4,967 research outputs found
Corrector theory for MsFEM and HMM in random media
We analyze the random fluctuations of several multi-scale algorithms such as
the multi-scale finite element method (MsFEM) and the finite element
heterogeneous multiscale method (HMM), that have been developed to solve
partial differential equations with highly heterogeneous coefficients. Such
multi-scale algorithms are often shown to correctly capture the homogenization
limit when the highly oscillatory random medium is stationary and ergodic. This
paper is concerned with the random fluctuations of the solution about the
deterministic homogenization limit. We consider the simplified setting of the
one dimensional elliptic equation, where the theory of random fluctuations is
well understood. We develop a fluctuation theory for the multi-scale algorithms
in the presence of random environments with short-range and long-range
correlations. What we find is that the computationally more expensive method
MsFEM captures the random fluctuations both for short-range and long-range
oscillations in the medium. The less expensive method HMM correctly captures
the fluctuations for long-range oscillations and strongly amplifies their size
in media with short-range oscillations. We present a modified scheme with an
intermediate computational cost that captures the random fluctuations in all
cases.Comment: 41 page
Time-dependent angularly averaged inverse transport
This paper concerns the reconstruction of the absorption and scattering
parameters in a time-dependent linear transport equation from knowledge of
angularly averaged measurements performed at the boundary of a domain of
interest. We show that the absorption coefficient and the spatial component of
the scattering coefficient are uniquely determined by such measurements. We
obtain stability results on the reconstruction of the absorption and scattering
parameters with respect to the measured albedo operator. The stability results
are obtained by a precise decomposition of the measurements into components
with different singular behavior in the time domain
Dynamics of parametric fluctuations induced by quasiparticle tunneling in superconducting flux qubits
We present experiments on the dynamics of a two-state parametric fluctuator
in a superconducting flux qubit. In spectroscopic measurements, the fluctuator
manifests itself as a doublet line. When the qubit is excited in resonance with
one of the two doublet lines, the correlation of readout results exhibits an
exponential time decay which provides a measure of the fluctuator transition
rate. The rate increases with temperature in the interval 40 to 158 mK. Based
on the magnitude of the transition rate and the doublet line splitting we
conclude that the fluctuation is induced by quasiparticle tunneling. These
results demonstrate the importance of considering quasiparticles as a source of
decoherence in flux qubits.Comment: 12 pages, including supplementary informatio
Inverse Transport Theory of Photoacoustics
We consider the reconstruction of optical parameters in a domain of interest
from photoacoustic data. Photoacoustic tomography (PAT) radiates high frequency
electromagnetic waves into the domain and measures acoustic signals emitted by
the resulting thermal expansion. Acoustic signals are then used to construct
the deposited thermal energy map. The latter depends on the constitutive
optical parameters in a nontrivial manner. In this paper, we develop and use an
inverse transport theory with internal measurements to extract information on
the optical coefficients from knowledge of the deposited thermal energy map. We
consider the multi-measurement setting in which many electromagnetic radiation
patterns are used to probe the domain of interest. By developing an expansion
of the measurement operator into singular components, we show that the spatial
variations of the intrinsic attenuation and the scattering coefficients may be
reconstructed. We also reconstruct coefficients describing anisotropic
scattering of photons, such as the anisotropy coefficient in a
Henyey-Greenstein phase function model. Finally, we derive stability estimates
for the reconstructions
Synesthesie: geur, klank en andere zintuiglijke ervaringen = Synaesthesis: smell, sound and other sense experiences
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