4,614 research outputs found
Steady water waves with multiple critical layers: interior dynamics
We study small-amplitude steady water waves with multiple critical layers.
Those are rotational two-dimensional gravity-waves propagating over a perfect
fluid of finite depth. It is found that arbitrarily many critical layers with
cat's-eye vortices are possible, with different structure at different levels
within the fluid. The corresponding vorticity depends linearly on the stream
function.Comment: 14 pages, 3 figures. As accepted for publication in J. Math. Fluid
Mec
On the particle paths and the stagnation points in small-amplitude deep-water waves
In order to obtain quite precise information about the shape of the particle
paths below small-amplitude gravity waves travelling on irrotational deep
water, analytic solutions of the nonlinear differential equation system
describing the particle motion are provided. All these solutions are not closed
curves. Some particle trajectories are peakon-like, others can be expressed
with the aid of the Jacobi elliptic functions or with the aid of the
hyperelliptic functions. Remarks on the stagnation points of the
small-amplitude irrotational deep-water waves are also made.Comment: to appear in J. Math. Fluid Mech. arXiv admin note: text overlap with
arXiv:1106.382
Equations of the Camassa-Holm Hierarchy
The squared eigenfunctions of the spectral problem associated with the
Camassa-Holm (CH) equation represent a complete basis of functions, which helps
to describe the inverse scattering transform for the CH hierarchy as a
generalized Fourier transform (GFT). All the fundamental properties of the CH
equation, such as the integrals of motion, the description of the equations of
the whole hierarchy, and their Hamiltonian structures, can be naturally
expressed using the completeness relation and the recursion operator, whose
eigenfunctions are the squared solutions. Using the GFT, we explicitly describe
some members of the CH hierarchy, including integrable deformations for the CH
equation. We also show that solutions of some - dimensional members of
the CH hierarchy can be constructed using results for the inverse scattering
transform for the CH equation. We give an example of the peakon solution of one
such equation.Comment: 10 page
Position-dependent exact-exchange energy for slabs and semi-infinite jellium
The position-dependent exact-exchange energy per particle
(defined as the interaction between a given electron at and its
exact-exchange hole) at metal surfaces is investigated, by using either jellium
slabs or the semi-infinite (SI) jellium model. For jellium slabs, we prove
analytically and numerically that in the vacuum region far away from the
surface , {\it
independent} of the bulk electron density, which is exactly half the
corresponding exact-exchange potential [Phys.
Rev. Lett. {\bf 97}, 026802 (2006)] of density-functional theory, as occurs in
the case of finite systems. The fitting of
to a physically motivated image-like expression is feasible, but the resulting
location of the image plane shows strong finite-size oscillations every time a
slab discrete energy level becomes occupied. For a semi-infinite jellium, the
asymptotic behavior of is somehow different.
As in the case of jellium slabs has
an image-like behavior of the form , but now with a
density-dependent coefficient that in general differs from the slab universal
coefficient 1/2. Our numerical estimates for this coefficient agree with two
previous analytical estimates for the same. For an arbitrary finite thickness
of a jellium slab, we find that the asymptotic limits of
and only
coincide in the low-density limit (), where the
density-dependent coefficient of the semi-infinite jellium approaches the slab
{\it universal} coefficient 1/2.Comment: 26 pages, 7 figures, to appear in Phys. Rev.
A 2-Component Generalization of the Camassa-Holm Equation and Its Solutions
An explicit reciprocal transformation between a 2-component generalization of
the Camassa-Holm equation, called the 2-CH system, and the first negative flow
of the AKNS hierarchy is established, this transformation enables one to obtain
solutions of the 2-CH system from those of the first negative flow of the AKNS
hierarchy. Interesting examples of peakon and multi-kink solutions of the 2-CH
system are presented.Comment: 15 pages, 16 figures, some typos correcte
Semilocal density functional theory with correct surface asymptotics
Semilocal density functional theory is the most used computational method for
electronic structure calculations in theoretical solid-state physics and
quantum chemistry of large systems, providing good accuracy with a very
attractive computational cost. Nevertheless, because of the non-locality of the
exchange-correlation hole outside a metal surface, it was always considered
inappropriate to describe the correct surface asymptotics. Here, we derive,
within the semilocal density functional theory formalism, an exact condition
for the image-like surface asymptotics of both the exchange-correlation energy
per particle and potential. We show that this condition can be easily
incorporated into a practical computational tool, at the simple
meta-generalized-gradient approximation level of theory. Using this tool, we
also show that the Airy-gas model exhibits asymptotic properties that are
closely related to the ones at metal surfaces. This result highlights the
relevance of the linear effective potential model to the metal surface
asymptotics.Comment: 6 pages, 4 figure
On a novel integrable generalization of the nonlinear Schr\"odinger equation
We consider an integrable generalization of the nonlinear Schr\"odinger (NLS)
equation that was recently derived by one of the authors using bi-Hamiltonian
methods. This equation is related to the NLS equation in the same way that the
Camassa Holm equation is related to the KdV equation. In this paper we: (a) Use
the bi-Hamiltonian structure to write down the first few conservation laws. (b)
Derive a Lax pair. (c) Use the Lax pair to solve the initial value problem. (d)
Analyze solitons.Comment: 20 pages, 1 figur
High-Level Correlated Approach to the Jellium Surface Energy, Without Uniform-Electron-Gas Input
We resolve the long-standing controversy over the surface energy of simple
metals: Density functional methods that require uniform-electron-gas input
agree with each other at many levels of sophistication, but not with high-level
correlated calculations like Fermi Hypernetted Chain and Diffusion Monte Carlo
(DMC) that predict the uniform-gas correlation energy. Here we apply a very
high-level correlated approach, the inhomogeneous Singwi-Tosi-Land-Sj\"olander
(ISTLS) method, and find that the density functionals are indeed reliable
(because the surface energy is "bulk-like"). ISTLS values are close to
recently-revised DMC values. Our work also vindicates the previously-disputed
use of uniform-gas-based nonlocal kernels in time-dependent density functional
theory.Comment: 4 pages, 1 figur
Sub-wavelength imaging at infrared frequencies using an array of metallic nanorods
We demonstrate that an array of metallic nanorods enables sub-wavelength
(near-field) imaging at infrared frequencies. Using an homogenization approach,
it is theoretically proved that under certain conditions the incoming radiation
can be transmitted by the array of nanorods over a significant distance with
fairly low attenuation. The propagation mechanism does not involve a resonance
of material parameters and thus the resolution is not strongly affected by
material losses and has wide bandwidth. The sub-wavelength imaging with
resolution by silver rods at 30 THz is demonstrated numerically
using full-wave electromagnetic simulator.Comment: 12 pages, 16 figures, submitted to PR
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