Results and questions on a nonlinear approximation approach for solving high-dimensional partial differential equations

We investigate mathematically a nonlinear approximation type approach recently introduced in [A. Ammar et al., J. Non-Newtonian Fluid Mech., 2006] to solve high dimensional partial differential equations. We show the link between the approach and the greedy algorithms of approximation theory studied e.g. in [R.A. DeVore and V.N. Temlyakov, Adv. Comput. Math., 1996]. On the prototypical case of the Poisson equation, we show that a variational version of the approach, based on minimization of energies, converges. On the other hand, we show various theoretical and numerical difficulties arising with the non variational version of the approach, consisting of simply solving the first order optimality equations of the problem. Several unsolved issues are indicated in order to motivate further research

Optimal Storage Rack Design for a 3-dimensional Compact AS/RS

In this paper, we consider a newly-designed compact three-dimensional automated storage and retrieval system (AS/RS). The system consists of an automated crane taking care of movements in the horizontal and vertical direction. A gravity conveying mechanism takes care of the depth movement. Our research objective is to analyze the system performance and optimally dimension of the system. We estimate the crane’s expected travel time for single-command cycles. From the expected travel time, we calculate the optimal ratio between three dimensions that minimizes the travel time for a random storage strategy. In addition, we derive an approximate closed-form travel time expression for dual command cycles. Finally, we illustrate the findings of the study by a practical example.AS/RS;Warehousing;Order Picking;Travel Time Model;Compact Storage Rack Design

Fast QMC matrix-vector multiplication

Quasi-Monte Carlo (QMC) rules $1/N \sum_{n=0}^{N-1} f(\boldsymbol{y}_n A)$ can be used to approximate integrals of the form $\int_{[0,1]^s} f(\boldsymbol{y} A) \,\mathrm{d} \boldsymbol{y}$, where $A$ is a matrix and $\boldsymbol{y}$ is row vector. This type of integral arises for example from the simulation of a normal distribution with a general covariance matrix, from the approximation of the expectation value of solutions of PDEs with random coefficients, or from applications from statistics. In this paper we design QMC quadrature points $\boldsymbol{y}_0, ..., \boldsymbol{y}_{N-1} \in [0,1]^s$ such that for the matrix $Y = (\boldsymbol{y}_{0}^\top, ..., \boldsymbol{y}_{N-1}^\top)^\top$ whose rows are the quadrature points, one can use the fast Fourier transform to compute the matrix-vector product $Y \boldsymbol{a}^\top$, $\boldsymbol{a} \in \mathbb{R}^s$, in $\mathcal{O}(N \log N)$ operations and at most $s-1$ extra additions. The proposed method can be applied to lattice rules, polynomial lattice rules and a certain type of Korobov $p$-set. The approach is illustrated computationally by three numerical experiments. The first test considers the generation of points with normal distribution and general covariance matrix, the second test applies QMC to high-dimensional, affine-parametric, elliptic partial differential equations with uniformly distributed random coefficients, and the third test addresses Finite-Element discretizations of elliptic partial differential equations with high-dimensional, log-normal random input data. All numerical tests show a significant speed-up of the computation times of the fast QMC matrix method compared to a conventional implementation as the dimension becomes large

HI Observations of the Asymptotic Giant Branch Star X Herculis: Discovery of an Extended Circumstellar Wake Superposed on a Compact High-Velocity Cloud

We report HI 21-cm line observations of the AGB star X Her obtained with the Green Bank Telescope (GBT) and the Very Large Array (VLA). We have detected HI emission totaling M_HI=2.1e-03 M_sun associated with the circumstellar envelope of the star. The HI distribution exhibits a head-tail morphology, similar to those previously observed around Mira and RS Cnc. The tail extends ~6.0' (0.24 pc) in the plane of the sky, along the direction of the star's space motion. We also detect a velocity gradient of ~6.5 km/s across the envelope, consistent with the HI tracing a turbulent wake that arises from the motion of a mass-losing star through the ISM. GBT mapping of a 2x2deg region around X Her reveals that the star lies (in projection) near the periphery of a much larger HI cloud that also exhibits signatures of ISM interaction. The properties of the cloud are consistent with those of compact high-velocity clouds. Using CO observations, we have placed an upper limit on its molecular gas content of N_H2<1.3e20 cm^-2. Although the distance to the cloud is poorly constrained, the probability of a chance coincidence in position, velocity, and apparent position angle of space motion between X Her and the cloud is extremely small, suggesting a possible physical association. However, the large HI mass of the cloud (~>2.4~M_sun) and the blueshift of its mean velocity relative to X Her are inconsistent with an origin tied directly to stellar ejection. (abridged)Comment: Accepted to AJ; 47 pages, 15 figures; version with full resolution figures available at http://www.haystack.mit.edu/hay/staff/lmatthew/matthews_XHer.pd

