Preconditioners for computing multiple solutions in three-dimensional fluid topology optimization

Topology optimization problems generally support multiple local minima, and real-world applications are typically three-dimensional. In previous work [I. P. A. Papadopoulos, P. E. Farrell, and T. M. Surowiec, Computing multiple solutions of topology optimization problems, SIAM Journal on Scientific Computing, (2021)], the authors developed the deflated barrier method, an algorithm that can systematically compute multiple solutions of topology optimization problems. In this work we develop preconditioners for the linear systems arising in the application of this method to Stokes flow, making it practical for use in three dimensions. In particular, we develop a nested block preconditioning approach which reduces the linear systems to solving two symmetric positive-definite matrices and an augmented momentum block. An augmented Lagrangian term is used to control the innermost Schur complement and we apply a geometric multigrid method with a kernel-capturing relaxation method for the augmented momentum block. We present multiple solutions in three-dimensional examples computed using the proposed iterative solver

Computing equilibrium states of cholesteric liquid crystals in elliptical channels with deflation algorithms

We study the problem of a cholesteric liquid crystal confined to an elliptical channel. The system is geometrically frustrated because the cholesteric prefers to adopt a uniform rate of twist deformation, but the elliptical domain precludes this. The frustration is resolved by deformation of the layers or introduction of defects, leading to a particularly rich family of equilibrium configurations. To identify the solution set, we adapt and apply a new family of algorithms, known as deflation methods, that iteratively modify the free energy extremisation problem by removing previously known solutions. A second algorithm, deflated continuation, is used to track solution branches as a function of the aspect ratio of the ellipse and preferred pitch of the cholesteric.Comment: 9 pages, 6 figure

A local Fourier analysis of additive Vanka relaxation for the Stokes equations

Multigrid methods are popular solution algorithms for many discretized PDEs, either as standalone iterative solvers or as preconditioners, due to their high efficiency. However, the choice and optimization of multigrid components such as relaxation schemes and grid-transfer operators is crucial to the design of optimally efficient algorithms. It is well--known that local Fourier analysis (LFA) is a useful tool to predict and analyze the performance of these components. In this paper, we develop a local Fourier analysis of monolithic multigrid methods based on additive Vanka relaxation schemes for mixed finite-element discretizations of the Stokes equations. The analysis offers insight into the choice of "patches" for the Vanka relaxation, revealing that smaller patches offer more effective convergence per floating point operation. Parameters that minimize the two-grid convergence factor are proposed and numerical experiments are presented to validate the LFA predictions.Comment: 30 pages, 12 figures. Add new sections: multiplicative Vanka results and sensitivity of convergence factors to mesh distortio

Computing multiple solutions of topology optimization problems

Topology optimization problems often support multiple local minima due to a lack of convexity. Typically, gradient-based techniques combined with continuation in model parameters are used to promote convergence to more optimal solutions; however, these methods can fail even in the simplest cases. In this paper, we present an algorithm to perform a systematic exploratory search for the solutions of the optimization problem via second-order methods without a good initial guess. The algorithm combines the techniques of deflation, barrier methods and primal-dual active set solvers in a novel way. We demonstrate this approach on several numerical examples, observe mesh-independence in certain cases and show that multiple distinct local minima can be recovered

Chiral carbene–borane adducts: precursors for borenium catalysts for asymmetric FLP hydrogenations

The carbene derived from (1R,3S)-camphoric acid was used to prepare the borane adduct with Piers’ borane 7. Subsequent hydride abstraction gave the borenium cation 8. Adducts with 9-BBN and the corresponding (1R,3S)-camphoric acid-derived carbene bearing increasingly sterically demanding N-substituents (R = Me 9, Et 10, i-Pr 11) and the corresponding borenium cations 12–14 were also prepared. These cations were not active as catalysts in hydrogenation, although 9–11 were shown to undergo carbene ring expansion reactions at 50 °C to give species 15–17. The IBOX-carbene precursors 18 and 19 derived from amino alcohols (S)-valinol and (S)-tert-leucinol (R = i-Pr, t-Bu) were used to prepare borane adducts 20–23. Reaction of the carbenes 1,3-dimethylimidazol-2-ylidene (IMe), 1,3-di-iso-propylimidazol-2-ylidene (IPr) 1-benzyl-3-methylimidazol-2-ylidene (IBnMe), 1-methyl-3-phenylimidazol-2-ylidene (IPhMe) and 1-tert-butyl-3-methylimidazol-2-ylidene (ItBuMe) with diisopinocampheylborane (Ipc2BH) gave chiral adducts: (IMe)(Ipc2BH) 24, (IPr)(Ipc2BH) 25, (IBnMe)(Ipc2BH) 26, (IPhMe)(Ipc2BH) 27, and (ItBuMe)(Ipc2BH) 28. Triazolylidene-type adducts including the (10)-phenyl-9-borabicyclo [3.3.2]decane adduct of 1,3,4-triphenyl-1H-1,2,3-triazolium, rac-29 and the 9-BBN derivative of (S)-2-amino-2′-methoxy-1,1′-binaphthalene-1,2,3-triazolium 34a/b were also prepared. In catalytic studies of these systems, while several species were competent catalysts for imine reduction, in general, low enantioselectivities, ranging from 1–20% ee, were obtained. The implications for chiral borenium cation catalyst design are considered

