On approximation theorems for controllability of non-linear parabolic problems

^** Email: anil{at}math.iitb.ac.in^*** Email: mcj{at}math.iitb.ac.in^**** Email: akp{at}math.iitb.ac.in In this paper, we consider the following control system governedby the non-linear parabolic differential equation of the form: [graphic: see PDF] where A is a linear operator with dense domain and f(t, y)is a non-linear function. We have proved that under Lipschitzcontinuity assumption on the non-linear function f(t, y), theset of admissible controls is non-empty. The optimal pair (u^*,y^*) is then obtained as the limit of the optimal pair sequence{(u_n^*, y_n^*)}, where u_n^* is a minimizer of the unconstrainedproblem involving a penalty function arising from the controllabilityconstraint and y_n^* is the solution of the parabolic non-linearsystem defined above. Subsequently, we give approximation theoremswhich guarantee the convergence of the numerical schemes tooptimal pair sequence. We also present numerical experimentwhich shows the applicability of our result.     

Purification and Characterization of a Cu,Zn-SOD from Garlic (Allium sativum L.). Antioxidant Effect on Tumoral Cell Lines

Crude garlic extract contains one Mn-superoxide dismutase designated as SOD1 and two Cu,Zn superoxide dismutases as SOD2 and SOD3. The major isoform SOD2 was purified to homogeneity by Sephacryl S200-HR gel filtration, DEAE Sepharose ion exchange chromatography, and chromatofocusing using PBE 94. SOD2 was purified 82-fold with a specific activity of 4,960 U/mg protein. This enzyme was stable in a broad pH range from 5.0 to 10.0 and at various temperatures from 25 to 60°C. The native molecular mass of SOD2 estimated by high performance liquid chromatography on TSK gel G2000SW column was 39 kDa. Sodium dodecyl sulfate–polyacrylamide gel electrophoresis analysis showed a single band near 18 kDa, suggesting that native enzyme was homodimeric. The isoelectric point as determined by chromatofocusing was 5. Analysis of its N terminal amino acid sequence revealed high sequence homology with several other cytosolic Cu,Zn-SODs from plants. Exposure of cancer cell lines to garlic Cu,Zn-SOD2 led to a significant decrease in superoxide content with a concomitant rise in intracellular peroxides, indicating that the enzyme is active in mammalian cells and could, therefore, be used in pharmacological applications.     

Sliding Motion and Stability of a Class of Discontinuous Dynamical Systems

A closed container with gas and liquid inflows and one outlet for outflow, described by a nonlinear hydraulic model, is shown to reach a state of sliding mode. Through a Lyapunov function, the sliding motion is shown to be stable for all positive exponents in the flow model. This property is independent of factors such as valve opening, valve coefficients, friction factor and initial states, making this device a suitable one to study two phase flow. The sliding solution of this system, with square root hydraulic model, is found using Filippov's equivalent dynamic approach. The discontinuous system is also solved using an accurate and efficient method that accounts for persistent discontinuity sticking. These two solutions are shown to be in exact agreement.     

Osmo-dehydration of apple pulp studied by means of classical and Knudsen thermogravimetric approach

Classical thermogravimetry and its modification with Knudsen cells were employed to quantitatively investigate the osmo-dehydration of apple pulp samples. The data allowed realization of the complex mechanism of the process, which is not a mere solvent depletion, since it also implies sugar exchanges between the apple tissue and the hypertonic syrup used to dehydrate the fruit. The comparison between different hypertonic syrups, all at the same water activity, showed that maltose is more effective than either sucrose or a mixture of sugars that mimics the saccharide content of the apple. The conclusions are supported by a thermodynamic analysis of the aqueous solutions of these sugars at a concentration level as large as that of the hypertonic syrups used for the osmo-dehydration process.     

