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We report using poly(acrylamide-co-2-(dimethylamino)ethyl methacrylate, methyl chloride quaternized) cationic microgels as a porous colloidal template for biomimetic in situ silica mineralization, allowing the well-controlled synthesis of submicrometer-sized hybrid microgel--silica particles and porous silica particles by subsequent calcination. The microgels were prepared by inverse emulsion polymerization in the presence of a bisacrylamide cross-linker. Silica deposition was achieved by simply stirring an aqueous mixture of the microgel particles and tetramethyl orthosilicate (TMOS) at 20 degrees C for 30 min. No experimental evidence was found for nontemplated silica, which indicated that silica deposition occurred exclusively within the cationic microgel template particles. The resulting microgel-silica hybrid particles were characterized by electron microscopy, dynamic light scattering, FT-IR spectroscopy, 1H NMR and solid-state 29Si magic angle spinning NMR spectroscopy, thermogravimetry, aqueous electrophoresis, and surface area measurements. Aqueous electrophoresis studies confirmed that the hybrid microgel-silica particles had positive zeta potentials over a wide pH range and isoelectric points could be tuned by varying the synthesis conditions. This suggests that these particles could form complexes with DNA for improved gene delivery. The porosity of the calcined silica particles could be controlled by varying the amount of TMOS, suggesting potential encapsulation/controlled release applications.

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Closed-form Green's functions for cylindrically stratified media are derived in terms of spherical waves and surface-wave contributions. The methodology is based on a two-level approximation of the spectral-domain Green's functions. In the first step, the large argument behavior of the zeroth-order Hankel functions is used for the extraction of the quasistatic images from the spectral-domain Green's functions with the use of the Sommerfeld identity. In the second step, the remaining part of the Green's functions are approximated in terms of pole-residue expressions via the rational function fitting method. This robust, efficient, and fully numerical approach does not call for an analytical cumbersome extraction of the surface wave poles, prior to the spectrum fitting. Moreover, it can be applied in both the near-and far-field. Numerical results for the Green's functions of one-layer and two-layer structures are presented to verify the accuracy and efficiency of this approach.Index Terms-Closed-form Green's functions, cylindrically stratified media, discrete complex images method (DCIM), rational function fitting method (RFFM).

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In this paper, we consider the well-posedness and exact controllability of a fourth-order multi-dimensional Schrödinger equation with hinged boundary by either moment or Dirichlet boundary control and collocated observation, respectively. It is shown that in both cases, the systems are well posed in the sense of D. Salamon, which implies that the systems are exactly controllable in some finite time interval if and only if its corresponding closed loop systems under the direct output proportional feedback are exponentially stable. This leads us to discuss further the exact controllability of the systems. In addition, the systems are consequently shown to be regular in the sense of G. Weiss as well, and the feedthrough operators are zero.