Linking number analysis of a self-assembled lemniscular Möbius-metallamacrocycle

A 26 membered, 24π-electron metallamacrocycle containing two Ag(I) centers is shown to be a double-twist Möbius cycle by a linking number analysis.

Some uniform stability and convergence results for integral equations on the real line and projection methods for their solution

The paper considers second kind equations of the form (abbreviated x=y + K2x) in which and the factor z is bounded but otherwise arbitrary so that equations of Wiener-Hopf type are included as a special case. Conditions on a set are obtained such that a generalized Fredholm alternative is valid: if W satisfies these conditions and I − Kz, is injective for each z ε W then I − Kz is invertible for each z ε W and the operators (I − Kz)−1 are uniformly bounded. As a special case some classical results relating to Wiener-Hopf operators are reproduced. A finite section version of the above equation (with the range of integration reduced to [−a, a]) is considered, as are projection and iterated projection methods for its solution. The operators (where denotes the finite section version of Kz) are shown uniformly bounded (in z and a) for all a sufficiently large. Uniform stability and convergence results, for the projection and iterated projection methods, are obtained. The argument generalizes an idea in collectively compact operator theory. Some new results in this theory are obtained and applied to the analysis of projection methods for the above equation when z is compactly supported and k(s − t) replaced by the general kernel k(s,t). A boundary integral equation of the above type, which models outdoor sound propagation over inhomogeneous level terrain, illustrates the application of the theoretical results developed.

Rossby number expansions, slaving principles, and balance dynamics

We consider the problem of constructing balance dynamics for rapidly rotating fluid systems. It is argued that the conventional Rossby number expansion—namely expanding all variables in a series in Rossby number—is secular for all but the simplest flows. In particular, the higher-order terms in the expansion grow exponentially on average, and for moderate values of the Rossby number the expansion is, at best, useful only for times of the order of the doubling times of the instabilities of the underlying quasi-geostrophic dynamics. Similar arguments apply in a wide class of problems involving a small parameter and sufficiently complex zeroth-order dynamics. A modified procedure is proposed which involves expanding only the fast modes of the system; this is equivalent to an asymptotic approximation of the slaving relation that relates the fast modes to the slow modes. The procedure is systematic and thus capable, at least in principle, of being carried to any order—unlike procedures based on truncations. We apply the procedure to construct higher-order balance approximations of the shallow-water equations. At the lowest order quasi-geostrophy emerges. At the next order the system incorporates gradient-wind balance, although the balance relations themselves involve only linear inversions and hence are easily applied. There is a large class of reduced systems associated with various choices for the slow variables, but the simplest ones appear to be those based on potential vorticity.

Projection of global wave climate change towards the end of the 21st century

Wind generated waves at the sea surface are of outstanding importance for both their practical relevance in many aspects, such as coastal erosion, protection, or safety of navigation, and for their scientific relevance in modifying fluxes at the air-sea interface. So far long-term changes in ocean wave climate have been studied mostly from a regional perspective with global dynamical studies emerging only recently. Here a global wave climate study is presented, in which a global wave model (WAM) is driven by atmospheric forcing from a global climate model (ECHAM5) for present day and potential future climate conditions represented by the IPCC (Intergovernmental Panel for Climate Change) A1B emission scenario. It is found that changes in mean and extreme wave climate towards the end of the twenty-first century are small to moderate, with the largest signals being a poleward shift in the annual mean and extreme significant wave heights in the mid-latitudes of both hemispheres, more pronounced in the Southern Hemisphere, and most likely associated with a corresponding shift in mid-latitude storm tracks. These changes are broadly consistent with results from the few studies available so far. The projected changes in the mean wave periods, associated with the changes in the wave climate in the mid to high latitudes, are also shown, revealing a moderate increase in the equatorial eastern side of the ocean basins. This study presents a step forward towards a larger ensemble of global wave climate projections required to better assess robustness and uncertainty of potential future wave climate change.

Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex

In this paper we study convergence of the L2-projection onto the space of polynomials up to degree p on a simplex in Rd, d >= 2. Optimal error estimates are established in the case of Sobolev regularity and illustrated on several numerical examples. The proof is based on the collapsed coordinate transform and the expansion into various polynomial bases involving Jacobi polynomials and their antiderivatives. The results of the present paper generalize corresponding estimates for cubes in Rd from [P. Houston, C. Schwab, E. Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002), no. 6, 2133-2163].

