DABCO-mediated aza-Michael addition of 4-aryl-1H-1,2,3-triazoles to cycloalkenones. Regioselective synthesis of disubstituted 1,2,3-triazoles

Aza-Michael addition of 4-aryl-1H-1,2,3-triazoles to 2-cycloalken-1-ones has been studied in the presence of DABCO as organic base. The reactions were carried out in acetonitrile at room temperature to provide 2,4-disubstituted 2H-1,2,3-triazoles as major adducts and 1,4-disubstituted 1H-1,2,3-triazoles as minor adducts. Though the reaction times are longer (4–8 days), the two regioisomers were separated by using column chromatography and the adducts were obtained in very good to excellent combined chemical yields. The electron-rich and electron-poor substituents on aryl moiety of 4-aryl-triazoles could tolerate the reaction conditions to afford the title adducts.     

Ring-closing metathesis as a tool for the efficient preparation of chiral spirocyclic ethers from homoallylic alcohols

The preparation of chiral spirocyclic ethers via allylic etherification/olefin metathesis of homoallylic alcohols is investigated. This reaction sequence transforms the enantiopure substrate alcohols, synthesized by a one-pot asymmetric rhodium-catalyzed conjugate addition/metal-mediated allylation procedure, into the desired spiro ethers with full conversions and in excellent isolated yields. The synthetic sequence provides an efficient means for a rapid construction of functionalized spiro ethers in a stereoselective manner.     

BEM SOLUTION OF THE 3D INTERNAL NEUMANN PROBLEM AND A REGULARIZED FORMULATION FOR THE POTENTIAL VELOCITY GRADIENTS

The direct boundary element method is an excellent candidate for imposing the normal flux boundary condition in vortex simulation of the three-dimensional Navier–Stokes equations. For internal flows, the Neumann problem governing the velocity potential that imposes the correct normal flux is ill-posed and, in the discrete form, yields a singular matrix. Current approaches for removing the singularity yield unacceptable results for the velocity and its gradients. A new approach is suggested based on the introduction of a pseudo-Lagrange multiplier, which redistributes localized discretization errors—endemic to collocation techniques— over the entire domain surface, and is shown to yield excellent results. Additionally, a regularized integral formulation for the velocity gradients is developed which reduces the order of the integrand singularity from four to two. This new formulation is necessary for the accurate evaluation of vorticity stretch, especially as the evaluation points approach the boundaries. Moreover, to guarantee second-order differentiability of the boundary potential distribution, a piecewise quadratic variation in the potential is assumed over triangular boundary elements. Two independent node-numbering systems are assigned to the potential and normal flux distribu- tions on the boundary to account for the single- and multi-valuedness of these variables, respectively. As a result, higher accuracy as well as significantly reduced memory and computational cost is achieved for the solution of the Neumann problem. © 1997 John Wiley & Sons, Ltd.     

In Situ Gold Nanoparticle Gradient Formation in a 3D Meso‐ and Macroporous Polymer Matrix

Herein, the development and characterization of a 3D gradient structure of gold nanoparticles is described. The gradient of gold nanoparticles is made in situ in a macroporous nonionic block copolymer hydrogel matrix, through gold ion diffusion control. The polymer provides a matrix for diffusion of gold ions, acts as a template for controlling nanoparticle growth, and facilitates the in situ reduction of gold ions to gold nanoparticles. A clear gradient in gold nanoparticles is observed across the 3D space of the polymer matrix using scanning electron microscopy, fluorescence microscopy, atomic force microscopy, and thermogravimetric analysis. The particle gradient is further functionalized with both hydrophobic and hydrophilic groups via thiol‐gold linkage to demonstrate the ability to form gradients with different chemical functionalities. Using additive manufacturing, the polymer can also be printed as a porous network with possible applications for 3D cell culturing in, e.g., biomaterials research.     

Gradient single-crystal plasticity with free energy dependent on dislocation densities

This study develops a small-deformation theory of strain-gradient plasticity for single crystals. The theory is based on: (i) a kinematical notion of a continuous distribution of edge and screw dislocations; (ii) a system of microscopic stresses consistent with a system of microscopic force balances, one balance for each slip system; (iii) a mechanical version of the second law that includes, via the microscopic stresses, work performed during viscoplastic flow; and (iv) a constitutive theory that allows:

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the free energy to depend on densities of edge and screw dislocations and hence on gradients of (plastic) slip;

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the microscopic stresses to depend on slip-rate gradients.

