38 research outputs found
Asymptotic boundary layer method for unstable trajectories : Semiclassical expansions for individual scar wavefunctions.
We extend the asymptotic boundary layer (ABL) method, originally developed for stable resonator modes, to the description of individual wave functions localized around unstable periodic orbits. The formalism applies to the description of scar states in fully or partially chaotic quantum systems, and also allows for the presence of smooth and sharp potentials, as well as magnetic fields. We argue that the separatrix wave function provides the largest contribution to the scars on a single wave function. This agrees with earlier results on the wave-function asymptotics and on the quantization condition of the scar states. Predictions of the ABL formalism are compared with the exact numerical solution for a strip resonator with a parabolic confinement potential and a magnetic field
Dynamic inverse problem in a weakly laterally inhomogeneous medium
An inverse problem of wave propagation into a weakly laterally inhomogeneous
medium occupying a half-space is considered in the acoustic approximation. The
half-space consists of an upper layer and a semi-infinite bottom separated with
an interface. An assumption of a weak lateral inhomogeneity means that the
velocity of wave propagation and the shape of the interface depend weakly on
the horizontal coordinates, , in comparison with the strong
dependence on the vertical coordinate, , giving rise to a small parameter
\e <<1. Expanding the velocity in power series with respect to \e, we
obtain a recurrent system of 1D inverse problems. We provide algorithms to
solve these problems for the zero and first-order approximations. In the
zero-order approximation, the corresponding 1D inverse problem is reduced to a
system of non-linear Volterra-type integral equations. In the first-order
approximation, the corresponding 1D inverse problem is reduced to a system of
coupled linear Volterra integral equations. These equations are used for the
numerical reconstruction of the velocity in both layers and the interface up to
O(\e^2).Comment: 12 figure
Reconstruction of the reflection coefficient and interface in homogeneous medium by means of Gaussian jets
This paper is devoted to the inverse problem of reconstruction of a shape of interface separating two homogeneous
media in acoustic approximation from from the knowledge of the scattered field data. It is assumed
that the infinitely smooth surface representing the interface is illuminated by an incident Gaussian jet described
as a high-frequency non-stationary localized asymptotic solution (wave package). The parameters
of the medium above the interface are known. Measuring the intensity of the reflected Gaussian jet along
a horizontal line placed at some height above the interface gives the inverse data to solve the problem of
reconstruction of a shape of interface as well as determination of velocity of wave propagation and density
below the interface. In the paper we describe a corresponding algorithm of solving the inverse problem and
demonstrate a few examples of its numerical testing
Electromagnetic guided waves on linear arrays of spheres
Guided electromagnetic waves propagating along one-dimensional arrays of dielectric spheres are studied. The quasi-periodic wave field is constructed as a superposition of vector spherical wavefunctions and then application of the boundary condition on the sphere surfaces leads to an infinite system of real linear algebraic equations. The vanishing of the determinant of the associated infinite matrix provides the condition for surface waves to exist and these are determined numerically after truncation of the infinite system. Dispersion curves are presented for a range of azimuthal modes and the effects of varying the sphere radius and electric permittivity are shown. We also demonstrate that a suitable truncation of the full system is precisely equivalent to the dipole approximation that has been used previously by other authors, in which the incident field on a sphere is approximated by its value at the centre of that sphere. © 2012 Elsevier B.V
Inverse problem of velocity reconstruction in weakly lateral heterogeneous half-space
A wave propagation generated by a boundary source into a weakly lateral heterogeneous medium (WLHM) occupying a half-space is considered in the acoustic approximation. WLHM means that the velocity of the wave propagation depends weakly on the horizontal coordinates in comparison with the strong dependence on the vertical coordinate z. We consider the problem of the reconstruction of the velocity inside the half-space from the knowledge of the medium response measured at z=0. We obtain a recurrent system of 1D inverse problems to find..
Localised States of Fabry-Perot Type in Graphene Nano-Ribbons
This book collects some new progresses on research of graphene from theoretical and experimental aspects in a variety of topics, such as graphene nanoribbons, graphene quantum dots, and graphene-based resistive switching memory. The authors of each chapter give a unique insight about the specific intense research area of graphene. This book is suitable for graduate students and researchers with background in physics, chemistry, and materials as reference
Regular Oscillation Sub-spectrum of Rapidly Rotating Stars
We present an asymptotic theory that describes regular frequency spacings of
pressure modes in rapidly rotating stars. We use an asymptotic method based on
an approximate solution of the pressure wave equation constructed from a stable
periodic solution of the ray limit. The approximate solution has a Gaussian
envelope around the stable ray, and its quantization yields the frequency
spectrum. We construct semi-analytical formulas for regular frequency spacings
and mode spatial distributions of a subclass of pressure modes in rapidly
rotating stars. The results of these formulas are in good agreement with
numerical data for oscillations in polytropic stellar models. The regular
frequency spacings depend explicitly on internal properties of the star, and
their computation for different rotation rates gives new insights on the
evolution of mode frequencies with rotation.Comment: 14 pages, 10 figure