Mixed-stock analysis of Atlantic herring (Clupea harengus): a tool for identifying management units and complex migration dynamics

We developed and validated a mixed-stock analysis (MSA) method with 59 single-nucleotide polymorphisms selected from genome-wide data to assign individuals to populations in mixed-stock samples of Atlantic herring from the North and Baltic seas. We analysed 3734 herring from spawning locations and scientific catches of mixed feeding stocks to demonstrate a "one-fits-all" tool with unprecedented accuracy for monitoring spatio-temporal dynamics throughout a large geographical range with complex stock mixing. We re-analysed time-series data (2002-2021) and compared inferences about stock composition with estimates from morphological data. We show that contributions from the western Baltic spring-spawning stock complex, which is under management concern, have likely been overestimated. We also show that a genetically distinctive population of western Baltic autumn spawners, ascribed low fisheries importance, contributes non-negligible and potentially temporally increasing proportions to mixed-stock aggregations, calling for a re-evaluation of stock definitions. MSA data can be implemented in stock assessment and in a variety of applications, including marine ecosystem description, impact assessment of specific fleets, and stock-rebuilding plans

Mechano-Electric Feedback in the Fish Heart

Mechanoelectric feedback (MEF) describes the modulation of electrical activity by mechanical activity. This may occur via the activation of mechanosensitive ion channels (MSCs). MEF has not previously been investigated in fish ventricular tissue even though fish can greatly increase ventricular end diastolic volume during exercise which should therefore provide a powerful mechanical stimulus for MEF.When the ventricles of extrinsically paced, isolated working trout hearts were dilated by increasing afterload, monophasic action potential (MAP) duration was significantly shortened at 25% repolarisation, unaltered at 50% repolarisation and significantly lengthened at 90% repolarisation. This observation is consistent with the activation of cationic non-selective MSCs (MSC(NS)s). We then cloned the trout ortholog of TRPC1, a candidate MSC(NS) and confirmed its presence in the trout heart.Our results have validated the use of MAP technology for the fish heart and suggest that, in common with amphibians and mammals, MEF operates in fish ventricular myocardium, possibly via the activation of mechanosensitive TRPC1 ion channels

A meta-analytic review of stand-alone interventions to improve body image

Objective Numerous stand-alone interventions to improve body image have been developed. The present review used meta-analysis to estimate the effectiveness of such interventions, and to identify the specific change techniques that lead to improvement in body image. Methods The inclusion criteria were that (a) the intervention was stand-alone (i.e., solely focused on improving body image), (b) a control group was used, (c) participants were randomly assigned to conditions, and (d) at least one pretest and one posttest measure of body image was taken. Effect sizes were meta-analysed and moderator analyses were conducted. A taxonomy of 48 change techniques used in interventions targeted at body image was developed; all interventions were coded using this taxonomy. Results The literature search identified 62 tests of interventions (N = 3,846). Interventions produced a small-to-medium improvement in body image (d+ = 0.38), a small-to-medium reduction in beauty ideal internalisation (d+ = -0.37), and a large reduction in social comparison tendencies (d+ = -0.72). However, the effect size for body image was inflated by bias both within and across studies, and was reliable but of small magnitude once corrections for bias were applied. Effect sizes for the other outcomes were no longer reliable once corrections for bias were applied. Several features of the sample, intervention, and methodology moderated intervention effects. Twelve change techniques were associated with improvements in body image, and three techniques were contra-indicated. Conclusions The findings show that interventions engender only small improvements in body image, and underline the need for large-scale, high-quality trials in this area. The review identifies effective techniques that could be deployed in future interventions

The macroecology of infectious diseases: a new perspective on global-scale drivers of pathogen distributions and impacts

© 2016 John Wiley & Sons Ltd/CNRS. Identifying drivers of infectious disease patterns and impacts at the broadest scales of organisation is one of the most crucial challenges for modern science, yet answers to many fundamental questions remain elusive. These include what factors commonly facilitate transmission of pathogens to novel host species, what drives variation in immune investment among host species, and more generally what drives global patterns of parasite diversity and distribution? Here we consider how the perspectives and tools of macroecology, a field that investigates patterns and processes at broad spatial, temporal and taxonomic scales, are expanding scientific understanding of global infectious disease ecology. In particular, emerging approaches are providing new insights about scaling properties across all living taxa, and new strategies for mapping pathogen biodiversity and infection risk. Ultimately, macroecology is establishing a framework to more accurately predict global patterns of infectious disease distribution and emergence