665 research outputs found
Solution of the inverse scattering problem by T-matrix completion. II. Simulations
This is Part II of the paper series on data-compatible T-matrix completion
(DCTMC), which is a method for solving nonlinear inverse problems. Part I of
the series contains theory and here we present simulations for inverse
scattering of scalar waves. The underlying mathematical model is the scalar
wave equation and the object function that is reconstructed is the medium
susceptibility. The simulations are relevant to ultrasound tomographic imaging
and seismic tomography. It is shown that DCTMC is a viable method for solving
strongly nonlinear inverse problems with large data sets. It provides not only
the overall shape of the object but the quantitative contrast, which can
correspond, for instance, to the variable speed of sound in the imaged medium.Comment: This is Part II of a paper series. Part I contains theory and is
available at arXiv:1401.3319 [math-ph]. Accepted in this form to Phys. Rev.
Nonlinear inverse problem by T-matrix completion. I. Theory
We propose a conceptually new method for solving nonlinear inverse scattering
problems (ISPs) such as are commonly encountered in tomographic ultrasound
imaging, seismology and other applications. The method is inspired by the
theory of nonlocality of physical interactions and utilizes the relevant
formalism. We formulate the ISP as a problem whose goal is to determine an
unknown interaction potential from external scattering data. Although we
seek a local (diagonally-dominated) as the solution to the posed problem,
we allow to be nonlocal at the intermediate stages of iterations. This
allows us to utilize the one-to-one correspondence between and the T-matrix
of the problem, . Here it is important to realize that not every
corresponds to a diagonal and we, therefore, relax the usual condition of
strict diagonality (locality) of . An iterative algorithm is proposed in
which we seek that is (i) compatible with the measured scattering data and
(ii) corresponds to an interaction potential that is as
diagonally-dominated as possible. We refer to this algorithm as to the
data-compatible T-matrix completion (DCTMC). This paper is Part I in a two-part
series and contains theory only. Numerical examples of image reconstruction in
a strongly nonlinear regime are given in Part II. The method described in this
paper is particularly well suited for very large data sets that become
increasingly available with the use of modern measurement techniques and
instrumentation.Comment: This is Part I of a paper series containing theory only. Part II
contains simulations and is available as arXiv:1505.06777 [math-ph]. Accepted
in this form to Phys. Rev.
Coherently tunable third-order nonlinearity in a nanojunction
A possibility of tuning the phase of the third-order Kerr-type nonlinear
susceptibility in a system consisting of two interacting metal nanospheres and
a nonlinearly polarizable molecule is investigated theoretically and
numerically. It is shown that by varying the relative inter-sphere separation,
it is possible to tune the phase of the effective nonlinear susceptibility
\chi^{(3)}(\omega;\omega,\omega,-\omega)2\pi$.Comment: 10 pages 5 figure
Multiple Projection Optical Diffusion Tomography with Plane Wave Illumination
We describe a new data collection scheme for optical diffusion tomography in
which plane wave illumination is combined with multiple projections in the slab
imaging geometry. Multiple projection measurements are performed by rotating
the slab around the sample. The advantage of the proposed method is that the
measured data can be much more easily fitted into the dynamic range of most
commonly used detectors. At the same time, multiple projections improve image
quality by mutually interchanging the depth and transverse directions, and the
scanned (detection) and integrated (illumination) surfaces. Inversion methods
are derived for image reconstructions with extremely large data sets. Numerical
simulations are performed for fixed and rotated slabs
Inversion of band-limited discrete Fourier transforms of binary images: Uniqueness and algorithms
Inversion of the two-dimensional discrete Fourier transform (DFT) typically
requires all DFT coefficients to be known. When only band-limited DFT
coefficients of a matrix are known, the original matrix can not be uniquely
recovered. Using a priori information that the matrix is binary (all elements
are either 0 or 1) can overcome the missing high-frequency DFT coefficients and
restore uniqueness. We theoretically investigate the smallest pass band that
can be applied while still guaranteeing unique recovery of an arbitrary binary
matrix. The results depend on the dimensions of the matrix. Uniqueness results
are proven for the dimensions , , and , where are primes numbers and an integer. An
inversion algorithm is proposed for practically recovering the unique binary
matrix. This algorithm is based on integer linear programming methods and
significantly outperforms naive implementations. The algorithm efficiently
reconstructs binary matrices using 81 out of the total 289 DFT
coefficients.Comment: 12 page
Bound whispering gallery modes in circular arrays of dielectric spherical particles
Low-dimensional ordered arrays of optical elements can possess bound modes
having an extremely high quality factor. Typically, these arrays consist of
metal elements which have significantly high light absorption thus restricting
performance. In this paper we address the following question: can bound modes
be formed in dielectric systems where the absorption of light is negligible?
