82 research outputs found
Dynamics of vibroprotecting system when using controlled damping fluids with hereditary factor
Oscillating system with a damper containing controlled damping fluid with hereditary electrorheological characteristics was investigated. Numerical calculation of the system in quasistationary approximation was carried out to prove the accuracy of applied assumptions
Manifestation of the Roughness-Square-Gradient Scattering in Surface-Corrugated Waveguides
We study a new mechanism of wave/electron scattering in multi-mode
surface-corrugated waveguides/wires. This mechanism is due to specific
square-gradient terms in an effective Hamiltonian describing the surface
scattering, that were neglected in all previous studies. With a careful
analysis of the role of roughness slopes in a surface profile, we show that
these terms strongly contribute to the expression for the inverse attenuation
length (mean free path), provided the correlation length of corrugations is
relatively small. The analytical results are illustrated by numerical data.Comment: 13 pages, 3 figure
Gradient and Amplitude Scattering in Surface-Corrugated Waveguides
We investigate the interplay between amplitude and square-gradient scattering
from the rough surfaces in multi-mode waveguides (conducting quantum wires).
The main result is that for any (even small in height) roughness the
square-gradient terms in the expression for the wave scattering length
(electron mean free path) are dominant, provided the correlation length of the
surface disorder is small enough. This important effect is missed in existing
studies of the surface scattering.Comment: 4 pages, one figur
The Effect of Random Surface Inhomogeneities on Microresonator Spectral Properties: Theory and Modeling at Millimeter Wave Range
The influence of random surface inhomogeneities on spectral properties of
open microresonators is studied both theoretically and experimentally. To solve
the equations governing the dynamics of electromagnetic fields the method of
eigen-mode separation is applied previously developed with reference to
inhomogeneous systems subject to arbitrary external static potential. We prove
theoretically that it is the gradient mechanism of wave-surface scattering
which is the highly responsible for non-dissipative loss in the resonator. The
influence of side-boundary inhomogeneities on the resonator spectrum is shown
to be described in terms of effective renormalization of mode wave numbers
jointly with azimuth indices in the characteristic equation. To study
experimentally the effect of inhomogeneities on the resonator spectrum, the
method of modeling in the millimeter wave range is applied. As a model object
we use dielectric disc resonator (DDR) fitted with external inhomogeneities
randomly arranged at its side boundary. Experimental results show good
agreement with theoretical predictions as regards the predominance of the
gradient scattering mechanism. It is shown theoretically and confirmed in the
experiment that TM oscillations in the DDR are less affected by surface
inhomogeneities than TE oscillations with the same azimuth indices. The DDR
model chosen for our study as well as characteristic equations obtained
thereupon enable one to calculate both the eigen-frequencies and the Q-factors
of resonance spectral lines to fairly good accuracy. The results of
calculations agree well with obtained experimental data.Comment: 17+ pages, 5 figure
Features in the diffraction of a scalar plane wave from doubly-periodic Dirichlet and Neumann surfaces
The diffraction of a scalar plane wave from a doubly-periodic surface on
which either the Dirichlet or Neumann boundary condition is imposed is studied
by means of a rigorous numerical solution of the Rayleigh equation for the
amplitudes of the diffracted Bragg beams. From the results of these
calculations the diffraction efficiencies of several of the lowest order
diffracted beams are calculated as functions of the polar and azimuthal angles
of incidence. The angular dependencies of the diffraction efficiencies display
features that can be identified as Rayleigh anomalies for both types of
surfaces. In the case of a Neumann surface additional features are present that
can be attributed to the existence of surface waves on such surfaces. Some of
the results obtained through the use of the Rayleigh equation are validated by
comparing them with results of a rigorous Green's function numerical
calculation.Comment: 16 pages, 5 figure
Theory of Tunneling for Rough Junctions
A formally exact expression for the tunneling current, for its separation
into specular and diffuse components, and for its directionality, is given for
a thick tunnel junction with rough interfaces in terms of the properties of
appropriately defined scattering amplitudes. An approximate evaluation yields
the relative magnitudes of the specular and diffuse components, and the angular
dependence of the diffuse component, in terms of certain statistical properties
of the junction interfaces.Comment: 4 page
A new application of reduced Rayleigh equations to electromagnetic wave scattering by two-dimensional randomly rough surfaces
The small perturbations method has been extensively used for waves scattering
by rough surfaces. The standard method developped by Rice is difficult to apply
when we consider second and third order of scattered fields as a function of
the surface height. Calculations can be greatly simplified with the use of
reduced Rayleigh equations, because one of the unknown fields can be
eliminated. We derive a new set of four reduced equations for the scattering
amplitudes, which are applied to the cases of a rough conducting surface, and
to a slab where one of the boundary is a rough surface. As in the
one-dimensional case, numerical simulations show the appearance of enhanced
backscattering for these structures.Comment: RevTeX 4 style, 38 pages, 16 figures, added references and comments
on the satellites peak
Two-Scale Kirchhoff Theory: Comparison of Experimental Observations With Theoretical Prediction
We introduce a non-perturbative two scale Kirchhoff theory, in the context of
light scattering by a rough surface. This is a two scale theory which considers
the roughness both in the wavelength scale (small scale) and in the scales much
larger than the wavelength of the incident light (large scale). The theory can
precisely explain the small peaks which appear at certain scattering angles.
These peaks can not be explained by one scale theories. The theory was assessed
by calculating the light scattering profiles using the Atomic Force Microscope
(AFM) images, as well as surface profilometer scans of a rough surface, and
comparing the results with experiments. The theory is in good agreement with
the experimental results.Comment: 6 pages, 8 figure
On a higher dimensional version of the Benjamin--Ono equation
We consider a higher dimensional version of the Benjamin--Ono equation,
, where
denotes the Riesz transform with respect to the first
coordinate. We first establish sharp space--time estimates for the associated
linear equation. These estimates enable us to show that the initial value
problem for the nonlinear equation is locally well-posed in -Sobolev
spaces , with if and if . We also provide ill-posedness results.Comment: We also show that in dimension 2 our results are shar
Conformal Mapping on Rough Boundaries I: Applications to harmonic problems
The aim of this study is to analyze the properties of harmonic fields in the
vicinity of rough boundaries where either a constant potential or a zero flux
is imposed, while a constant field is prescribed at an infinite distance from
this boundary. We introduce a conformal mapping technique that is tailored to
this problem in two dimensions. An efficient algorithm is introduced to compute
the conformal map for arbitrarily chosen boundaries. Harmonic fields can then
simply be read from the conformal map. We discuss applications to "equivalent"
smooth interfaces. We study the correlations between the topography and the
field at the surface. Finally we apply the conformal map to the computation of
inhomogeneous harmonic fields such as the derivation of Green function for
localized flux on the surface of a rough boundary
- …