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 $g(x)$ in a Henyey-Greenstein phase function model. Finally, we derive stability estimates for the reconstructions

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

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

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

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 $\mu$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 $\mu$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

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

Measuring Performance to Engage the Extended Project Team in Construction

In construction, stakeholders of extended project team play a key role in the overall project performance. Successful integration of stakeholders demands for good management practices at strategic, operational and project levels. Targets and measures to improve the stakeholder performance encourage the creativity and willingness of stakeholders of extended project team to develop the better ways to achieve the project objectives. This paper presents a generic descriptive method, showing how stakeholder's ability and influence impacts on project performance in the construction sector. The findings of a series of interviews with key informants are presented and the following main conclusion is drawn: improving project performance through stakeholder's contribution and measuring their performance can strengthen the project performance. This innovative approach which redefines the process of improving the project performance in construction projects will be of interest to those who intend to manage the projects in practice as well as to those who interested in advancing theory