Language and thought in bilinguals: the case of grammatical number and nonverbal classification preferences

Recent research shows that speakers of languages with obligatory plural marking (English) preferentially categorize objects based on common shape, whereas speakers of nonplural-marking classifier languages (Yucatec and Japanese) preferentially categorize objects based on common material. The current study extends that investigation to the domain of bilingualism. Japanese and English monolinguals, and Japanese–English bilinguals were asked to match novel objects based on either common shape or color. Results showed that English monolinguals selected shape significantly more than Japanese monolinguals, whereas the bilinguals shifted their cognitive preferences as a function of their second language proficiency. The implications of these findings for conceptual representation and cognitive processing in bilinguals are discussed.

On the Nusselt number for frazil ice growth—a correction to ”Frazil evolution in channels“ by Lars Hammar and Hung-Tao Shen

The growth (melt) rate of frazil ice is governed by heat transfer away from (towards) the ice crystal, which can be represented by the Nusselt number. We discuss choices for the Nusselt number and turbulent length scale appropriate for frazil ice and note an inaccuracy in the study ”Frazil evolution in channels“ by Lars Hammar and Hung-Tao Shen, which has also led to potentially significant errors in several other papers. We correct this error and suggest an appropriate strategy for determining the Nusselt number applicable to frazil ice growth and melting.

The processing of number and gender agreement in Spanish: an event related potential investigation of the effects of structural distance

Previous research suggests that the processing of agreement is affected by the distance between the agreeing elements. However, the unique contribution of structural distance (number of intervening syntactic phrases) to the processing of agreement remains an open question, since previous investigations do not tease apart structural and linear distance (number of intervening words). We used event related potentials (ERPs) to examine the extent to which structural distance impacts the processing of Spanish number and gender agreement. Violations were realized both within the phrase and across the phrase. Across both levels of structural distance, linear distance was kept constant, as was the syntactic category of the agreeing elements. Number and gender agreement violations elicited a robust P600 between 400 and 900ms, a component associated with morphosyntactic processing. No amplitude differences were observed between number and gender violations, suggesting that the two features are processed similarly at the brain level. Within-phrase agreement yielded more positive waveforms than across-phrase agreement, both for agreement violations and for grammatical sentences (no agreement by distance interaction). These effects can be interpreted as evidence that structural distance impacts the establishment of agreement overall, consistent with sentence processing models which predict that hierarchical structure impacts the processing of syntactic dependencies. However, due to the lack of an agreement by distance interaction, the possibility cannot be ruled out that these effects are driven by differences in syntactic predictability between the within-phrase and across-phrase configurations, notably the fact that the syntactic category of the critical word was more predictable in the within-phrase conditions.

Examining second language development using event-related potentials: a cross-sectional study on the processing of gender and number agreement

This cross-sectional study examines the role of L1-L2 differences and structural distance in the processing of gender and number agreement by English-speaking learners of Spanish at three different levels of proficiency. Preliminary results show that differences between the L1 and L2 impact L2 development, as sensitivity to gender agreement violations, as opposed to number agreement violations, emerges only in learners at advanced levels of proficiency. Results also show that the establishment of agreement dependencies is impacted by the structural distance between the agreeing elements for native speakers and for learners at intermediate and advanced levels of proficiency but not for low proficiency. The overall pattern of results suggests that the linguistic factors examined here impact development but do not constrain ultimate attainment; for advanced learners, results suggest that second language processing is qualitatively similar to native processing.

Social equality in the number of choice options is represented in the ventromedial prefrontal cortex

A distinct aspect of the sense of fairness in humans is that we care not only about equality in material rewards but also about equality in non-material values. One such value is the opportunity to choose freely among many options, often regarded as a fundamental right to economic freedom. In modern developed societies, equal opportunities in work, living, and lifestyle are enforced by anti-discrimination laws. Despite the widespread endorsement of equal opportunity, no studies have explored how people assign value to it. We used functional magnetic resonance imaging to identify the neural substrates for subjective valuation of equality in choice opportunity. Participants performed a two-person choice task in which the number of choices available was varied across trials independently of choice outcomes. By using this procedure, we manipulated the degree of equality in choice opportunity between players and dissociated it from the value of reward outcomes and their equality. We found that activation in the ventromedial prefrontal cortex tracked the degree to which the number of options between the two players was equal. In contrast, activation in the ventral striatum tracked the number of options available to participants themselves but not the equality between players. Our results demonstrate that the vmPFC, a key brain region previously implicated in the processing of social values, is also involved in valuation of equality in choice opportunity between individuals. These findings may provide valuable insight into the human ability to value equal opportunity, a characteristic long emphasized in politics, economics, and philosophy.

