BiCGstab(l) and other hybrid Bi-CG methods

It is well-known that Bi-CG can be adapted so that the operations withA ^T can be avoided, and hybrid methods can be constructed in which it is attempted to further improve the convergence behaviour. Examples of this are CGS, Bi-CGSTAB, and the more general BiCGstab(l) method. In this paper it is shown that BiCGstab(l) can be implemented in different ways. Each of the suggested approaches has its own advantages and disadvantages. Our implementations allow for combinations of Bi-CG with arbitrary polynomial methods. The choice for a specific implementation can also be made for reasons of numerical stability. This aspect receives much attention. Various effects have been illustrated by numerical examples.     

The orientation of porphins in n-alkane Shpolskii hosts

When a solution of a porphin in n-octane is slowly frozen the guests predominantly occupy a single site (A) in which the porphin has been shown to replace a number of host molecules displaced along the b-direction; if the solution is quickly frozen the optical spectra reveal the presence of a second site (B). In the present paper it is shown that the occurrence of these two types of sites, A and B, is a common phenomenon throughout the series from n-heptane (C₇) to n-decane (C ₁₀) as hosts and phenomenological criteria are formulated to distinguish between the two kinds of sites.

The orientation of palladiumporphin (PdP) in the A and B sites of a C₇ host is determined from Zeeman experiments on the S ₁← S ₀ and T ₀ →S ₀ transitions in a single crystal of C₇ doped with PdP. The porphin nuclei in the B sites replace a number of alkanes displaced along the a-axis. In the course of the experiments signals related to a third type of site, B', grew in intensity in the spectra. This site is coplanar with the B site and it differs from the latter by an in-plane rotation of the trapped molecule over 20°. The origins of the S ₁ ←S ₀ transition for the two types of site are assigned for H₂P, ZnP and PdP as solutes in C₇, C₈, C₉ and C₁₀ as hosts.

Finally, the Zeeman shifts observed in the S ₁ ←S ₀ transition of PdP in the three sites of C₇ yield an effective orbital angular momentum for PdP in the state S ₁ of (4·4 ± 0·1)?, in excellent agreement with previous determinations.     

Stochastic programming with simple integer recourse

Stochastic integer programs are notoriously difficult. Very few properties are known and solution algorithms are very scarce. In this paper, we introduce the class of stochastic programs with simple integer recourse, a natural extension of the simple recourse case extensively studied in stochastic continuous programs.Analytical as well as computational properties of the expected recourse function of simple integer recourse problems are studied. This includes sharp bounds on this function and the study of the convex hull. Finally, a finite termination algorithm is obtained that solves two classes of stochastic simple integer recourse problems.Supported by the National Operations Research Network in the Netherlands (LNMB).     

Automatic segmentation of cerebral white matter hyperintensities using only 3D FLAIR images

Magnetic Resonance (MR) white matter hyperintensities have been shown to predict an increased risk of developing cognitive decline. However, their actual role in the conversion to dementia is still not fully understood. Automatic segmentation methods can help in the screening and monitoring of Mild Cognitive Impairment patients who take part in large population-based studies. Most existing segmentation approaches use multimodal MR images. However, multiple acquisitions represent a limitation in terms of both patient comfort and computational complexity of the algorithms. In this work, we propose an automatic lesion segmentation method that uses only three-dimensional fluid-attenuation inversion recovery (FLAIR) images. We use a modified context-sensitive Gaussian mixture model to determine voxel class probabilities, followed by correction of FLAIR artifacts. We evaluate the method against the manual segmentation performed by an experienced neuroradiologist and compare the results with other unimodal segmentation approaches. Finally, we apply our method to the segmentation of multiple sclerosis lesions by using a publicly available benchmark dataset. Results show a similar performance to other state-of-the-art multimodal methods, as well as to the human rater.     