Model Independent Parametric Decision Making

Accurate knowledge of the effect of parameter uncertainty on process design and operation is essential for optimal and feasible operation of a process plant. Existing approaches dealing with uncertainty in the design and process operations level assume the existence of a well defined model to represent process behavior and in almost all cases convexity of the involved equations. However, most of the realistic case studies cannot be described by well characterised models. Thus, a new approach is presented in this paper based on the idea of High Dimensional Model Reduction technique which utilize a reduced number of model runs to build an uncertainty propagation model that expresses process feasibility. Building on this idea a systematic iterative procedure is developed for design under uncertainty with a unique characteristic of providing parametric expression of the optimal objective with respect to uncertain parameters. The proposed approach treats the system as a black box since it does not rely on the nature of the mathematical model of the process, as is illustrated through a number of examples.     

Morphology Controlled Growth of Chitosan‐Bound Microtubes and a Study of their Biocompatibility and Antibacterial Activity

Self‐assembled peptide microtubes are fabricated with the biopolymer chitosan. The microtubes are covalently attached to chitosan and the morphology of the chitosan assembled on the surface of the microtubes can be tuned by altering the pH of the growth solution. Cytotoxicity studies in the presence of mouse embryonic fibroblasts indicate that the chitosan‐bound microtubes are highly biocompatible and the cells are able to survive and proliferate at a similar rate to the control. Antibacterial studies in the presence of E. coli prove that the chitosan‐bound microtubes are bactericidal. This simple method for the development of biocompatible microstructures will facilitate cell targeting, fabrication of efficient carrier devices, and the preparation of highly efficient antibacterial materials.

     

New photoactivators for multiphoton excited three-dimensional submicron cross-linking of proteins: bovine serum albumin and type 1 collagen

We report the synthesis and optical characterization of two new photoactivators and demonstrate their use for multiphoton excited three-dimensional free-form fabrication with proteins. These reagents were developed with the goal of cross-linking Type 1 collagen. This cross-linking process produces structures on the micron and submicron size scales. A rose bengal diisopropyl amine derivative combines the classic photoactivator and co-initiator system into one molecule, reducing the reaction kinetics and increasing cross-linking efficiency. This derivative was successful at producing stable structures from collagen, whereas rose bengal alone was not effective. A benzophenone dimer connected by a flexible diamine tether was also synthesized. This activator has two photochemically reactive groups and is highly efficient in cross-linking bovine serum albumin and Type 1 collagen to form stable, robust structures. This approach is more flexible in terms of cross-linking a variety of proteins than by traditional benzophenone photochemistry. The photophysical properties vary greatly from that of benzophenone, with the appearance of a new, lower energy absorption band (lambda max approximately 370 nm in water) and broad, visible emission band (approximately 500 nm maximum). This absorption band is highly solvatochromic, suggesting it arises, at least in part, from a charge transfer interaction. Collagens are typically difficult to cross-link photochemically, and the results here suggest that these two new activators will be suitable for cross-linking other forms of collagen and additional proteins for biomedical applications such as the de novo assembly of biomimetic tissue scaffolds.     

A qualocation method for a unidimensional single phase semilinear Stefan problem

Based on straightening the free boundary, a qualocation methodis proposed and analysed for a single phase unidimensional Stefanproblem. This method may be considered as a discrete versionof the H¹-Galerkin method in which the discretization is achievedby approximating the integrals by a composite Gauss quadraturerule. Optimal error estimates are derived in L(W^j,), j = 0,1,and L (H^j), j = 0,1,2, norms for a semidiscrete scheme withoutany quasi-uniformity assumption on the finite element mesh.     

Immobilization of invertase in germania matrix and a study of its enzymatic activity

A novel and easy synthesis route to mesoporous nanocrystalline TiO₂ samples using soluble starch as the structural agent and mainly titanium(IV) isopropoxide as the inorganic precursor was described. The effect of key parameters, including soluble starch removal process, the solvent nature and the type of titanium precursor were discussed. Using soluble starch in cyclohexane as non polar solvent, a surface area of 94 m².g⁻¹ associated with 23 nm crystallites size was obtained. TiO₂ samples were characterized by means of N₂ adsorption-desorption, X-ray Diffraction (XRD), TG-DTA, Scanning Electron Microscopy (SEM) and ATR-FTIR spectroscopy. Dedicated to Dr. Jean-Claude Volta on the occasion for his retirement