16,413 research outputs found
Fluctuating volume-current formulation of electromagnetic fluctuations in inhomogeneous media: incandecence and luminescence in arbitrary geometries
We describe a fluctuating volume--current formulation of electromagnetic
fluctuations that extends our recent work on heat exchange and Casimir
interactions between arbitrarily shaped homogeneous bodies [Phys. Rev. B. 88,
054305] to situations involving incandescence and luminescence problems,
including thermal radiation, heat transfer, Casimir forces, spontaneous
emission, fluorescence, and Raman scattering, in inhomogeneous media. Unlike
previous scattering formulations based on field and/or surface unknowns, our
work exploits powerful techniques from the volume--integral equation (VIE)
method, in which electromagnetic scattering is described in terms of
volumetric, current unknowns throughout the bodies. The resulting trace
formulas (boxed equations) involve products of well-studied VIE matrices and
describe power and momentum transfer between objects with spatially varying
material properties and fluctuation characteristics. We demonstrate that thanks
to the low-rank properties of the associatedmatrices, these formulas are
susceptible to fast-trace computations based on iterative methods, making
practical calculations tractable. We apply our techniques to study thermal
radiation, heat transfer, and fluorescence in complicated geometries, checking
our method against established techniques best suited for homogeneous bodies as
well as applying it to obtain predictions of radiation from complex bodies with
spatially varying permittivities and/or temperature profiles
Adaptive time-frequency detection and filtering for imaging in heavy clutter
Abstract. We introduce an adaptive approach for the detection of a reflector in a strongly scattering medium using a timefrequency representation of the array response matrix followed by a Singular Value Decomposition (SVD). We use the Local Cosine Transform (LCT) for the time-frequency representation and introduce a detection criterion that identifies anomalies in the top singular values, across frequencies and in different time windows, that are due to the reflector. The detection is adaptive because the time windows that contain the primary echoes from the reflector are not determined in advance. Their location and width is identified by searching through the time-frequency binary tree of the LCT. After detecting the presence of the reflector we filter the array response matrix to retain information only in the time windows that have been selected. We also project the filtered array response matrix to the subspace associated with the top singular value and then image using travel time migration. We show with extensive numerical simulations that this approach to detection and imaging works well in heavy clutter that is calibrated using random matrix theory so as to simulate regimes close to the experiments in [3]. While the detection and filtering algorithm presented here works well in general clutter it has been analyzed theoretically only for the case of randomly layered media [1]
Filtering random layering effects in imaging
Objects that are buried deep in heterogeneous media produce faint echoes which are difficult to distinguish from the backscattered field. Sensor array imaging in such media cannot work unless we filter out the backscattered echoes and enhance the coherent arrivals that carry information about the objects that we wish to image. We study such filters for imaging in strongly backscattering, finely layered media. The filters are based on a travel time transformation of the array data, the normal move-out, used frequently in connection with differential semblance velocity estimation in seismic imaging. In a previous paper [10] we showed that the filters can be used to remove coherent signals from strong plane reflectors. In this paper we show theoretically and with extensive numerical simulations that these filters, based on the normal move-out, can also remove the incoherent arrivals in the array data that are due to fine random layering in the medium. Key words. array imaging, randomly layered media, filtering
Frequency-robust preconditioning of boundary integral equations for acoustic transmission
The scattering and transmission of harmonic acoustic waves at a penetrable
material are commonly modelled by a set of Helmholtz equations. This system of
partial differential equations can be rewritten into boundary integral
equations defined at the surface of the objects and solved with the boundary
element method (BEM). High frequencies or geometrical details require a fine
surface mesh, which increases the number of degrees of freedom in the weak
formulation. Then, matrix compression techniques need to be combined with
iterative linear solvers to limit the computational footprint. Moreover, the
convergence of the iterative linear solvers often depends on the frequency of
the wave field and the objects' characteristic size. Here, the robust PMCHWT
formulation is used to solve the acoustic transmission problem. An operator
preconditioner based on on-surface radiation conditions (OSRC) is designed that
yields frequency-robust convergence characteristics. Computational benchmarks
compare the performance of this novel preconditioned formulation with other
preconditioners and boundary integral formulations. The OSRC preconditioned
PMCHWT formulation effectively simulates large-scale problems of engineering
interest, such as focused ultrasound treatment of osteoid osteoma
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