Double Greedy Algorithms: Reduced Basis Methods for Transport Dominated Problems

The central objective of this paper is to develop reduced basis methods for parameter dependent transport dominated problems that are rigorously proven to exhibit rate-optimal performance when compared with the Kolmogorov $n$-widths of the solution sets. The central ingredient is the construction of computationally feasible "tight" surrogates which in turn are based on deriving a suitable well-conditioned variational formulation for the parameter dependent problem. The theoretical results are illustrated by numerical experiments for convection-diffusion and pure transport equations. In particular, the latter example sheds some light on the smoothness of the dependence of the solutions on the parameters

From West to East and Back Again: Faith, Doubt and Education in Hermann Hesse's Later Work

This paper examines Hermann Hesse’s penultimate novel, The Journey to the East, from an educational point of view. Hesse was a man of the West who turned to the idea of ‘the East’ in seeking to understand himself and his society. While highly critical of elements of Western modernism, Hesse nonetheless viewed ‘the East’ through Western lenses and drew inspiration from other Western thinkers. At the end of The Journey to the East, the main character, H.H., believes he has found the solution to his despair. This paper argues that he has not, at least not in the fullest sense Hesse came to see was possible. H.H. relies too heavily on faith and abandons reason too quickly in seeking to become ‘absorbed’ into the Other he regards as his higher self. An answer to H.H.’s existential angst can be found in Hesse’s final novel, The Glass Bead Game, where educational growth through the development of a critical, questioning, inquiring attitude is a central theme

Multilevel Preconditioning of Discontinuous-Galerkin Spectral Element Methods, Part I: Geometrically Conforming Meshes

This paper is concerned with the design, analysis and implementation of preconditioning concepts for spectral Discontinuous Galerkin discretizations of elliptic boundary value problems. While presently known techniques realize a growth of the condition numbers that is logarithmic in the polynomial degrees when all degrees are equal and quadratic otherwise, our main objective is to realize full robustness with respect to arbitrarily large locally varying polynomial degrees degrees, i.e., under mild grading constraints condition numbers stay uniformly bounded with respect to the mesh size and variable degrees. The conceptual foundation of the envisaged preconditioners is the auxiliary space method. The main conceptual ingredients that will be shown in this framework to yield "optimal" preconditioners in the above sense are Legendre-Gauss-Lobatto grids in connection with certain associated anisotropic nested dyadic grids as well as specially adapted wavelet preconditioners for the resulting low order auxiliary problems. Moreover, the preconditioners have a modular form that facilitates somewhat simplified partial realizations. One of the components can, for instance, be conveniently combined with domain decomposition, at the expense though of a logarithmic growth of condition numbers. Our analysis is complemented by quantitative experimental studies of the main components.Comment: 41 pages, 11 figures; Major revision: rearrangement of the contents for better readability, part on wavelet preconditioner adde

Optimized imaging using non-rigid registration

The extraordinary improvements of modern imaging devices offer access to data with unprecedented information content. However, widely used image processing methodologies fall far short of exploiting the full breadth of information offered by numerous types of scanning probe, optical, and electron microscopies. In many applications, it is necessary to keep measurement intensities below a desired threshold. We propose a methodology for extracting an increased level of information by processing a series of data sets suffering, in particular, from high degree of spatial uncertainty caused by complex multiscale motion during the acquisition process. An important role is played by a nonrigid pixel-wise registration method that can cope with low signal-to-noise ratios. This is accompanied by formulating objective quality measures which replace human intervention and visual inspection in the processing chain. Scanning transmission electron microscopy of siliceous zeolite material exhibits the above-mentioned obstructions and therefore serves as orientation and a test of our procedures

