3,258 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 Scattering and Acousto-Optic Imaging
We propose a tomographic method to reconstruct the optical properties of a
highly-scattering medium from incoherent acousto-optic measurements. The method
is based on the solution to an inverse problem for the diffusion equation and
makes use of the principle of interior control of boundary measurements by an
external wave field.Comment: 10 page
Radiation- and Phonon-Bottleneck-Induced Tunneling in the Fe8 Single-Molecule Magnet
We measure magnetization changes in a single crystal of the single-molecule
magnet Fe8 when exposed to intense, short (<20 s) pulses of microwave
radiation resonant with the m = 10 to 9 transition. We find that radiation
induces a phonon bottleneck in the system with a time scale of ~5 s. The
phonon bottleneck, in turn, drives the spin dynamics, allowing observation of
thermally assisted resonant tunneling between spin states at the 100-ns time
scale. Detailed numerical simulations quantitatively reproduce the data and
yield a spin-phonon relaxation time of T1 ~ 40 ns.Comment: 6 RevTeX pages, including 4 EPS figures, version accepted for
publicatio
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
The Cop Number of the One-Cop-Moves Game on Planar Graphs
Cops and robbers is a vertex-pursuit game played on graphs. In the classical
cops-and-robbers game, a set of cops and a robber occupy the vertices of the
graph and move alternately along the graph's edges with perfect information
about each other's positions. If a cop eventually occupies the same vertex as
the robber, then the cops win; the robber wins if she can indefinitely evade
capture. Aigner and Frommer established that in every connected planar graph,
three cops are sufficient to capture a single robber. In this paper, we
consider a recently studied variant of the cops-and-robbers game, alternately
called the one-active-cop game, one-cop-moves game or the lazy-cops-and-robbers
game, where at most one cop can move during any round. We show that Aigner and
Frommer's result does not generalise to this game variant by constructing a
connected planar graph on which a robber can indefinitely evade three cops in
the one-cop-moves game. This answers a question recently raised by Sullivan,
Townsend and Werzanski.Comment: 32 page
Inverse Diffusion Theory of Photoacoustics
This paper analyzes the reconstruction of diffusion and absorption parameters
in an elliptic equation from knowledge of internal data. In the application of
photo-acoustics, the internal data are the amount of thermal energy deposited
by high frequency radiation propagating inside a domain of interest. These data
are obtained by solving an inverse wave equation, which is well-studied in the
literature. We show that knowledge of two internal data based on well-chosen
boundary conditions uniquely determines two constitutive parameters in
diffusion and Schroedinger equations. Stability of the reconstruction is
guaranteed under additional geometric constraints of strict convexity. No
geometric constraints are necessary when internal data for well-chosen
boundary conditions are available, where is spatial dimension. The set of
well-chosen boundary conditions is characterized in terms of appropriate
complex geometrical optics (CGO) solutions.Comment: 24 page
Inversion formulas for the broken-ray Radon transform
We consider the inverse problem of the broken ray transform (sometimes also
referred to as the V-line transform). Explicit image reconstruction formulas
are derived and tested numerically. The obtained formulas are generalizations
of the filtered backprojection formula of the conventional Radon transform. The
advantages of the broken ray transform include the possibility to reconstruct
the absorption and the scattering coefficients of the medium simultaneously and
the possibility to utilize scattered radiation which, in the case of the
conventional X-ray tomography, is typically discarded.Comment: To be submitted to Inverse Problem
Corticothalamic projections control synchronization in locally coupled bistable thalamic oscillators
Thalamic circuits are able to generate state-dependent oscillations of
different frequencies and degrees of synchronization. However, only little is
known how synchronous oscillations, like spindle oscillations in the thalamus,
are organized in the intact brain. Experimental findings suggest that the
simultaneous occurrence of spindle oscillations over widespread territories of
the thalamus is due to the corticothalamic projections, as the synchrony is
lost in the decorticated thalamus. Here we study the influence of
corticothalamic projections on the synchrony in a thalamic network, and uncover
the underlying control mechanism, leading to a control method which is
applicable in wide range of stochastic driven excitable units.Comment: 4 pages with 4 figures (Color online on p.3-4) include
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