Renormalized proton- neutron QRPA and double beta decay of 82Se to excited states in 82Kr

We apply the self-consistent renormalized proton-neutron QRPA (RQRPA) method to calculate the two-neutrino double beta (2νββ) decay matrix elements associated with the ground-state and excited-state transitions of the ⁸²Se → ⁸²Kr decay. The RQRPA method is an extension of the pnQRPA method and promotes the Pauli exclusion principle violated by the pnQRPA ground state and yields more stable nuclear matrix elements with increasing strength of the proton-neutron interaction. In the present work the RQRPA wave functions are also used to evaluate 2νββ-decay rates to excited final states. The resulting theoretical half lives are compared with the new stringent experimental limits obtained by using a HPGe detector and external sources of enriched selenium.     

A fast Fourier transform based direct solver for the Helmholtz problem

This article is devoted to the efficient numerical solution of the Helmholtz equation in a two‐ or three‐dimensional (2D or 3D) rectangular domain with an absorbing boundary condition (ABC). The Helmholtz problem is discretized by standard bilinear and trilinear finite elements on an orthogonal mesh yielding a separable system of linear equations. The main key to high performance is to employ the fast Fourier transform (FFT) within a fast direct solver to solve the large separable systems. The computational complexity of the proposed FFT‐based direct solver is $\mathrm{??}(N\log N)$ operations. Numerical results for both 2D and 3D problems are presented confirming the efficiency of the method discussed.     

A damping preconditioner for time-harmonic wave equations in fluid and elastic material

A physical damping is considered as a preconditioning technique for acoustic and elastic wave scattering. The earlier preconditioners for the Helmholtz equation are generalized for elastic materials and three-dimensional domains. An algebraic multigrid method is used in approximating the inverse of damped operators. Several numerical experiments demonstrate the behavior of the method in complicated two-dimensional and three-dimensional domains.     

Sum-rule analysis of the renormalized quasiparticle random-phase approximation

The renormalized quasiparticle random-phase approximation (RQRPA) is analyzed by the use of sum-rule techniques in realistic model calculations. It is found that the RQRPA does not satisfy the Gamow-TellerS ₋ −S ₊=3(N − Z) sum rule and that the violation mostly comes from theS ₋ part of it. The violation also seems to be mass-dependent increasing towards lighter masses. At the same time also the double Gamow-Teller sum rule is seen to be violated. Possible restoration of the sum rule is seen in the inclusion of the scattering terms in the definition of the RQRPA phonon operators. Presented by J. Suhonen at the Workshop on calculation of odouble-beta-decay matrix elements (MEDEX’97), Prague, May 27–31, 1997.     

A Projected Algebraic Multigrid Method for Linear Complementarity Problems

We present an algebraic version of an iterative multigrid method for obstacle problems, called projected algebraic multigrid (PAMG) here. We show that classical algebraic multigrid algorithms can easily be extended to deal with this kind of problem. This paves the way for efficient multigrid solution of obstacle problems with partial differential equations arising, for example, in financial engineering.     

Validation of a new measuring system for water turbidity field measurements

Turbidity is an essential parameter for describing water quality by direct and indirect impacts on fish, invertebrates and aquatic plants. Currently, environmental monitoring measurements are carried out with appropriate quality by accredited testing laboratories, but there is also a need for employing the third sector, i.e. citizens and voluntaries in environmental monitoring. A device called “Secchi3000” was developed as a low-cost and simple-to-operate tool so that water quality measurements can also be carried out by non-experts and citizens. The measurement using the new device is simple: The user fills the container with water and places the measurement structure in the container. The user takes a photograph with the camera on a mobile phone through a hole in the lid. The software sends the photograph to a server, which analyses the photographs automatically. Finally, the results are returned to the user’s mobile phone and stored on a database for further analysis. In this study, the measuring system for turbidity measurements in natural waters was validated. Validation included an estimation of the limit of quantification, investigations of the influence of water colour and illumination conditions on turbidity measurement values and the estimation of measurement uncertainty. A comparison of turbidity results obtained with the new device and laboratory instrument in natural water samples was carried out, and turbidity values obtained with different mobile phones were compared. According to the validation results, the new device was appropriate for the measurement of turbidity lower than 7 FNU (Formazine Nephelometric Unit). An algorithm applied for present turbidity calculations is not fully suitable for higher turbidities. For potential routine use, this is not a major problem, since most Finnish natural waters have turbidities lower than 7 FNU. For official monitoring purposes, the limit of the quantification needs to be lower than presently achieved (1.7 FNU). Although the present configuration of the Secchi3000 device is not yet fully suitable for official environmental monitoring, it will already enable the involvement of the third sector in water quality monitoring, and in this way, citizens’ observations could then serve at least as supplementary information for reporting and surveys.     

Numerical Comparison of Some Penalty-Based Constraint Handling Techniques in Genetic Algorithms

We study five penalty function-based constraint handling techniques to be used with genetic algorithms in global optimization. Three of them, the method of superiority of feasible points, the method of parameter free penalties and the method of adaptive penalties have already been considered in the literature. In addition, we introduce two new modifications of these methods. We compare all the five methods numerically in 33 test problems and report and analyze the results obtained in terms of accuracy, efficiency and reliability. The method of adaptive penalties turned out to be most efficient while the method of parameter free penalties was the most reliable.     

Interactive Solution Approach to a Multiobjective Optimization Problem in a Paper Machine Headbox Design

A successful application of the interactive multiobjective optimization method NIMBUS to a design problem in papermaking technology is described. Namely, an optimal shape design problem related to the paper machine headbox is studied. First, the NIMBUS method, the numerical headbox model, and the associated multiobjective optimization problem are described. Then, the results of numerical experiments are presented.     

Weak Harnack Estimates for Quasiminimizers with Non-Standard Growth and General Structure

We establish the weak Harnack estimates for locally bounded sub- and superquasiminimizers u of

$${\int}_{\Omega} f(x,u,\nabla u)\,dx $$

with f subject to the general structural conditions

$$|z|^{p(x)} - b(x)|y|^{p(x)}-g(x) \leq f(x,y,z) \leq \mu|z|^{p(x)} + b(x)|y|^{p(x)} + g(x), $$

where p : Ω →] 1, ∞[ is a variable exponent. The upper weak Harnack estimate is proved under the assumption that b, g ∈ L ^t (Ω) for some t > n/p ^?, and the lower weak Harnack estimate is proved under the stronger assumption that b, g ∈ L ^∞(Ω). As applications we obtain the Harnack inequality for quasiminimizers and the fact that locally bounded quasisuperminimizers have Lebesgue points everywhere whenever b, g ∈ L ^∞(Ω). Throughout the paper, we make the standard assumption that the variable exponent p is logarithmically Hölder-continuous.