565 research outputs found
Numerical studies of confined states in rotated bilayers of graphene
Rotated graphene multilayers form a new class of graphene related systems
with electronic properties that drastically depend on the rotation angles. It
has been shown that bilayers behave like two isolated graphene planes for large
rotation angles. For smaller angles, states in the Dirac cones belonging to the
two layers interact resulting in the appearance of two van Hove singularities.
States become localised as the rotation angle decreases and the two van Hove
singularities merge into one peak at the Dirac energy. Here we go further and
consider bilayers with very small rotation angles. In this case, well defined
regions of AA stacking exist in the bilayer supercell and we show that states
are confined in these regions for energies in the [-\gamma_t, +\gamma_t] range
with \gamma_t the interplane mean interaction. As a consequence, the local
densities of states show discrete peaks for energies different from the Dirac
energy.Comment: 8 page
Conditional stability of particle alignment in finite-Reynolds-number channel flow
Finite-size neutrally buoyant particles in a channel flow are known to
accumulate at specific equilibrium positions or spots in the channel
cross-section if the flow inertia is finite at the particle scale. Experiments
in different conduit geometries have shown that while reaching equilibrium
locations, particles tend also to align regularly in the streamwise direction.
In this paper, the Force Coupling Method was used to numerically investigate
the inertia-induced particle alignment, using square channel geometry. The
method was first shown to be suitable to capture the quasi-steady lift force
that leads to particle cross-streamline migration in channel flow. Then the
particle alignment in the flow direction was investigated by calculating the
particle relative trajectories as a function of flow inertia and of the ratio
between the particle size and channel hydraulic diameter. The flow streamlines
were examined around the freely rotating particles at equilibrium, revealing
stable small-scale vortices between aligned particles. The streamwise
inter-particle spacing between aligned particles at equilibrium was calculated
and compared to available experimental data in square channel flow (Gao {\it et
al.} Microfluidics and Nanofluidics {\bf 21}, 154 (2017)). The new result
highlighted by our numerical simulations is that the inter-particle spacing is
unconditionally stable only for a limited number of aligned particles in a
single train, the threshold number being dependent on the confinement
(particle-to-channel size ratio) and on the Reynolds number. For instance, when
the particle Reynolds number is and the particle-to-channel height
size ratio is , the maximum number of stable aligned particles per
train is equal to 3. This agrees with statistics realized on the experiments of
(Gao {\it et al.} Microfluidics and Nanofluidics {\bf 21}, 154 (2017)).Comment: 13 pages, 13 figure
Impact of local stacking on the graphene-impurity interaction: theory and experiments
We investigate the graphene-impurity interaction problem by combining
experimental - scanning tunneling microscopy (STM) and spectroscopy (STS) - and
theoretical - Anderson impurity model and density functional theory (DFT)
calculations - techniques. We use graphene on the SiC(000-1)(2x2)_C
reconstruction as a model system. The SiC substrate reconstruction is based on
silicon adatoms. Graphene mainly interacts with the dangling bonds of these
adatoms which act as impurities. Graphene grown on SiC(000-1)(2x2)_C shows
domains with various orientations relative to the substrate so that very
different local graphene/Si adatom stacking configurations can be probed on a
given grain. The position and width of the adatom (impurity) state can be
analyzed by STM/STS and related to its local environment owing to the high bias
electronic transparency of graphene. The experimental results are compared to
Anderson's model predictions and complemented by DFT calculations for some
specific local environments. We conclude that the adatom resonance shows a
smaller width and a larger shift toward the Dirac point for an adatom at the
center of a graphene hexagon than for an adatom just on top of a C graphene
atom.Comment: 13 pages, 6 figures, Accepted for publication in Phys. Rev.
Graphene on the C-terminated SiC (000 ) surface: An ab initio study
The atomic and electronic structures of a graphene layer on top of the
reconstruction of the SiC (000) surface are studied from
ab initio calculations. At variance with the (0001) face, no C bufferlayer is
found here. Si adatoms passivate the substrate surface so that the very first C
layer presents a linear dispersion characteristic of graphene. A small
graphene-substrate interaction remains in agreement with scanning tunneling
experiments (F.Hiebel et al. {\it Phys. Rev. B} {\bf 78} 153412 (2008)). The
stacking geometry has little influence on the interaction which explains the
rotational disorder observed on this face.Comment: 4 pages, 3 figures, additional materia
Pragmatic Isomorphism Proofs Between Coq Representations: Application to Lambda-Term Families
There are several ways to formally represent families of data, such as lambda terms, in a type theory such as the dependent type theory of Coq. Mathematical representations are very compact ones and usually rely on the use of dependent types, but they tend to be difficult to handle in practice. On the contrary, implementations based on a larger (and simpler) data structure combined with a restriction property are much easier to deal with.
In this work, we study several families related to lambda terms, among which Motzkin trees, seen as lambda term skeletons, closable Motzkin trees, corresponding to closed lambda terms, and a parameterized family of open lambda terms. For each of these families, we define two different representations, show that they are isomorphic and provide tools to switch from one representation to another. All these datatypes and their associated transformations are implemented in the Coq proof assistant. Furthermore we implement random generators for each representation, using the QuickChick plugin
Formalizing a Discrete Model of the Continuum in Coq from a Discrete Geometry Perspective
International audienceThis work presents a formalization of the discrete model of the continuum introduced by Harthong and Reeb, the Harthong-Reeb line. This model was at the origin of important developments in the Discrete Geometry field. The formalization is based on previous work by Chollet, Fuchs et al. where it was shown that the Harthong-Reeb line satisfies the axioms for constructive real numbers introduced by Bridges. Laugwitz-Schmieden numbers are then introduced and their limitations with respect to being a model of the Harthong-Reeb line is investigated. In this paper, we transpose all these definitions and properties into a formal description using the Coq proof assistant. We also show that Laugwitz-Schmieden numbers can be used to actually compute continuous functions. We hope that this work could improve techniques for both implementing numeric computations and reasoning about them in geometric systems
Universal classification of twisted, strained and sheared graphene moir\'e superlattices
Moir\'e superlattices in graphene supported on various substrates have opened
a new avenue to engineer graphene's electronic properties. Yet, the exact
crystallographic structure on which their band structure depends remains highly
debated. In this scanning tunneling microscopy and density functional theory
study, we have analysed graphene samples grown on multilayer graphene prepared
onto SiC and on the close-packed surfaces of Re and Ir with ultra-high
precision. We resolve small-angle twists and shears in graphene, and identify
large unit cells comprising more than 1,000 carbon atoms and exhibiting
non-trivial nanopatterns for moir\'e superlattices, which are commensurate to
the graphene lattice. Finally, a general formalism applicable to any hexagonal
moir\'e is presented to classify all reported structures.Comment: 14 pages, 6 figure
François Burgat, Comprendre lâislam politique. Une trajectoire de recherche sur lâaltĂ©ritĂ© islamiste, 1973-2016
Pourquoi les islamistes font-ils un retour en force dans le monde arabo-musulman et sur la scĂšne politique dont ils ont Ă©tĂ© longtemps exclus ? Quelles rĂ©actions ce phĂ©nomĂšne suscite-t-il de lâautre cĂŽtĂ© de la MĂ©diterranĂ©e et plus largement en Occident ? En quoi est-il rĂ©vĂ©lateur des relations que ce dernier a entretenu et continue dâentretenir avec un Orient dâautant plus aimĂ© quâil nous ressemble ? Ce sont en filigrane les questions qui sous-tendent le livre de François Burgat car, in fine, ..
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