Multilayer graphene under vertical electric field

We study the effect of vertical electric field (E-field) on the electronic properties of multilayer graphene. We show that the effective mass, electron velocity and density-of-state of a bilayer graphene are modified under the E-field. We also study the transformation of the band structure of multilayer graphenes. E-field induces finite (zero) bandgap in the even (odd)-layer ABA-stacking graphene. On the other hand, finite bandgap is induced in all ABC-stacking graphene. We also identify the optimum E-field to obtain the maximum bandgap in the multilayer graphenes. Finally we compare our results with the experimental results of a field-effect-transistor.Comment: 10 pag

On the backward behavior of some dissipative evolution equations

We prove that every solution of a KdV-Burgers-Sivashinsky type equation blows up in the energy space, backward in time, provided the solution does not belong to the global attractor. This is a phenomenon contrast to the backward behavior of the periodic 2D Navier-Stokes equations studied by Constantin-Foias-Kukavica-Majda [18], but analogous to the backward behavior of the Kuramoto-Sivashinsky equation discovered by Kukavica-Malcok [50]. Also we study the backward behavior of solutions to the damped driven nonlinear Schrodinger equation, the complex Ginzburg-Landau equation, and the hyperviscous Navier-Stokes equations. In addition, we provide some physical interpretation of various backward behaviors of several perturbations of the KdV equation by studying explicit cnoidal wave solutions. Furthermore, we discuss the connection between the backward behavior and the energy spectra of the solutions. The study of backward behavior of dissipative evolution equations is motivated by the investigation of the Bardos-Tartar conjecture stated in [5].Comment: 34 page

Iterative Detection of Diagonal Block Space Time Trellis Codes, TCM and Reversible Variable Length Codes for Transmission over Rayleigh Fading Channels

Iterative detection of Diagonal Block Space Time Trellis Codes (DBSTTCs), Trellis Coded Modulation (TCM) and Reversible Variable Length Codes (RVLCs) is proposed. With the aid of efficient iterative decoding, the proposed scheme is capable of providing full transmit diversity and a near channel capacity performance. The performance of the proposed scheme was evaluated when communicating over uncorrelated Rayleigh fading channels. Explicitly, significant iteration gains were achieved by the proposed scheme, which was capable of performing within 2~dB from the channel capacity