Local null controllability of a class of non-Newtonian incompressible viscous fluids

<p style='text-indent:20px;'>We investigate the null controllability property of systems that mathematically describe the dynamics of some non-Newtonian incompressible viscous flows. The principal model we study was proposed by O. A. Ladyzhenskaya, although the techniques we develop here apply to other fluids having a shear-dependent viscosity. Taking advantage of the Pontryagin Minimum Principle, we utilize a bootstrapping argument to prove that sufficiently smooth controls to the forced linearized Stokes problem exist, as long as the initial data in turn has enough regularity. From there, we extend the result to the nonlinear problem. As a byproduct, we devise a quasi-Newton algorithm to compute the states and a control, which we prove to converge in an appropriate sense. We finish the work with some numerical experiments.</p>

Lubrication Approximation for Fluids with Shear-Dependent Viscosity

We present dimensionally reduced Reynolds type equations for steady lubricating flows of incompressible non-Newtonian fluids with shear-dependent viscosity by employing a rigorous perturbation analysis on the governing equations of motion. Our analysis shows that, depending on the strength of the power-law character of the fluid, the novel equation can either present itself as a higher-order correction to the classical Reynolds equation or as a completely new nonlinear Reynolds type equation. Both equations are applied to two classic problems: the flow between a rolling rigid cylinder and a rigid plane and the flow in an eccentric journal bearing.

Novel Endotype Xanthanase from Xanthan-DegradingMicrobacteriumsp. Strain XT11

ABSTRACTUnder general aqueous conditions, xanthan appears in an ordered conformation, which makes its backbone largely resistant to degradation by known cellulases. Therefore, the xanthan degradation mechanism is still unclear because of the lack of an efficient hydrolase. Here, we report the catalytic properties of MiXen, a xanthan-degrading enzyme identified from the genusMicrobacterium. MiXen is a 952-amino-acid protein that is unique to strain XT11. Both the sequence and structural features suggested that MiXen belongs to a new branch of the GH9 family and has a multimodular structure in which a catalytic (α/α)6barrel is flanked by an N-terminal Ig-like domain and by a C-terminal domain that has very few homologues in sequence databases and functions as a carbohydrate-binding module (CBM). Based on circular dichroism, shear-dependent viscosity, and reducing sugar and gel permeation chromatography analysis, we demonstrated that recombinant MiXen efficiently and randomly cleaved glucosidic bonds within the highly ordered xanthan substrate. A MiXen mutant free of the C-terminal CBM domain partially lost its xanthan-hydrolyzing ability because of decreased affinity toward xanthan, indicating the CBM domain assisted MiXen in hydrolyzing highly ordered xanthan via recognizing and binding to the substrate. Furthermore, side chain substituents and the terminal mannosyl residue significantly influenced the activity of MiXen via the formation of barriers to enzymolysis. Overall, the results of this study provide insight into the hydrolysis mechanism and enzymatic properties of a novel endotype xanthanase that will benefit future applications.IMPORTANCEThis work characterized a novel endotype xanthanase, MiXen, and elucidated that the C-terminal carbohydrate-binding module of MiXen could drastically enhance the hydrolysis activity of the enzyme toward highly ordered xanthan. Both the sequence and structural analysis demonstrated that the catalytic domain and carbohydrate-binding module of MiXen belong to the novel branch of the GH9 family and CBMs, respectively. This xanthan cleaver can help further reveal the enzymolysis mechanism of xanthan and provide an efficient tool for the production of molecular modified xanthan with new physicochemical and physiological functions.