Off-equilibrium photon production during the chiral phase transition

In the early stage of ultrarelativistic heavy-ion collisions chiral symmetry is restored temporarily. During this so-called chiral phase transition, the quark masses change from their constituent to their bare values. This mass shift leads to the spontaneous non-perturbative creation of quark–antiquark pairs, which effectively contributes to the formation of the quark–gluon plasma. We investigate the photon production induced by this creation process. We provide an approach that eliminates possible unphysical contributions from the vacuum polarization and renders the resulting photon spectra integrable in the ultraviolet domain. The off-equilibrium photon numbers are of quadratic order in the perturbative coupling constants while a thermal production is only of quartic order. Quantitatively, we find, however, that for the most physical mass-shift scenarios and for photon momenta larger than 1 GeV the off-equilibrium processes contribute less photons than the thermal processes.     

Parallelism across the steps in iterated Runge-Kutta methods for stiff initial value problems

For the parallel integration of stiff initial value problems (IVPs) three main approaches can be distinguished: approaches based on parallelism across the problem, on parallelism across the method and on parallelism across the steps. The first type of parallelism does not require special integration methods can be exploited within any available IVP solver. The methodparallel approach received some attention in the case of Runge-Kutta based methods. For these methods, the required number of processors is roughly half the order of the generating Runge-Kutta method and the speed-up with respect to a good sequential IVP solver is about a factor 2. The third type of parallelism (step-parallelism) can be achieved in any IVP solver based on predictor-corrector iteration. Most step-parallel methods proposed so far employ a large number of processors, but lack the property of robustness, due to a poor convergence behaviour in the iteration process. Hence, the effective speed-up is rather poor. The step-parallel iteraction process proposed in the present paper is less massively parallel, but turns out to be sufficiently robust to solve the four-stage Radau IIA corrector used in our experiments within a few effective iterations per step and to achieve speed-up factors up to 10 with respect to the best sequential codes.The research reported in this paper was partly supported by the Technology Foundation (STW) in the Netherlands.     

On the existence of certain generalized Moore geometries,part II

The existence of generalized Moore geometries of type GM_m(s,t,s+1),with st>1, is investigated. In a previous paper it was shown that if the diameter m is odd such a geometry can exist only if m?7; as a consequence of the main result of the present paper the restriction ‘m is odd’ has become superfluous.     

Löwner expansions

A fundamental problem is to estimate the logarithmic coefficients of a power series with constant coefficient zero which represents a function which has distinct values at distinct points of the unit disk. A source of estimates is an expansion theorem for the Löwner equations which is obtained from a study of contractive substitutions in Hilbert spaces of analytic functions. The methods are an outgrowth of the theory of square summable power series [1]. Assume that σ_n is a given function of nonnegative integers n, with nonnegative values, such that σ₀ = 0 and such that σ_{n ? 1} ? σ_n when n is positive. Infinite values are allowed. The underlying Hilbert space is the set $\text{G}$_σ(0) of equivalence classes of power series f(z) = ∑ a_nzⁿ with constant coefficient zero such that f(z)²_{$\text{G}$σ⁽⁰⁾} = ∑(n/σ_n)|a_n|² is finite. Equivalence of power series f(z) and g(z) means that the coefficient of zⁿ in f(z) is equal to the coefficient of zⁿ in g(z) when σ_n is finite.     

Dislocation glide through non-randomly distributed point obstacles

Abstract

Classical meso-scale models for dislocation–obstacle interactions have, by and large, assumed a random distribution of obstacles on the glide plane. While a good approximation in many situations, this does not represent materials where obstacles are clustered on the glide plane. In this work, we have investigated the statistical problem of a dislocation sampling a set of clustered point obstacles in the glide plane using a modified areal-glide model. The results of these simulations show two clear regimes. For weak obstacles, the spatial distribution does not matter and the critically resolved shear stress is found to be independent of the degree of clustering. In contrast, above a critical obstacle strength determined by the degree of clustering, the critical resolved shear strength becomes constant. It is shown that this behaviour can be explained semi-analytically by considering the probability of interaction between the dislocation line and obstacles at a given level of stress. The consequences for alloys exhibiting solute clustering are discussed.