Hysteresis, Avalanches, and Noise: Numerical Methods

In studying the avalanches and noise in a model of hysteresis loops we have developed two relatively straightforward algorithms which have allowed us to study large systems efficiently. Our model is the random-field Ising model at zero temperature, with deterministic albeit random dynamics. The first algorithm, implemented using sorted lists, scales in computer time as O(N log N), and asymptotically uses N (sizeof(double)+ sizeof(int)) bits of memory. The second algorithm, which never generates the random fields, scales in time as O(N \log N) and asymptotically needs storage of only one bit per spin, about 96 times less memory than the first algorithm. We present results for system sizes of up to a billion spins, which can be run on a workstation with 128MB of RAM in a few hours. We also show that important physical questions were resolved only with the largest of these simulations

Экранное трубчатое многопараметровое вихретоковое устройство

Рассмотрено экранное трубчатое многопараметровое устройство, с помощью которого определяются четыре параметра ферромагнитной трубы: относительная магнитная проницаемость µrt, удельное электрическое сопротивление Pt, температура трубы t и коэффициент затухания магнитного поля в трубчатом изделии ht.The screen tubular mnogoparametrovoe device is considered, which four parameters of ferromagnetic pipe are determined by: relative permeance µrt, specific electric resistance Pt, temperature of pipe of t and coefficient of fading of the magnetic field in tubular good of ht

Extended Molecular Gas in the Nearby Starburst Galaxy Maffei 2

We present a 9'x9' fully-sampled map of the CO J=1-0 emission in the nearby starburst galaxy Maffei 2 obtained at the Five College Radio Astronomy Observatory. The map reveals previously known strong CO emission in the central starburst region as well as an extended asymmetric distribution with bright CO lines at the ends of the bar and in a feature at the north-east edge of the molecular disk. This northern feature, proposed previously to be an interacting companion galaxy, could be a dwarf irregular galaxy, although the CO data are also consistent with the feature being simply an extension of one of the spiral arms. We estimate the total molecular gas mass of Maffei 2 to be (1.4-1.7)x10^9 Mo or ~3-4% of its dynamical mass. Adopting the recently determined lower value for the CO-to-H2 conversion factor in the central region, our data lead to the surprising result that the largest concentrations of molecular gas in Maffei 2 lie at the bar ends and in the putative dwarf companion rather than in the central starburst. A gravitational stability analysis reveals that the extended disk of Maffei 2 lies above the critical density for star formation; however, whether the central region is also gravitationally unstable depends both on the details of the rotation curve and the precise value of the CO-to-H2 conversion factor in this region.Comment: accepted to ApJ (Sept 10 2004 issue

Electron tomography at 2.4 {\AA} resolution

Transmission electron microscopy (TEM) is a powerful imaging tool that has found broad application in materials science, nanoscience and biology(1-3). With the introduction of aberration-corrected electron lenses, both the spatial resolution and image quality in TEM have been significantly improved(4,5) and resolution below 0.5 {\AA} has been demonstrated(6). To reveal the 3D structure of thin samples, electron tomography is the method of choice(7-11), with resolutions of ~1 nm^3 currently achievable(10,11). Recently, discrete tomography has been used to generate a 3D atomic reconstruction of a silver nanoparticle 2-3 nm in diameter(12), but this statistical method assumes prior knowledge of the particle's lattice structure and requires that the atoms fit rigidly on that lattice. Here we report the experimental demonstration of a general electron tomography method that achieves atomic scale resolution without initial assumptions about the sample structure. By combining a novel projection alignment and tomographic reconstruction method with scanning transmission electron microscopy, we have determined the 3D structure of a ~10 nm gold nanoparticle at 2.4 {\AA} resolution. While we cannot definitively locate all of the atoms inside the nanoparticle, individual atoms are observed in some regions of the particle and several grains are identified at three dimensions. The 3D surface morphology and internal lattice structure revealed are consistent with a distorted icosahedral multiply-twinned particle. We anticipate that this general method can be applied not only to determine the 3D structure of nanomaterials at atomic scale resolution(13-15), but also to improve the spatial resolution and image quality in other tomography fields(7,9,16-20).Comment: 27 pages, 17 figure