nonlinear Fokker-Planck equations with time independent drift forces characterized by a general spatial dependence. Received 25 April 2001 and Received in final form 6 June 2001     

Full groups of Cantor minimal systems

We associate different types of full groups to Cantor minimal systems. We show how these various groups (as abstract groups) are complete invariants for orbit equivalence, strong orbit equivalence and flip conjugacy, respectively. Furthermore, we introduce a group homomorphism, the socalled mod map, from the normalizers of the various full groups to the automorphism groups of the (ordered)K ⁰-groups, which are associated to the Cantor minimal systems. We show how this in turn is related to the automorphisms of the associatedC ^*-crossed products. Our results are analogues in the topological dynamical setting of results obtained by Dye, Connes-Krieger and Hamachi-Osikawa in measurable dynamics. Research supported in part by operating grants from NSERC (Canada). Research supported in part by the Norwegian Research Council for Science and Humanities.     

On the One-Dimensional Transition State Theory and the Relation between Statistical and Deterministic Oscillation Frequencies of Anharmonic Energy Wells

The transition state theory allows the development of approximated models useful to study the non-equilibrium evolution of systems undergoing transformations between two states (e.g., chemical reactions). In a simplified 1D setting, the characteristic rate constants are typically written in terms of a temperature-dependent characteristic oscillation frequency ${\nu }_s$, describing the exploration of the phase space. As a particular case, this statistical oscillation frequency ${\nu }_s$ can be defined for an arbitrary convex potential energy well. This value is compared here with the deterministic oscillation frequency ${\nu }_d$ of the corresponding anharmonic oscillator. It is proved that there is a universal relationship between statistical and deterministic frequencies, which is the same for classical and relativistic mechanics. The independence of this relationship from the adopted physical laws gives it an interesting thermodynamic and pedagogical meaning. Several examples clarify the meaning of this relationship from both physical and mathematical viewpoints.     

Thermorheological Simplicity and Fragility of Azobenzene Nematogenic Side-Chain Polymers

Summary: The linear viscoelastic response of polymers from a nematogenic azobenzene methacrylate and its copolymers with nonmesogenic methyl methacrylate was studied. These samples showed thermorheological simplicity in the whole investigated temperature range, even across the nematic-isotropic transition. The temperature dependence of the zero-shear viscosity confirmed a thermorheologically simple behavior, which allowed interpretation of η(T) in the framework of free-volume theory. The way the relaxation mechanisms tended to their asymptotic behavior was described in terms of fragility parameters, and a comparison of fragilities of the samples was carried out. The analysis of fragility and temperature dependence of viscosity provided better understanding of the way the architecture of these nematic polymers influences free-volume quantities and determines relaxation mechanisms.