The influence of plant species number on productivity, ground coverage and floral performance in grass-free lawns

The grass-free lawn is a novel development in modern ornamental horticulture where the traditional monoculture of grass is replaced by a variety of mowing-tolerant clonal forbs. It brings floral aesthetics and a diverse species approach to the use of lawn space. How the number of constituent forb species affects the aesthetic and structural performance of grass-free lawns was investigated using grass-free lawns composed of four, six and twelve British native clonal perennial forb species. Lawn productivity was seen to increase with increasing species number but the relationship was not linear. Plant cover was dynamic in all lawn types, varied between years and was not representative of individual species' floral performance. The behaviour of component species common to all lawns suggested that lawns with 12 species show greater structural stability than the lawns with a lower species number. Visual performance in lawns with the greatest species number was lower than in lawns with fewer species, with increasing variety in floral size and individual species floral productivity leading to a trade-off between diversity and floral performance. Individual species were seen to have different aesthetic functions in grass-free lawns either by providing flowers, ground coverage or both.

Centennial variations in sunspot number, open solar flux and streamer belt width: 1. correction of the sunspot number record since 1874

We analyse the widely-used international/ Zürich sunspot number record, R, with a view to quantifying a suspected calibration discontinuity around 1945 (which has been termed the “Waldmeier discontinuity” [Svalgaard, 2011]). We compare R against the composite sunspot group data from the Royal Greenwich Observatory (RGO) network and the Solar Optical Observing Network (SOON), using both the number of sunspot groups, N{sub}G{\sub}, and the total area of the sunspots, A{sub}G{\sub}. In addition, we compare R with the recently developed interdiurnal variability geomagnetic indices IDV and IDV(1d). In all four cases, linearity of the relationship with R is not assumed and care is taken to ensure that the relationship of each with R is the same before and after the putative calibration change. It is shown the probability that a correction is not needed is of order 10{sup}−8{\sup} and that R is indeed too low before 1945. The optimum correction to R for values before 1945 is found to be 11.6%, 11.7%, 10.3% and 7.9% using A{sub}G{\sub}, N{sub)G{\sub}, IDV, and IDV(1d), respectively. The optimum value obtained by combining the sunspot group data is 11.6% with an uncertainty range 8.1-14.8% at the 2σ level. The geomagnetic indices provide an independent yet less stringent test but do give values that fall within the 2σ uncertainty band with optimum values are slightly lower than from the sunspot group data. The probability of the correction needed being as large as 20%, as advocated by Svalgaard [2011], is shown to be 1.6 × 10{sup}−5{\sup}.

Centennial variations in sunspot number, open solar flux and streamer belt width: 2. Comparison with the geomagnetic data

We investigate the relationship between interdiurnal variation geomagnetic activity indices, IDV and IDV(1d), corrected sunspot number, R{sub}C{\sub}, and the group sunspot number R{sub}G{\sub}. R{sub}C{\sub} uses corrections for both the “Waldmeier discontinuity”, as derived in Paper 1 [Lockwood et al., 2014c], and the “Wolf discontinuity” revealed by Leussu et al. [2013]. We show that the simple correlation of the geomagnetic indices with R{sub}C{\sub}{sup}n{\sup} or R{sub}G{\sub}{sup}n{\sup} masks a considerable solar cycle variation. Using IDV(1d) or IDV to predict or evaluate the sunspot numbers, the errors are almost halved by allowing for the fact that the relationship varies over the solar cycle. The results indicate that differences between R{sub}C{\sub} and R{sub}G{\sub} have a variety of causes and are highly unlikely to be attributable to errors in either R{sub}G{\sub} alone, as has recently been assumed. Because it is not known if R{sub}C{\sub} or R{sub}G{\sub} is a better predictor of open flux emergence before 1874, a simple sunspot number composite is suggested which, like R{sub}G{\sub}, enables modelling of the open solar flux for 1610 onwards in Paper 3, but maintains the characteristics of R{sub}C{\sub}.

Centennial variations in sunspot number, open solar flux and streamer belt width: 3. Modelling

From the variation of near-Earth interplanetary conditions, reconstructed for the mid-19th century to the present day using historic geomagnetic activity observations, Lockwood and Owens [2014] have suggested that Earth remains within a broadened streamer belt during solar cycles when the Open Solar Flux (OSF) is low. From this they propose that the Earth was immersed in almost constant slow solar wind during the Maunder minimum (c. 1650-1710). In this paper, we extend continuity modelling of the OSF to predict the streamer belt width using both group sunspot numbers and corrected international sunspot numbers to quantify the emergence rate of new OSF. The results support the idea that the solar wind at Earth was persistently slow during the Maunder minimum because the streamer belt was broad.