1,614 research outputs found
On Boussinesq's equation for water waves
A century and a half ago, J. Boussinesq derived an equation for the
propagation of shallow water waves in a channel. Despite the fundamental
importance of this equation for a number of physical phenomena, mathematical
results on it remain scarce. One reason for this is that the equation is
ill-posed. In this paper, we establish several results on the Boussinesq
equation. First, by solving the direct and inverse problems for an associated
third-order spectral problem, we develop an Inverse Scattering Transform (IST)
approach to the initial value problem. Using this approach, we establish a
number of existence, uniqueness, and blow-up results. For example, the IST
approach allows us to identify physically meaningful global solutions and to
construct, for each , solutions that blow up exactly at time . Our
approach also yields an expression for the solution of the initial value
problem for the Boussinesq equation in terms of the solution of a
Riemann--Hilbert problem. By analyzing this Riemann--Hilbert problem, we arrive
at asymptotic formulas for the solution. We identify ten main asymptotic
sectors in the -plane; in each of these sectors, we compute an exact
expression for the leading asymptotic term together with a precise error
estimate. The asymptotic picture that emerges consists, roughly speaking, of
two nonlinearly coupled copies of the corresponding picture for the
(unidirectional) KdV equation, one copy for right-moving and one for
left-moving waves. Of particular interest are the sectors which describe the
interaction of right and left moving waves, which present qualitatively new
phenomena.Comment: 111 pages, 23 figure
Room temperature Peierls distortion in small radius nanotubes
By means of {\it ab initio} simulations, we investigate the phonon band
structure and electron-phonon coupling in small 4-\AA diameter nanotubes. We
show that both the C(5,0) and C(3,3) tubes undergo above room temperature a
Peierls transition mediated by an acoustical long-wavelength and an optical
phonons respectively. In the armchair geometry, we verify that the
electron-phonon coupling parameter originates mainly from phonons at
and is strongly enhanced when the diameter decreases. These results
question the origin of superconductivity in small diameter nanotubes.Comment: submitted 21oct2004 accepted 6jan2005 (Phys.Rev.Lett.
Probing the electron-phonon coupling in ozone-doped graphene by Raman spectroscopy
We have investigated the effects of ozone treatment on graphene by Raman
scattering. Sequential ozone short-exposure cycles resulted in increasing the
doping levels as inferred from the blue shift of the 2 and peak
frequencies, without introducing significant disorder. The two-phonon 2 and
2 Raman peak intensities show a significant decrease, while, on the
contrary, the one-phonon G Raman peak intensity remains constant for the whole
exposure process. The former reflects the dynamics of the photoexcited
electrons (holes) and, specifically, the increase of the electron-electron
scattering rate with doping. From the ratio of 2 to 2 intensities, which
remains constant with doping, we could extract the ratio of electron-phonon
coupling parameters. This ratio is found independent on the number of layers up
to ten layers. Moreover, the rate of decrease of 2 and 2 intensities
with doping was found to slowdown inversely proportional to the number of
graphene layers, revealing the increase of the electron-electron collision
probability
Thermal rectification in carbon nanotube intramolecular junctions: Molecular dynamics calculations
We study heat conduction in (n, 0)/(2n, 0) intramolecular junctions by using
molecular dynamics method. It is found that the heat conduction is asymmetric,
namely, heat transports preferably in one direction. This phenomenon is also
called thermal rectification. The rectification is weakly dependent on the
detailed structure of connection part, but is strongly dependent on the
temperature gradient. We also study the effect of the tube radius and
intramolecular junction length on the rectification. Our study shows that the
tensile stress can increase rectification. The physical mechanism of the
rectification is explained
Determination of the Intershell Conductance in Multiwalled Carbon Nanotubes
We report on the intershell electron transport in multiwalled carbon
nanotubes (MWNT). To do this, local and nonlocal four-point measurements are
used to study the current path through the different shells of a MWNT. For
short electrode separations 1 m the current mainly flows
through the two outer shells, described by a resistive transmission line with
an intershell conductance per length of ~(10 k\Omega)^{-1}/m. The
intershell transport is tunnel-type and the transmission is consistent with the
estimate based on the overlap between -orbitals of neighboring shells.Comment: 5 pages, 4 figure
The "good'' Boussinesq equation: long-time asymptotics
We consider the initial-value problem for the ``good'' Boussinesq equation on
the line. Using inverse scattering techniques, the solution can be expressed in
terms of the solution of a -matrix Riemann-Hilbert problem. We
establish formulas for the long-time asymptotics of the solution by performing
a Deift-Zhou steepest descent analysis of a regularized version of this
Riemann-Hilbert problem.Comment: 34 pages, 13 figure
Electrical conductivity measured in atomic carbon chains
The first electrical conductivity measurements of monoatomic carbon chains
are reported in this study. The chains were obtained by unraveling carbon atoms
from graphene ribbons while an electrical current flowed through the ribbon
and, successively, through the chain. The formation of the chains was
accompanied by a characteristic drop in the electrical conductivity. The
conductivity of carbon chains was much lower than previously predicted for
ideal chains. First-principles calculations using both density functional and
many-body perturbation theory show that strain in the chains determines the
conductivity in a decisive way. Indeed, carbon chains are always under varying
non-zero strain that transforms its atomic structure from cumulene to polyyne
configuration, thus inducing a tunable band gap. The modified electronic
structure and the characteristics of the contact to the graphitic periphery
explain the low conductivity of the locally constrained carbon chain.Comment: 21 pages, 9 figure
First-Principle Description of Correlation Effects in Layered Materials
We present a first-principles description of anisotropic materials
characterized by having both weak (dispersion-like) and strong covalent bonds,
based on the Adiabatic--Connection Fluctuation--Dissipation Theorem within
Density Functional Theory. For hexagonal boron nitride the in-plane and out of
plane bonding as well as vibrational dynamics are well described both at
equilibrium and when the layers are pulled apart. Also bonding in covalent and
ionic solids is described. The formalism allows to ping-down the deficiencies
of common exchange-correlation functionals and provides insight towards the
inclusion of dispersion interactions into the correlation functional.Comment: Accepted for publication in Physical Review Letter
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