54,047 research outputs found
Magnetic miniband and magnetotransport property of a graphene superlattice
The eigen energy and the conductivity of a graphene sheet subject to a
one-dimensional cosinusoidal potential and in the presence of a magnetic field
are calculated. Such a graphene superlattice presents three distinct magnetic
miniband structures as the magnetic field increases. They are, respectively,
the triply degenerate Landau level spectrum, the nondegenerate minibands with
finite dispersion and the same Landau level spectrum with the pristine
graphene. The ratio of the magnetic length to the period of the potential
function is the characteristic quantity to determine the electronic structure
of the superlattice. Corresponding to these distinct electronic structures, the
diagonal conductivity presents very strong anisotropy in the weak and moderate
magnetic field cases. But the predominant magnetotransport orientation changes
from the transverse to the longitudinal direction of the superlattice. More
interestingly, in the weak magnetic field case, the superlattice exhibits
half-integer quantum Hall effect, but with large jump between the Hall
plateaux. Thus it is different from the one of the pristine graphene.Comment: 7 pages, 5 figure
A trace formula for the forcing relation of braids
The forcing relation of braids has been introduced for a 2-dimensional
analogue of the Sharkovskii order on periods for maps of the interval. In this
paper, by making use of the Nielsen fixed point theory and a representation of
braid groups, we deduce a trace formula for the computation of the forcing
order.Comment: 24 pages, 9 figure
Global Existence and Asymptotic Behavior of Solutions to a Chemotaxis-Fluid System on General Bounded Domain
In this paper, we investigate an initial-boundary value problem for a
chemotaxis-fluid system in a general bounded regular domain (), not necessarily being convex. Thanks to the
elementary lemma given by Mizoguchi & Souplet [10], we can derive a new type of
entropy-energy estimate, which enables us to prove the following: (1) for
, there exists a unique global classical solution to the full
chemotaxis-Navier-Stokes system, which converges to a constant steady state
as , and (2) for , the existence of a
global weak solution to the simplified chemotaxis-Stokes system. Our results
generalize the recent work due to Winkler [15,16], in which the domain
is essentially assumed to be convex
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