Vesicle formed by amphiphilc cucurbit[6]uril: versatile, noncovalent modification of the vesicle surface, and multivalent binding of sugar-decorated vesicles to lectin

We report a novel vesicle formed by an amphiphilic CB[6] derivative, the surface of which can be easily modified via host-guest interactions by taking advantage of molecular cavities, readily accessible at the vesicle surface, and their strong affinity toward polyamines. Amphiphilic CB[6] derivative 1 synthesized by reaction between (allyloxy)12CB[6] and 2-[2-(2-methoxyethoxy)ethoxy]ethanethiol affords a vesicle that has been characterized by TEM, light scattering, and fluorescent dye entrapment experiments. Treatment of vesicle 1 with FITC (fluorescein isothiocyanate)-spermine conjugate ligand 2, in which spermine serves as a binding motif to CB[6] and FITC as a fluorescent tag, produced a surface-modified vesicle, which can be easily visualized by a confocal microscope. This result provides us with a new noncovalent, modular approach to the modification of vesicle surfaces. By treating the vesicle derived from the amphiphilic CB[6] with a tag-attached polyamine, we can easily decorate the surface of the vesicle with the tag. Sugar-decorated vesicles were prepared by this noncovalent method, and their interactions with concanavalin A (ConA) were studied. The binding constant of the vesicle decorated with mannose-spermidine conjugate 3 to ConA was measured to be approximately 3 x 104 M-1, which is almost 3 orders of magnitude higher than that of free ligand 3 to ConA (K = approximately 50 M-1). On the other hand, the binding constant of the vesicle coated with galactose-spermidine conjugate 4 to ConA was too small to be measured. These results illustrate the specific and multivalent interactions between the mannose-decorated vesicle and ConA. The ability for facile surface modification suggests many practical applications, including its use in targeted drug delivery and immunization.     

Finite element methods for an acoustic well-logging problem associated with a porous medium saturated by a two-phase immiscible fluid

A mathematical model is presented concerning wave propagation in a domain that arises in geophysical well-logging problems. The domain consists of a borehole Ω_f surrounded by a porous medium Ω_p. Ω_f is filled with a compressible inviscid fluid, and Ω_p is saturated by a two-phase immiscible fluid. Absorbing boundary conditions for artificial boundaries and boundary conditions on the interface between Ω_f and Ω_p are used. The existence and uniqueness theorems are stated for the resulting initial-boundary value problem. Stability and convergence estimates for a finite element method are also studied. © 1993 John Wiley & Sons, Inc.     

Analysis of a cell boundary element method

The CBEM (cell boundary element method) was proposed as a numerical method for second-order elliptic problems by the first author in the earlier paper [10]. In this paper we prove a quasi-optimal order of convergence of the method, O(h^1–) for >0 in H¹-norm for the triangular mesh; also a stability result is obtained. We provide numerical examples and it is observed that the method conserves flux exactly when a certain condition on meshes is satisfied. This work was supported by KOSEF 2000-1-10300-001-5.AMS subject classification 65N30, 65N38, 65N50     

A nonconforming quadrilateral element with maximal inf‐sup constant

A new nonconforming element is introduced for quadrilateral meshes. The element is designed to maximize the inf‐sup constant for a Stokes element pair. Numerical results are presented and we observe that the maximizing inf‐sup constant results in efficiency of computing time. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 12‐132, 2014     

Finite element analysis of quasistatic crack propagation in brittle media with voids or inclusions

A three-level finite element scheme is proposed for simulation of crack propagation in heterogeneous media including randomly distributed voids or inclusions. To reduce total degrees of freedom in the view of mesh gradation, the entire domain is categorized into three regions of different-level meshes: a region of coarse-level mesh, a region of intermediate-level mesh, and a region of fine-level mesh. The region of coarse-level mesh is chosen to be far from the crack to treat the material inhomogeneities in the sense of coarse-graining through homogenization, while the region near the crack is composed of the intermediate-level mesh to model the presence of inhomogeneities in detail. Furthermore, the region very near the crack tip is refined into the fine-level mesh to capture a steep gradient of elastic field due to the crack tip singularity. Variable-node finite elements are employed to satisfy the nodal connectivity and compatibility between the neighboring different-level meshes. Local remeshing is needed for readjustment of mesh near the crack tip in accordance with crack growth, and this is automatically made according to preset values of parameters determining the propagation step size of crack, and so the entire process is fully automatic. The effectiveness of the proposed scheme is demonstrated through several numerical examples. Meanwhile, the effect of voids and inclusions on the crack propagation is discussed in terms of T-stresses, with the aid of three-level adaptive scheme.     

Pyrene-Appended Fluorescent Tweezers Generated via the Weak-Link Approach and Their Halide Recognition Properties

Through the Weak-Link Approach, fluorescent condensed and open Cu(I) tweezer complexes were prepared and characterized. These complexes exhibit fluorescence-sensitive binding properties for halide anions. The solid-state structure of a non-fluorescent Rh(I) tweezer analogue, determined by X-ray crystallography, shows that the counter anion, Cl⁻, is trapped inbetween the two amide groups of the tweezer arms through hydrogen bonds. Although the tweezer binds Cl⁻, the open complex also binds Cl⁻, showing that the main role of the metal is to increase the local concentration of the pyrenyl amide moieties so that 2:1 binding can take place.     

Three‐dimensional quadratic nonconforming brick element

A new nonconforming brick element with quadratic convergence for the energy norm is introduced. The nonconforming element consists of on a cube [?1,1]³, and 14 degree of freedom (DOF). Two types of DOF are introduced. One consists of the value at the eight vertices and six face‐centroids and the other consists of the value at the eight vertices and the integration value of six faces. Error estimates of optimal order are derived in both broken energy and norms for second‐order elliptic problems. If a genuine hexahedron, which is not a parallelepiped, is included in the partition, the proposed element is also convergent, but with a lower order. Copyright © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 158–174, 2014