3,608,559 research outputs found
Uniqueness theorem for inverse scattering problem with non-overdetermined data
Let be real-valued compactly supported sufficiently smooth function,
, . It is proved that the
scattering data ,
determine uniquely. here is the scattering amplitude,
corresponding to the potential
Uniqueness of the solution to inverse scattering problem with scattering data at a fixed direction of the incident wave
Let be real-valued compactly supported sufficiently smooth function.
It is proved that the scattering data , determine uniquely. Here is a fixed
direction of the incident plane wave
Creating materials with a desired refraction coefficient
A method is given for creating material with a desired refraction
coefficient. The method consists of embedding into a material with known
refraction coefficient many small particles of size . The number of
particles per unit volume around any point is prescribed, the distance between
neighboring particles is as ,
is a fixed parameter. The total number of the embedded particle is
. The physical properties of the particles are described by
the boundary impedance of the particle,
as . The refraction coefficient is the
coefficient in the wave equation
The vacuum backreaction on a pair creating source
Solution is presented to the simplest problem about the vacuum backreaction
on a pair creating source. The backreaction effect is nonanalytic in the
coupling constant and restores completely the energy conservation law. The
vacuum changes the kinematics of motion like relativity theory does and imposes
a new upper bound on the velocity of the source.Comment: 9 pages including 2 figures. Latex 2.09. Figures by Metafont, 300
dpi. Keep all files in a separate director
High-Resolution 4.7 Micron Keck/NIRSPEC Spectra of Protostars. II. Detection of the ^(13)CO Isotope in Icy Grain Mantles
The high-resolution (R = 25,000) infrared M-band spectrum of the massive protostar NGC 7538 IRS 9 shows a narrow absorption feature at 4.779 μm (2092.3 cm^(-1)) that we attribute to the vibrational stretching mode of the ^(13)CO isotope in pure CO icy grain mantles. This is the first detection of ^(13)CO in icy grain mantles in the interstellar medium. The ^(13)CO band is a factor of 2.3 narrower than the apolar component of the ^(12)CO band. With this in mind, we discuss the mechanisms that broaden solid-state absorption bands. It is shown that ellipsoidally shaped pure CO grains fit the bands of both isotopes at the same time. Slightly worse but still reasonable fits are also obtained by CO embedded in N_2-rich ices and thermally processed O_2-rich ices. In addition, we report new insights into the nature and evolution of interstellar CO ices by comparing the very high resolution multicomponent solid ^(12)CO spectrum of NGC 7538 IRS 9 with that of the previously studied low-mass source L1489 IRS. The narrow absorption of apolar CO ices is present in both spectra but much stronger in NGC 7538 IRS 9. It is superposed on a smooth broad absorption feature well fitted by a combination of CO_2 and H_2O-rich laboratory CO ices. The abundances of the latter two ices, scaled to the total H_2O ice column, are the same in both sources. We thus suggest that thermal processing manifests itself as evaporation of apolar ices only and not the formation of CO_2 or polar ices. Finally, the decomposition of the ^(12)CO band is used to derive the ^(12)CO/^(13)CO abundance ratio in apolar ices. A ratio of ^(12)CO/^(13)CO = 71 ± 15 (3 σ) is deduced, in good agreement with gas-phase CO studies (~77) and the solid ^(12)CO_2/^(13)CO_2 ratio of 80 ± 11 found in the same line of sight. The implications for the chemical path along which CO_2 is formed are discussed
Monodromy transform and the integral equation method for solving the string gravity and supergravity equations in four and higher dimensions
The monodromy transform and corresponding integral equation method described
here give rise to a general systematic approach for solving integrable
reductions of field equations for gravity coupled bosonic dynamics in string
gravity and supergravity in four and higher dimensions. For different types of
fields in space-times of dimensions with commuting isometries
-- stationary fields with spatial symmetries, interacting waves or partially
inhomogeneous cosmological models, the string gravity equations govern the
dynamics of interacting gravitational, dilaton, antisymmetric tensor and any
number of Abelian vector gauge fields (all depending only on two
coordinates). The equivalent spectral problem constructed earlier allows to
parameterize the infinite-dimensional space of local solutions of these
equations by two pairs of \cal{arbitrary} coordinate-independent holomorphic
- and - matrix functions of a spectral parameter which constitute a complete set
of monodromy data for normalized fundamental solution of this spectral problem.
The "direct" and "inverse" problems of such monodromy transform --- calculating
the monodromy data for any local solution and constructing the field
configurations for any chosen monodromy data always admit unique solutions. We
construct the linear singular integral equations which solve the inverse
problem. For any \emph{rational} and \emph{analytically matched} (i.e.
and
) monodromy data the solution for string
gravity equations can be found explicitly. Simple reductions of the space of
monodromy data leads to the similar constructions for solving of other
integrable symmetry reduced gravity models, e.g. 5D minimal supergravity or
vacuum gravity in dimensions.Comment: RevTex 7 pages, 1 figur
Unification Theory of Angular Magnetoresistance Oscillations in Quasi-One-Dimensional Conductors
We present a unification theory of angular magnetoresistance oscillations,
experimentally observed in quasi-one-dimensional organic conductors, by solving
the Boltzmann kinetic equation in the extended Brillouin zone. We find that, at
commensurate directions of a magnetic field, resistivity exhibits strong
minima. In two limiting cases, our general solution reduces to the results,
previously obtained for the Lebed Magic Angles and Lee-Naughton-Lebed
oscillations. We demonstrate that our theoretical results are in good
qualitative and quantitative agreement with the existing measurements of
resistivity in (TMTSF)ClO conductor.Comment: 6 pages, 2 figure
- …