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 $2n$ internal data for well-chosen boundary conditions are available, where $n$ 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