Nonlinear Galerkin methods and mixed finite elements: two-grid algorithms for the Navier-Stokes equations

Summary. A nonlinear Galerkin method using mixed finite elements is presented for the two-dimensional incompressible Navier-Stokes equations. The scheme is based on two finite element spaces and for the approximation of the velocity, defined respectively on one coarse grid with grid size and one fine grid with grid size and one finite element space for the approximation of the pressure. Nonlinearity and time dependence are both treated on the coarse space. We prove that the difference between the new nonlinear Galerkin method and the standard Galerkin solution is of the order of $H^2$, both in velocity ( and pressure norm). We also discuss a penalized version of our algorithm which enjoys similar properties. Received October 5, 1993 / Revised version received November 29, 1993     

2D water layer enclathrated between Mn(II)-Ni(CN)4 coordination frameworks

A [Ni(CN)₄]²⁻-based two-dimensional Mn(II) coordination polymer {Mn(H₂O)₂[NiCN]₄·4H₂O}, in which the coordination layers are stacked on top of each other sandwiching 2D water layer of boat-shaped hexagonal water clusters has been synthesized. The complex exhibits high thermal decomposition temperature and reversible water absorption, which were clearly demonstrated by thermal and PXRD studies on the parent and rehydrated complex after dehydration.     

Strong enhancement and extinction of single harmonic intensity in the mid- and end-plateau regions of the high harmonics generated in weakly excited laser plasmas

Strong intensity enhancement or extinction of some single harmonics is observed in high-harmonic generation from 48 fs Ti:sapphire laser pulses propagating through preformed low-excited laser-produced plasmas of various materials (GaAs, Cr, InSb, stainless steel). The intensities of some of the harmonics in the mid- and end-plateau regions vary from ~23-fold enhancement to near disappearance compared with those of the neighboring ones. It is also shown that the observed intensity enhancement (or extinction) can be varied by controlling the chirp of the driving laser radiation.     

Prediction of flow stress at hot working condition

A mathematical model has been developed to determine flow stress at hot deformation condition. The proposed model is capable of including work softening due to dynamic phase transformations as well as the effect of temperature and strain rate variation on flow stress utilizing the additivity rule for strain. To verify the model, hot compression tests for two grades of steels has been carried out. The comparison between the experimental and theoretical results confirms the validity of the model.     

Delay equations with fluctuating delay related to the regenerative chatter

The mathematical models representing machine tool chatter dynamics have been cast as differential equations with delay. In this paper, non-linear delay differential equations with periodic delays which model the machine tool chatter with continuously modulated spindle speed are studied. The explicit time-dependent delay terms, due to spindle speed modulation, are replaced by state-dependent delay terms by augmenting the original equations. The augmented system of equations is autonomous and has two pairs of pure imaginary eigenvalues without resonance. The reduced bifurcation equation is obtained by making use of Lyapunov-Schmidt Reduction method. By using the reduced bifurcation equations, the periodic solutions are determined to analyze the tool motion. Analytical results show both modest increase of stability and existence of periodic solutions near the new stability boundary.     

Plastic flow in oriented glassy polymers

A manufactured product often possesses residual texture which was either incidentally or deliberately acquired during its processing history. This is particularly true for the case of polymers, where the ability to easily preferentially preorient the material in specific directions is exploited in order to obtain a higher strength product. Specific examples include synthetic fibers, and biaxially-oriented films and containers. The response of the preoriented/textured product to normal service life loading conditions will differ considerably from that of a product composed of isotropic material. This paper addresses the issue of the effects of texture on the deformation behavior of glassy polymers. Here, the physically-based constitutive model of Boyce, Parks, and Argon describing the rate, temperature, and pressure dependent inelastic deformation of initially isotropic glassy polymers is used to model the effects of preorientation (i.e., initial texture), via the use of appropriate initial conditions on internal state variables. The model is then utilized in an analysis of the effects of texture on the yield of glassy polymers and the shear localization which normally follows yielding in oriented polymers. These results are compared with trends found in experiments as reported in the literature. The effectiveness of the proposed model for the present application is also compared with earlier models of yielding of anisotropic materials such as Hill's criterion.     

Stability Analysis of a Vertical Curved Channel Flow with a Radial Temperature Gradient

The linear stability analysis of a Newtonian incompressible fluid in a vertical curved channel formed by two coaxial cylindrical surfaces with a radial temperature gradient and an azimuthal pressure gradient shows that critical modes are oscillatory and non-axisymmetric. We have derived a generalized Rayleigh discriminant which includes both the curvature and buoyancy effects. Centrifugal buoyancy induces weak asymmetry of the dependence of the control parameter critical values on the sign of the temperature gradient. The critical parameters depend on the temperature gradient, the radius ratio and the nature of the fluid. For a wide curvature channel flow, there are two critical modes: oscillatory Dean modes for small temperature gradients and oscillatory centrifugal-thermal modes for relatively large temperature gradients. Received 14 November 2001 and accepted 29 March 2002 Published online: 2 October 2002 Communicated by H.J.S. Fernando     

Synthetic Covalent and Non‐Covalent 2D Materials

The creation of synthetic 2D materials represents an attractive challenge that is ultimately driven by their prospective uses in, for example, electronics, biomedicine, catalysis, sensing, and as membranes for separation and filtration. This Review illustrates some recent advances in this diverse field with a focus on covalent and non‐covalent 2D polymers and frameworks, and self‐assembled 2D materials derived from nanoparticles, homopolymers, and block copolymers.     

Selective and Simultaneous Determination of Dihydroxybenzene Isomers Based on Green Synthesized Gold Nanoparticles Decorated Reduced Graphene Oxide

In the present study, we report the simultaneous electrochemical determination of hydroquinone (HQ), catechol (CC) and resorcinol (RC) at gold nanoparticles (Au‐NPs) decorated reduced graphene oxide (RGO) modified electrode. An enhanced and well defined peak current response with a better peak separation of HQ, CC and RC is observed at RGO/Au‐NPs composite than that of RGO and Au‐NPs modified electrodes. The fabricated modified electrode shows a wide linear response in the concentration range of 3–90 µM, 3–300 µM and 15–150 µM for HQ, CC and RC, respectively. The detection limit of HQ, CC and RC is found as 0.15 µM, 0.12 µM and 0.78 µM, respectively.