Niobium pentoxide reacts actively with concentrate NaOH solution under hydrothermal conditions at as low as 120 degrees C. The reaction ruptures the corner-sharing of NbO(7) decahedra and NbO(6) octahedra in the reactant Nb(2)O(5), yielding various niobates, and the structure and composition of the niobates depend on the reaction temperature and time. The morphological evolution of the solid products in the reaction at 180 degrees C is monitored via SEM: the fine Nb(2)O(5) powder aggregates first to irregular bars, and then niobate fibers with an aspect ratio of hundreds form. The fibers are microporous molecular sieve with a monoclinic lattice, Na(2)Nb(2)O(6).(2)/(3)H(2)O. The fibers are a metastable intermediate of this reaction, and they completely convert to the final product NaNbO(3) cubes in the prolonged reaction of 1 h. This study demonstrates that by carefully optimizing the reaction condition, we can selectively fabricate niobate structures of high purity, including the delicate microporous fibers, through a direct reaction between concentrated NaOH solution and Nb(2)O(5). This synthesis route is simple and suitable for the large-scale production of the fibers. The reaction first yields poorly crystallized niobates consisting of edge-sharing NbO(6) octahedra, and then the microporous fibers crystallize and grow by assembling NbO(6) octahedra or clusters of NbO(6) octahedra and NaO(6) units. Thus, the selection of the fibril or cubic product is achieved by control of reaction kinetics. Finally, niobates with different structures exhibit remarkable differences in light absorption and photoluminescence properties. Therefore, this study is of importance for developing new functional materials by the wet-chemistry process.

Abstract.This paper studies the blowup profile near the blowup time for the heat equation ut = Am with the nonlinear boundary condition un = up on dil x [0, T). Under certain assumptions, the exact rate of the blowup is established. It is also proved that the blowup will not occur in the interior of the domain. The asymptotic behavior near the blowup point is also studied.

No abstract

No abstract

In this paper we study the following reaction-diusion equation u t = u + f (u; k(t)) subject to appropriate initial and boundary conditions, where f(u; k(t)) = u p k(t) o r k (t) u p with p > 1 and k(t) is an unknown function. An additional energy type condition is imposed in order to nd the solution u(x; t) and k(t). This type of problem is frequently encountered in nuclear reaction process, where the reaction is known to be very strong, but the total energy is controlled. It is shown that the solution blows up in nite time for the rst class of function f for some initial data. For the second class of function f, the solution blows up in nite time if p > n = (n 2) while it exists globally in time if 1 < p < n = (n 2), no matter how large the initial value is. Partial results are generalized into the case where f(u; k(t)) appears on the boundary.

In this paper we first study the regularity of weak solution for time-harmonic Maxwell's equations in a bounded anisotropic medium O: It is shown that the weak solution to the linear degenerate system, r  ðgðxÞr  EÞ þ xðxÞE ¼ JðxÞ; xAOCR 3 ; is Ho¨lder continuous under the minimum regularity assumptions on the complex coefficients gðxÞ and xðxÞ: We then study a coupled system modeling a microwave heating process. The dynamic interaction between electric and temperature fields is governed by Maxwell's equations coupled with an equation of heat conduction. The electric permittivity, electric conductivity and magnetic permeability are assumed to be dependent of temperature. It is shown that under certain conditions the coupled system has a weak solution. Moreover, regularity of weak solution is studied. Finally, existence of a global classical solution is established for a special case where the electric wave is assumed to be propagating in one direction. r

In some chemical reaction-diffusion processes, the reaction takes place only at some local sites, due to the presence of a catalyst. In this paper we study the well-posedness of a model problem of this type. Sufficient conditions are found to ensure global existence and finite time blowup. The blowup rate and the blowup set are also investigated in the case of special nonlinearity.

No abstract