Reorientational Correlation Functions,Quaternions and Wigner Rotation Matrices

Abstract

The main results of this paper are tabulations of Wigner rotation matrix elements in terms of quaternion parameters and direction cosines. These will be useful for the calculation of orientational probability functions or reorientational correlation functions from simulations of molecular systems using programs based either on quaternions or constraints. We review the relationship between quaternions and the L = ½ Wigner rotation matrix, give some useful properties of quaternions and Wigner rotation matrices and show how the Lth Wigner rotation matrix can be constructed from the quaternion parameters without first obtaining the Euler angles.     

Contradictory results from different methods for measuring direction of insect flight

1. Stream ecologists have been puzzled by the apparent paradox that invertebrate populations persist in headwater streams despite the high frequency with which individuals drift downstream. To resolve this ‘drift paradox’, directions and distances of both larval and adult movement must be identified. Using over 50 interception traps in combination with results from several mark–capture experiments using ¹⁵N as a label, we tested the assumption that interception traps accurately represent the ultimate direction of adult insect flight. 2. In several streams in the Hubbard Brook Experimental Forest, 76% of ¹⁵N‐labelled stoneflies (Leuctra ferruginea) had flown upstream from where they emerged to where they were captured. In contrast, over 60% of stoneflies were flying downstream when captured, i.e. on the upstream side of an interception trap. 3. The instantaneous direction, as indicated by the side of the interception trap on which they were captured, indicated the ultimate flight direction for fewer than 1/3 of the individuals captured. Thus, such traps did not accurately reflect the ultimate flight patterns of individuals, as indicated by mark–capture data. 4. Conclusions drawn from interception trap counts regarding the direction of movement and the distribution and persistence of populations may need to be re‐evaluated. We suggest that better tracking methods, including mass mark–capture studies using stable isotopes, be used to evaluate the potentially complex patterns of adult insect movement and the consequences of that movement for individuals and populations.     

Tracking leatherback turtles (Dermochelys coriacea) during consecutive inter-nesting intervals: Further support for direct transmitter attachment

Over recent years there have been substantial efforts to record and interpret the post-nesting movements of leatherback turtles (Dermochelys coriacea) breeding in tropical regions. Less well documented are the movements undertaken by individual turtles during the breeding season itself, or more specifically between sequential nesting events. Such movements are of interest for two reasons: (1) gravid female leatherbacks may range extensively into the territorial waters and nesting beaches of neighbouring countries, raising questions for conservationists and population ecologists; and (2) the magnitude of movements themselves help elucidate underlying reproductive strategies (e.g. whether to rest near to the nesting or forage extensively). Here, satellite relay data loggers are used (SRDLs) to detail the movements and behaviour of two female leatherback turtles throughout three consecutive inter-nesting intervals in the Commonwealth of Dominica, West Indies. Both near-shore residence and extensive inter-nesting movements were recorded, contrasting previous studies, with movements away from the nesting beach increasing towards the end of the nesting season. Using this behavioural study as a backdrop, the suitability of attaching satellite transmitters directly to the carapace was additionally explored as an alternative approach to conventional harness deployments. Specifically, the principal aims were to (1) gather empirical data on speed of travel and (2) assess dive performance (aerobic dive limit) to enable comparisons with turtles previously fitted with harnesses elsewhere in the Caribbean (n = 6 turtles; Grenada, WI). This produced mixed results with animals bearing directly attached transmitters travelling significantly faster (55.21 km day^− 1; SD 6.68) than harnessed individuals (39.80 km day^− 1; SD 6.19); whilst no discernable difference in dive performance could be found between the two groups of study animals.     

Locomotion of the Eurasian nuthatch on vertical and horizontal substrates

Legged locomotion of the Eurasian nuthatch Sitta europaea on horizontal and vertical substrates was examined using field observations and experiments. Although previous studies have reported that nuthatches use 'walking' on vertical substrates, we found that they usually used 'hopping' on both vertical and horizontal substrates. When climbing up a vertical substrate, the feet were staggered in position and small phase differences were observed between the left and right leg movements in the gait. In upward climbing, the body was inclined towards the substrate during the first stance phase similar to other tree-trunk climbers, but the tail was not used for helping body rotation unlike most tree-trunk climbers. The staggered position of the feet may allow the legs to play different roles in pulling towards and pushing away from the substrate. In downward climbing, the feet were staggered in position, but the phase difference was quite small. In field observations, the Eurasian nuthatch preferred to move vertically, rather than in an inclined direction.     

Ontogeny and phylogeny of Upper Cenomanian rotaliporids (Foraminifera)

The fossil record of planktonic foraminifera is a key source of data on the evolution of marine plankton. One of the most distinctive groups of Cretaceous foraminifera, the rotaliporids, widely used as a stratigraphic index, has always been considered to be a monophyletic clade. New data on the coiling direction and persistent morphological features of the late rotaliporids from the Upper Cenomanian of the Western Interior Seaway, USA, and the Vocontian Basin of southeast France is used as a phylogenetic proxy. Dealing with key morphological features, the coiling pattern of these keeled morphotypes proves that the rotaliporids group is polyphyletic and composed of Thalmanninella, that displays a dextral-coiling preference, and Rotalipora s.s., that have a proportionate-coiling mode. The stratigraphically youngest rotaliporids with keels co-occur with globular forms; and all morphologies transitional between these morphotypes are observed. The ontogenetic relationships between them are investigated, indicating that loss of the keel was a selective advantage that enabled those rotaliporids to remain in the surface water, thereby avoiding the expansion of the oxygen minimum zone. Two species are observed: Thalmanninella multiloculata and Rotalipora planoconvexa. These species are interpreted as having arisen by neoteny from Thalmanninella greenhornensis and Rotalipora cushmani respectively.     

大数据支持下的城市公共空间活力测度研究

城市公共空间是人们进行社交活动的开放性场所，其活力的测度研究具有重要意义。人群及其活动是公共空间活力的主体和外在表现，传统的测度方法往往是对空间活力的间接反映。大数据能全面反映人群活动的行为特征和时空规律，从而使真实描述公共空间活力本质成为可能。从反映人群活动的稳定性、聚集性与多样性等3个基本特征的视角，提出了以大数据为基础的公共空间活力评价体系和定量计算方法。指出大数据质量及适用性研究、公共空间活力评价及其与物理空间的耦合机制研究应是未来的研究方向。