3,457 research outputs found
Energy solutions to one-dimensional singular parabolic problems with data are viscosity solutions
We study one-dimensional very singular parabolic equations with periodic
boundary conditions and initial data in , which is the energy space. We
show existence of solutions in this energy space and then we prove that they
are viscosity solutions in the sense of Giga-Giga.Comment: 15 page
On the existence of traveling waves in the 3D Boussinesq system
We extend earlier work on traveling waves in premixed flames in a
gravitationally stratified medium, subject to the Boussinesq approximation. For
three-dimensional channels not aligned with the gravity direction and under the
Dirichlet boundary conditions in the fluid velocity, it is shown that a
non-planar traveling wave, corresponding to a non-zero reaction, exists, under
an explicit condition relating the geometry of the crossection of the channel
to the magnitude of the Prandtl and Rayleigh numbers, or when the advection
term in the flow equations is neglected.Comment: 15 pages, to appear in Communications in Mathematical Physic
A caricature of a singular curvature flow in the plane
We study a singular parabolic equation of the total variation type in one
dimension. The problem is a simplification of the singular curvature flow. We
show existence and uniqueness of weak solutions. We also prove existence of
weak solutions to the semi-discretization of the problem as well as convergence
of the approximating sequences. The semi-discretization shows that facets must
form. For a class of initial data we are able to study in details the facet
formation and interactions and their asymptotic behavior. We notice that our
qualitative results may be interpreted with the help of a special composition
of multivalued operators
Anomalous thermoelectric power of Mg1-xAlxB2 system with x = 0.0 to 1.0
Thermoelectric power, S(T) of the Mg1-xAlxB2 system has been measured for x =
0.0, 0.1, 0.2, 0.4, 0.6, 0.8 and 1.0. XRD, resistivity and magnetization
measurements are also presented. It has been found that the thermoelectric
power is positive for x = 0.4 and is negative for x = 0.6 over the entire
temperature range studied up to 300 K. The thermoelectric power of x = 0.4
samples vanishes discontinuously below a certain temperature, implying
existence of superconductivity. In general, the magnitude of the thermoelectric
power increases with temperature up to a certain temperature, and then it
starts to decrease towards zero base line. In order to explain the observed
behavior of the thermoelectric power, we have used a model in which both
diffusion and phonon drag processes are combined by using a phenomenological
interpolation between the low and high temperature behaviors of the
thermoelectric power. The considered model provides an excellent fit to the
observed data. It is further found that Al doping enhances the Debye
temperature.Comment: 19 pages Text + Figs.
suggestions/comments([email protected]
The electronic properties of bilayer graphene
We review the electronic properties of bilayer graphene, beginning with a
description of the tight-binding model of bilayer graphene and the derivation
of the effective Hamiltonian describing massive chiral quasiparticles in two
parabolic bands at low energy. We take into account five tight-binding
parameters of the Slonczewski-Weiss-McClure model of bulk graphite plus intra-
and interlayer asymmetry between atomic sites which induce band gaps in the
low-energy spectrum. The Hartree model of screening and band-gap opening due to
interlayer asymmetry in the presence of external gates is presented. The
tight-binding model is used to describe optical and transport properties
including the integer quantum Hall effect, and we also discuss orbital
magnetism, phonons and the influence of strain on electronic properties. We
conclude with an overview of electronic interaction effects.Comment: review, 31 pages, 15 figure
Determination of interatomic coupling between two-dimensional crystals using angle-resolved photoemission spectroscopy
Lack of directional bonding between two-dimensional crystals like graphene or
monolayer transition metal dichalcogenides provides unusual freedom in
selection of components for vertical van der Waals heterostructures. However,
even for identical layers, their stacking, in particular the relative angle
between their crystallographic directions, modifies properties of the
structure. We demonstrate that the interatomic coupling between two
two-dimensional crystals can be determined from angle-resolved photoemission
spectra of a trilayer structure with one aligned and one twisted interface.
Each of the interfaces provides complementary information and together they
enable self-consistent determination of the coupling. We parametrize
interatomic coupling for carbon atoms by studying twisted trilayer graphene and
show that the result can be applied to structures with different twists and
number of layers. Our approach demonstrates how to extract fundamental
information about interlayer coupling in a stack of two-dimensional crystals
and can be applied to many other van der Waals interfaces.Comment: This is a post-peer-review, pre-copyedit version of an article
published in Nature Communications. The final authenticated version is
available online at: http://dx.doi.org/10.1038/s41467-020-17412-
Magneto-optical Selection Rules in Bilayer Bernal Graphene
The low-frequency magneto-optical properties of bilayer Bernal graphene are
studied by the tight-binding model with four most important interlayer
interactions taken into account. Since the main features of the wave functions
are well depicted, the Landau levels can be divided into two groups based on
the characteristics of the wave functions. These Landau levels lead to four
categories of absorption peaks in the optical absorption spectra. Such
absorption peaks own complex optical selection rules and these rules can be
reasonably explained by the characteristics of the wave functions. In addition,
twin-peak structures, regular frequency-dependent absorption rates and complex
field-dependent frequencies are also obtained in this work. The main features
of the absorption peaks are very different from those in monolayer graphene and
have their origin in the interlayer interactions
Band dispersion in the deep 1s core level of graphene
Chemical bonding in molecules and solids arises from the overlap of valence
electron wave functions, forming extended molecular orbitals and dispersing
Bloch states, respectively. Core electrons with high binding energies, on the
other hand, are localized to their respective atoms and their wave functions do
not overlap significantly. Here we report the observation of band formation and
considerable dispersion (up to 60 meV) in the core level of the carbon
atoms forming graphene, despite the high C binding energy of 284
eV. Due to a Young's double slit-like interference effect, a situation arises
in which only the bonding or only the anti-bonding states is observed for a
given photoemission geometry.Comment: 12 pages, 3 figures, including supplementary materia
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