A polymer‐memory device based on a copolymer containing carbazole (donor) and Eu‐complex (acceptor) groups in a metal/insulator/metal architecture is described. The nonvolatile device has two distinctive bistable conductivity states, and exhibits a high ON/OFF current ratio, a fast response time, and acceptable retention under ambient conditions. Application of a potential sets the device to the high‐conductivity ON state by generating holes (see Figure).
In this paper, we investigate an initial boundary value problem for 1D compressible isentropic Navier-Stokes equations with large initial data, density-dependent viscosity, external force, and vacuum. Making full use of the local estimates of the solutions in Cho and Kim (2006) [3] and the one-dimensional properties of the equations and the Sobolev inequalities, we get a unique) for any T > 0. As it is pointed out in Xin (1998) [31] that the smooth solution (ρ, u) ∈ C 1 ([0, T ]; H 3 (R 1 )) (T is large enough) of the Cauchy problem must blow up in finite time when the initial density is of nontrivial compact support. It seems that the regularities of the solutions we obtained can be improved, which motivates us to obtain some new estimates with the help of a new test function ρ 2 u tt , such as Lemmas 3.2-3.6. This leads to further regularities of (ρ, u)T ]; H 3 ([0, 1])). It is still open whether the regularity of u could be improved to C 1 ([0, T ]; H 3 ([0, 1])) with the appearance of vacuum, since it is not obvious that the solutions in C 1 ([0, T ]; H 3 ([0, 1])) to the initial boundary value problem must blow up in finite time.Crown
We consider the equation modeling the compressible hydrodynamic flow of liquid crystals in one dimension. In this paper, we establish the existence of a weak solution (ρ, u, n) of such a system when the initial density function 0 ≤ ρ 0 ∈ L γ for γ > 1, u 0 ∈ L 2 , and n 0 ∈ H 1 . This extends a previous result by [12], where the existence of a weak solution was obtained under the stronger assumption that the initial density function 0 < c ≤ ρ
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