Turing patterns for a coupled two-cell generalized Schnakenberg model

ABSTRACT

We consider a system for a generalized Schnakenberg model, showing Turing pattern formation for a wide class of nonlinearities.     

New approach for natural products screening by real-time monitoring of hemoglobin hydrolysis using quartz crystal microbalance

The hemoglobin (Hb) released from erythrocytes is a primary nutritive component for many blood-feeding parasites. The aspartic protease cathepsin D is a hemoglobinase that is involved in the Hb degradation process and is considered an interesting target for chemotherapy intervention. However, traditional enzymatic assays for studying Hb degradation utilize spectrophotometric techniques, which do not allow real-time monitoring and can present serious interference problems. Herein, we describe a biosensor using simple approach for the real-time monitoring of Hb hydrolysis as well as an efficient screening method for natural products as enzymatic inhibitors using a quartz crystal microbalance (QCM) technique. Hemoglobin was anchored on the quartz crystal surface using mixed self-assembled monolayers. The addition of the enzyme caused a mass change (frequency shift) due to Hb hydrolysis, which was monitored in real time. From the frequency change patterns of the Hb-functionalized QCM, we evaluated the enzymatic reaction by determining the kinetic parameters of product formation (k_cat). The QCM enzymatic assay using immobilized human Hb was shown to be an excellent approach for screening possible inhibitors in complex mixtures, opening up a new avenue for the discovery of novel inhibitors.     

Vulgarisins B–D,three novel diterpenoids with a rare skeleton isolated from Prunella vulgaris Linn

Three new diterpenoids, vulgarisins B–D (1–3), have been isolated from a medicinal plant Prunella vulgaris Linn. These diterpenoids contain a rare 5/6/4/5 fused tetracyclic ring skeleton. Their structures were determined through the analysis of spectroscopic data, and the absolute configuration were further confirmed by single crystal X-ray diffraction as well as CD analysis. All the compounds were evaluated for their cytotoxicity activity, vulgarisins B (1) and C (2) demonstrated modest cytotoxicity activity against human lung carcinoma A549 cell line.     

Plastic surface strain mapping of bent sheets by image correlation

A technique using a single CCD camera, a precision rotation/translation stage, a telecentric zoom lens, and digital image correlation software is described for measuring surface profiles and surface plastic strain distributions of a bent thin sheet. The measurement principles, based on both parallel and pinhole perspective projections, are outlined and the relevant mathematical equations for computing the profiles and displacement fields on a curved surface are presented. The typical optical setup as well as the experimental measurement and digital image correlation analysis procedure are described. The maximum errors in the in-plane and out-of-plane coordinates or displacements are about ±5 and ±25 μm, respectively, and the maximum errors in surface strain mapping are about 0.1% or less based on a series of evaluation tests on flat and curved sample surfaces over a physical field of view of 15.2 × 11.4 mm². As an application example, the shape and surface plastic strain distribution example, the shape and surface plastic strain distributions around a bent apex of a flat 2 mm thick automotive aluminum AA5182-O sheet, which underwent a 90° bend with three bend ratios of 2t, 1t, and 0.6t, are determined using the proposed technique.     

Stability of a Steady Viscous Incompressible Flow Past an Obstacle

We derive a sufficient condition for stability of a steady solution of the Navier–Stokes equation in a 3D exterior domain Ω. The condition is formulated as a requirement on integrability on the time interval (0, +∞) of a semigroup generated by the linearized problem for perturbations, applied to a finite family of certain functions. The norm of the semigroup is measured in a bounded sub-domain of Ω. We do not use any condition on “smallness” of the basic steady solution.      

Stopping a Viscous Fluid by a Feedback Dissipative Field: I. The Stationary Stokes Problem

We consider a planar stationary flow of an incompressible viscous fluid in a semiinfinite strip governed by the Stokes system with a body forces field. We show how this fluid can be stopped at a finite distance of the entrance of the semi-infinite strip by means of a feedback field depending in a sub-linear way on the velocity field. This localization effect is proved reducing the problem to a non-linear bi-harmonic type one for which the localization of solutions is obtained by means of the application of a suitable energy method. Since the presence of the non-linear terms defined through the body forces field is not standard in the fluid mechanics literature, we establish also some results about the existence and uniqueness of weak solutions for this problem.     

Existence of Solutions with the Prescribed Flux of the Navier–Stokes System in an Infinite Cylinder

The existence and uniqueness of a solution to the nonstationary Navier–Stokes system having a prescribed flux in an infinite cylinder is proved. We assume that the initial data and the external forces do not depend on x₃ and find the solution (u, p) having the following form

The Fundamental Solution of the Linearized Navier–Stokes Equations for Spinning Bodies in Three Spatial Dimensions – Time Dependent Case

Explicit formulae for the fundamental solution of the linearized time dependent Navier–Stokes equations in three spatial dimensions are obtained. The linear equations considered in this paper include those used to model rigid bodies that are translating and rotating at a constant velocity. Estimates extending those obtained by Solonnikov in [23] for the fundamental solution of the time dependent Stokes equations, corresponding to zero translational and angular velocity, are established. Existence and uniqueness of solutions of these linearized problems is obtained for a class of functions that includes the classical Lebesgue spaces L^p(R³), 1 < p < ∞. Finally, the asymptotic behavior and semigroup properties of the fundamental solution are established.     

On a Serrin-Type Regularity Criterion for the Navier–Stokes Equations in Terms of the Pressure

We prove a Serrin-type regularity result for Leray–Hopf solutions to the Navier–Stokes equations, extending a recent result of Zhou [28].