3,314 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
A Unified Treatment of the Characters of SU(2) and SU(1,1)
The character problems of SU(2) and SU(1,1) are reexamined from the
standpoint of a physicist by employing the Hilbert space method which is shown
to yield a completely unified treatment for SU(2) and the discrete series of
representations of SU(1,1). For both the groups the problem is reduced to the
evaluation of an integral which is invariant under rotation for SU(2) and
Lorentz transformation for SU(1,1). The integrals are accordingly evaluated by
applying a rotation to a unit position vector in SU(2) and a Lorentz
transformation to a unit SO(2,1) vector which is time-like for the elliptic
elements and space-like for the hyperbolic elements in SU(1,1). The details of
the procedure for the principal series of representations of SU(1,1) differ
substantially from those of the discrete series.Comment: 31 pages, RevTeX, typos corrected. To be published in Journal of
Mathematical Physic
Real-Time Dedispersion for Fast Radio Transient Surveys, using Auto Tuning on Many-Core Accelerators
Dedispersion, the removal of deleterious smearing of impulsive signals by the
interstellar matter, is one of the most intensive processing steps in any radio
survey for pulsars and fast transients. We here present a study of the
parallelization of this algorithm on many-core accelerators, including GPUs
from AMD and NVIDIA, and the Intel Xeon Phi. We find that dedispersion is
inherently memory-bound. Even in a perfect scenario, hardware limitations keep
the arithmetic intensity low, thus limiting performance. We next exploit
auto-tuning to adapt dedispersion to different accelerators, observations, and
even telescopes. We demonstrate that the optimal settings differ between
observational setups, and that auto-tuning significantly improves performance.
This impacts time-domain surveys from Apertif to SKA.Comment: 8 pages, accepted for publication in Astronomy and Computin
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
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
Sensing the Present: “Conceptual Art of the Senses”
After Rachel E. Burke briefly introduces the essays presented with a focus on our contemporary relationship to modern subjectivity, Mieke Bal will make the case for the sense of presentness on an affective and sensuous level in Munch’s paintings and Flaubert’s writing by selecting a few topics and cases from the book Emma and Edvard Looking Sideways: Loneliness and the Cinematic, published by the Munch Museum in conjunction with the exhibition Emma & Edvard. It is this foregrounded presentness that not only produces the ongoing thematic relevance of these works, but more importantly, the sense-based conceptualism that declares art and life tightly bound together. If neither artist eliminated figuration in favour of abstraction, they had a good reason for that. Art is not a representation of life, but belongs to it, illuminates it and helps us cope with it by sharpening our senses. As an example, a few paintings will clarify what I mean by the noun-qualifier “cinematic” and how that aesthetic explains the production of loneliness
Measurement of Magnetization Dynamics in Single-Molecule Magnets Induced by Pulsed Millimeter-Wave Radiation
We describe an experiment aimed at measuring the spin dynamics of the Fe8
single-molecule magnet in the presence of pulsed microwave radiation. In
earlier work, heating was observed after a 0.2-ms pulse of intense radiation,
indicating that the spin system and the lattice were out of thermal equilibrium
at millisecond time scale [Bal et al., Europhys. Lett. 71, 110 (2005)]. In the
current work, an inductive pick-up loop is used to probe the photon-induced
magnetization dynamics between only two levels of the spin system at much
shorter time scales (from ns to us). The relaxation time for the magnetization,
induced by a pulse of radiation, is found to be on the order of 10 us.Comment: 3 RevTeX pages, including 3 eps figures. The paper will appear in the
Journal of Applied Physics as MMM'05 conference proceeding
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