On the vanishing viscosity limit in a disk

We say that the solution u to the Navier-Stokes equations converges to a solution v to the Euler equations in the vanishing viscosity limit if u converges to v in the energy norm uniformly over a finite time interval. Working specifically in the unit disk, we show that a necessary and sufficient condition for the vanishing viscosity limit to hold is the vanishing with the viscosity of the time-space average of the energy of u in a boundary layer of width proportional to the viscosity due to modes (eigenfunctions of the Stokes operator) whose frequencies in the radial or the tangential direction lie between L and M. Here, L must be of order less than 1/(viscosity) and M must be of order greater than 1/(viscosity)

Listening to sad music in adverse situations: Music selection strategies, self-regulatory goals, listening effect, and mood-enhancement

Adults’ (N = 220) reported motivations for listening to sad music after experiencing adverse negative circumstances were examined by exploring how their music selection strategies related to (a) their self-regulatory goals, and (b) reported effects of listening. The effects of music selection strategies, self-regulatory goals, and reported effects on the achievement of mood enhancement were also explored using a retrospective survey design. The findings indicate that music choice is linked to the individual’s identified self-regulatory goals for music listening and to expected effects. Additionally, the results show that if individuals had intended to achieve mood enhancement through music listening, this was often achieved by first experiencing cognitive reappraisal or distraction. The selection of music with perceived high aesthetic value was the only music selection strategy that directly predicted mood enhancement. Where respondents indicated that they chose music with the intention of triggering memories, this was negatively related to the self-regulatory goal of mood enhancement

The content of nostalgic memories among people living with dementia

Although dementia may affect the reliability of autobiographical memories, the psychological properties of nostalgic memories may be preserved. We compared the content of nostalgic (n = 36) and ordinary (n = 31) narratives of 67 participants living with dementia. Narratives were rated according to their self-oriented, social, and existential properties, as well as their affective content. Social properties and affective content were assessed using a linguistic word count procedure. Compared to the ordinary narratives described in the control condition, nostalgic narratives described atypical events, expressed more positive affect, and had more expressions of self-esteem and self-continuity. They were also rated higher on companionship, connectedness and the closeness of relationships, and reflected life as being meaningful. Despite their cognitive impairment, people living with dementia experience nostalgia in similar ways to cognitively healthy adults, with their nostalgic narratives containing self-oriented, social, and existential propertie

Real-Space Mesh Techniques in Density Functional Theory

This review discusses progress in efficient solvers which have as their foundation a representation in real space, either through finite-difference or finite-element formulations. The relationship of real-space approaches to linear-scaling electrostatics and electronic structure methods is first discussed. Then the basic aspects of real-space representations are presented. Multigrid techniques for solving the discretized problems are covered; these numerical schemes allow for highly efficient solution of the grid-based equations. Applications to problems in electrostatics are discussed, in particular numerical solutions of Poisson and Poisson-Boltzmann equations. Next, methods for solving self-consistent eigenvalue problems in real space are presented; these techniques have been extensively applied to solutions of the Hartree-Fock and Kohn-Sham equations of electronic structure, and to eigenvalue problems arising in semiconductor and polymer physics. Finally, real-space methods have found recent application in computations of optical response and excited states in time-dependent density functional theory, and these computational developments are summarized. Multiscale solvers are competitive with the most efficient available plane-wave techniques in terms of the number of self-consistency steps required to reach the ground state, and they require less work in each self-consistency update on a uniform grid. Besides excellent efficiencies, the decided advantages of the real-space multiscale approach are 1) the near-locality of each function update, 2) the ability to handle global eigenfunction constraints and potential updates on coarse levels, and 3) the ability to incorporate adaptive local mesh refinements without loss of optimal multigrid efficiencies.Comment: 70 pages, 11 figures. To be published in Reviews of Modern Physic

Construction of 3D models of the CYP11B family as a tool to predict ligand binding characteristics

Aldosterone is synthesised by aldosterone synthase (CYP11B2). CYP11B2 has a highly homologous isoform, steroid 11β-hydroxylase (CYP11B1), which is responsible for the biosynthesis of aldosterone precursors and glucocorticoids. To investigate aldosterone biosynthesis and facilitate the search for selective CYP11B2 inhibitors, we constructed three-dimensional models for CYP11B1 and CYP11B2 for both human and rat. The models were constructed based on the crystal structure of Pseudomonas Putida CYP101 and Oryctolagus Cuniculus CYP2C5. Small steric active site differences between the isoforms were found to be the most important determinants for the regioselective steroid synthesis. A possible explanation for these steric differences for the selective synthesis of aldosterone by CYP11B2 is presented. The activities of the known CYP11B inhibitors metyrapone, R-etomidate, R-fadrazole and S-fadrazole were determined using assays of V79MZ cells that express human CYP11B1 and CYP11B2, respectively. By investigating the inhibitors in the human CYP11B models using molecular docking and molecular dynamics simulations we were able to predict a similar trend in potency for the inhibitors as found in the in vitro assays. Importantly, based on the docking and dynamics simulations it is possible to understand the enantioselectivity of the human enzymes for the inhibitor fadrazole, the R-enantiomer being selective for CYP11B2 and the S-enantiomer being selective for CYP11B1