The microscopic force balances when augmented by constitutive relations for the microscopic stresses results in a system of nonlocal flow rules in the form of second-order partial differential equations for the slips. When the free energy depends on the dislocation densities the microscopic stresses are partially energetic, and this, in turn, leads to backstresses in the flow rules; on the other hand, a dependence of these stresses on slip-rate gradients leads to a strengthening. The flow rules, being nonlocal, require microscopic boundary conditions; as an aid to numerical solutions a weak (virtual power) formulation of the flow rule is derived.     

The effect of temperature gradients on the sharkskin surface instability in polymer extrusion through a slit die

The sharkskin surface instability is commonly observed in the extrusion of polymer melts. We present a series of experiments in which a specifically designed rectangular slit die with insulated and independently heated sides and is used to induce precise temperature gradients across a flowing polyethylene melt. Our previous experiments demonstrated that the character of the surface distortions produced by the sharkskin instability was a function of the die wall temperature and therefore the extrudate had viscoelastic properties at the surface. In this paper, we explore the role of temperature and viscoelastic property gradients near the capillary wall. The amplitude of the sharkskin instability is quantified and plotted against apparent shear and extension rates. Analysis of the data demonstrates that the amplitude and frequency of the instability is independent of bulk temperature and temperature gradient and is dependent only on wall temperature. The data are normalized using a dimensionless Weissenberg number based on the extension rate to collapse the data collected over all temperatures and gradients onto a single master curve. We conclude with an example of a rectangular extrudate exhibiting varying surface roughness due to differential die heating and discuss the implications of our observations on the sharkskin surface instability mechanism and on commercial applications.     

Conjugate conduction-natural convection in an enclosure with time-periodic sidewall temperature and inclination

The unsteady conjugate conduction-natural convection in enclosure is of great theoretical significance and is widely encountered in engineering applications in the areas of fluid dynamics and heat transfer. However, there are relatively few efforts to investigate the unsteady flow physics and heat transfer characteristics in the inclined enclosure of finite thickness walls. In the present work, this problem is numerically investigated by a high accuracy multidomain temporal-spatial pseudospectral method. The enclosure is filled with Boussinesq fluid and is bounded by four finite thickness and conductive walls; one of the vertical sidewall is exposed to time-periodic temperature environment while the opposite sidewall holds constant temperature; the top and bottom walls are assumed to be adiabatic. Particular efforts are focused on the effects of three types of influential factors: the wall thermophysical properties, the time-periodic temperature patterns and the inclination, and the time-periodic flow patterns and heat transfer characteristics are presented. Numerical results reveal that within the present parameter range, the heat transfer rate increases almost linearly with the thermal conductivity ratio and thermal diffusivity ratio but decreases with the inclination angle. Moreover, the heat transfer could be enhanced or weakened by selecting different temperature pulsating period in the case of finite thickness wall, while it is always enhanced if the walls are zero thickness. The back heat transfer and heat transfer resonance phenomena are observed, and their relationships with the time-periodic flow patterns and temperature distributions are analyzed. The findings are helpful to the understandings of the fluid flow and heat transfer mechanisms in the related enclosure configurations, and may be of engineering use in thermal design improvement.     

“射流松动泥沙”的机理及工程应用试验研究——射流引起的非均匀流全河段水面比降及垂线流速分布

泥沙清淤技术及其基础研究需要不断发展,通过自制射流发生装置,在水槽中对射流引起的非均匀流水面比降及垂线流速分布全河段变化特点进行了系统试验研究。由于射流的存在,水面比降及垂线流速分布发生较大变化。水面比降射流段上游的比无射流的小,射流段及其下游比无射流的大,而全河段水面比降比无射流时增大。垂线流速分布在射流段及其下游附近发生根本的变化,有射流时,水面附近的流速比底部流速小,垂线平均流速一般小于无射流。上述这些特点与水槽流量和射流量有关,一般而言,水槽流量越大,射流量越大,这些变化越显著。     

A Duality Theory for a Class of Generalized Fractional Programs

In generalized fractional programming, one seeks to minimize the maximum of a finite number of ratios. Such programs are, in general, nonconvex and consequently are difficult to solve. Here, we consider a particular case in which the ratio is the quotient of a quadratic form and a positive concave function. The dual of such a problem is constructed and a numerical example is given.     

Graph theoretical duality perspective on conjugate structures and its applications

The paper shows that representing structures, beams and frames by mathematical models based on graph theory enables to provide new perspective on known conjugate structure theorems in mechanics. It is shown that the latter theorems can be derived from the graph theoretical duality principle applied upon the graph representations of the structures. The results reported indicate upon theoretical value of the approach, as the established mathematical foundation can be employed in a variety of mechanical disciplines.