Our investigation of circular arrays of spherical particles shows that (1) high
quality modes in an array of 10 or more particles can be attained at least for
a refractive index , so optical materials like TiO or GaAs can
be used; (2) the most bound modes have nearly transverse polarization
perpendicular to the circular plane; (3) in a particularly interesting case of
TiO particles (rutile phase, ), the quality factor of the most
bound mode increases almost by an order of magnitude with the addition of 10
extra particles, while for particles made of GaAs the quality factor increases
by almost two orders of magnitude with the addition of ten extra particles. We
hope that this preliminary study will stimulate experimental investigations of
bound modes in low-dimensional arrays of dielectric particles.Comment: Submitted to Physical Review
The natural resources of Bolinas Lagoon: their status and future
This publication is an integral part of the Department's high-priority inventory and assessment of coastal marshland and tideflat resources. It is intended as a guide for citizens, planners, administrators, and all others interested in the use and development of coastal lands and waters.
Although the resources and problems of Bolinas Lagoon have probably been the subject of more biological and physical investigations than any small estuarine area of the California coast, many of the pertinent reports and information are not readily available to the public.
Consequently, it is one purpose of this report to summarize the lagoon's history, ecological attractions, educational values and the problems facing its continued existence. At the same time, it should provide concerned citizens with a knowledge of the sources of additional and more specific information.
Publication of this report is consistent with the obligation of the Department of Fish and Game to do everything in its power to protect and maintain the State's fish and wildlife resources. Therefore, its purpose transcends local issues on pollution and development, and the Department is, in fact, submitting a report to the people on the status and future of part of its inheritance and the dowry of coming generations.
The report is the third of a scheduled series. It follows similar releases on Upper Newport Bay (Orange County) and Goleta Slough (Santa Barbara county) in March and June of 1970. Documentation of the resources of other critical areas is in progress. There will be future reports of this nature on Elkhorn Slough, Morro Bay, Tomales Bay, Humboldt Bay, and highly threatened marshlands in southern California. (137 pp.
Homogenization of Maxwell's equations in periodic composites
We consider the problem of homogenizing the Maxwell equations for periodic
composites. The analysis is based on Bloch-Floquet theory. We calculate
explicitly the reflection coefficient for a half-space, and derive and
implement a computationally-efficient continued-fraction expansion for the
effective permittivity. Our results are illustrated by numerical computations
for the case of two-dimensional systems. The homogenization theory of this
paper is designed to predict various physically-measurable quantities rather
than to simply approximate certain coefficients in a PDE.Comment: Significantly expanded compared to v1. Accepted to Phys.Rev.E. Some
color figures in this preprint may be easier to read because here we utilize
solid color lines, which are indistinguishable in black-and-white printin
Bubble-Driven Inertial Micropump
The fundamental action of the bubble-driven inertial micropump is
investigated. The pump has no moving parts and consists of a thermal resistor
placed asymmetrically within a straight channel connecting two reservoirs.
Using numerical simulations, the net flow is studied as a function of channel
geometry, resistor location, vapor bubble strength, fluid viscosity, and
surface tension. Two major regimes of behavior are identified: axial and
non-axial. In the axial regime, the drive bubble either remains inside the
channel or continues to grow axially when it reaches the reservoir. In the
non-axial regime the bubble grows out of the channel and in all three
dimensions while inside the reservoir. The net flow in the axial regime is
parabolic with respect to the hydraulic diameter of the channel cross-section
but in the non-axial regime it is not. From numerical modeling, it is
determined that the net flow is maximal when the axial regime crosses over to
the non-axial regime. To elucidate the basic physical principles of the pump, a
phenomenological one-dimensional model is developed and solved. A linear array
of micropumps has been built using silicon-SU8 fabrication technology, and
semi-continuous pumping across a 2 mm-wide channel has been demonstrated
experimentally. Measured variation of the net flow with fluid viscosity is in
excellent agreement with simulation results.Comment: 18 pages, 18 figures, single colum
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