CO and HI observations of an enigmatic cloud

An isolated HI cloud with peculiar properties has recently been discovered by Dedes, Dedes, & Kalberla (2008, A&A, 491, L45) with the 300-m Arecibo telescope, and subsequently imaged with the VLA. It has an angular size of ~6', and the HI emission has a narrow line profile of width ~ 3 km/s. We explore the possibility that this cloud could be associated with a circumstellar envelope ejected by an evolved star. Observations were made in the rotational lines of CO with the IRAM-30m telescope, on three positions in the cloud, and a total-power mapping in the HI line was obtained with the Nancay Radio Telescope. CO was not detected and seems too underabundant in this cloud to be a classical late-type star circumstellar envelope. On the other hand, the HI emission is compatible with the detached-shell model that we developed for representing the external environments of AGB stars. We propose that this cloud could be a fossil circumstellar shell left over from a system that is now in a post-planetary-nebula phase. Nevertheless, we cannot rule out that it is a Galactic cloud or a member of the Local Group, although the narrow line profile would be atypical in both cases.Comment: Accepted for publication in Astronomy and Astrophysic

Raman Scattering Study of the Lattice Dynamics of Superconducting LiFeAs

We report an investigation of the lattice dynamical properties of LiFeAs using inelastic light scattering. Five out of the six expected phonon modes are observed. The temperature evolution of their frequencies and linewidths is in good agreement with an anharmonic-decay model. We find no evidence for substantial electron-phonon coupling, and no superconductivity-induced phonon anomalies.Comment: 5 pages, 3 figures, 1 tabl

Circumstellar HI and CO around the carbon stars V1942 Sgr and V CrB

Context. The majority of stars that leave the main sequence are undergoing extensive mass loss, in particular during the asymptotic giant branch (AGB) phase of evolution. Observations show that the rate at which this phenomenon develops differs highly from source to source, so that the time-integrated mass loss as a function of the initial conditions (mass, metallicity, etc.) and of the stage of evolution is presently not well understood. Aims. We are investigating the mass loss history of AGB stars by observing the molecular and atomic emissions of their circumstellar envelopes. Methods. In this work we have selected two stars that are on the thermally pulsing phase of the AGB (TP-AGB) and for which high quality data in the CO rotation lines and in the atomic hydrogen line at 21 cm could be obained. Results. V1942 Sgr, a carbon star of the Irregular variability type, shows a complex CO line profile that may originate from a long-lived wind at a rate of ~ 10^-7 Msol/yr, and from a young (< 10^4 years) fast outflow at a rate of ~ 5 10^-7 Msol/yr. Intense HI emission indicates a detached shell with 0.044 Msol of hydrogen. This shell probably results from the slowing-down, by surrounding matter, of the same long-lived wind observed in CO that has been active during ~ 6 10^5 years. On the other hand, the carbon Mira V CrB is presently undergoing mass loss at a rate of 2 10^-7 Msol/yr, but was not detected in HI. The wind is mostly molecular, and was active for at most 3 10^4 years, with an integrated mass loss of at most 6.5 10^-3 Msol. Conclusions. Although both sources are carbon stars on the TP-AGB, they appear to develop mass loss under very different conditions, and a high rate of mass loss may not imply a high integrated mass loss.Comment: Accepted for publication in Astron. Astrophy

Vietnamese Graduate International Student Repatriates: Reverse Adjustment

The purpose of this study is to explore the experiences of Vietnamese international students who have returned to Vietnam after graduation from a U.S. higher education institution. The findings suggest that participants found it harder to readjust to Vietnam than to adjust to the U.S. even though they had lived most of their lives in Vietnam. Time in the U.S. had changed them considerably, making it difficult for them to fit back into their old lives in Vietnam. Most of them did not expect to experience reserve culture shock, and most had made real efforts to fit back into the Vietnamese environment and culture