Our climate future depends on the delicate, fine balance of earth processes first elaborated on by James Croll, born 200 years ago in 1821. A childhood victim of the Scottish clearances, Croll, after following various indifferent occupations, managed to remove to the then rapidly industrialising city of Glasgow and eventually to Scotland's capital, Edinburgh. He blossomed as a most original, outside-the-box, thinker of great intellectual strength and modesty. He carried out scores of studies across a broad range of research topics, many related to the physical causes of climate change. He is well known for his astronomical theory of the ice ages, but should be much better regarded for his incisive physical insights into the central importance of feedbacks in the Earth system. Although humble, Croll was an ardent controversialist who strongly, perhaps over-strongly, always defended his corner. As well as his many accomplishments as a man of science, Croll was committed to exploring philosophical questions of theism and determinism, topics which occupied his earliest and last publications. A ‘top ten’ selection out of the varied subject areas that Croll tackled are explored herein, along with a brisk survey of their legacy to contemporary modelling studies and to Earth's climate future: (1) causes of climate change (1864); (2) ice-cap melt and sea-level rise (1865); (3) predicting future climates using eccentricity (1866); (4) combining orbital precession, eccentricity and obliquity (1867); (5) geological time and the date of the glacial epochs (1868); (6) geological time and denudation rates (1868); (7) ocean currents and the hemispherical temperature difference (1869); (8) feedbacks – a remarkable circumstance which led to changes of climate (1875); (9) temperature of space and its bearing on terrestrial physics (1880); (10) the causes of mild polar climates (1884).

James Croll's Physical Theory of Secular Changes of Climate emerged during an age of revolution in geology that included the rise of the glacial theory and the search for its underlying causes. According to Croll, periods of high eccentricity are associated with the persistence of long glacial epochs, within which glaciations occur in alternate hemispheres when winter is at aphelion every ~11,000 years; however, astronomical forcing is only able to produce glaciation by means of physical agencies (climate feedbacks) that amplify the small effects of varying seasonal irradiation. Croll understood the importance of interglacial deposits because they provided evidence for the occurrence of multiple glaciations within his long glacial epochs. He was aware of the limitations of the terrestrial record and suggested that deep-sea sediments would contain a continuous succession of glacial-interglacial cycles. Contrary to a widespread view, however, Croll was not envisaging the advent of palaeoceanographic exploration avant la lettre, but instead was drawing attention to the inadequacy of the land record as a testbed of his astronomical theory. Yet, the marine record did eventually deliver a test of astronomical theories almost exactly 100 years after the publication of his 1875 book Climate and Time in their Geological Relations. Here, we provide an historical account of the technological and scientific developments that led to this and a summary of insights on astronomically paced climate changes from marine, terrestrial and ice core records. We finally assess Croll's ideas in the context of our current understanding of the theory of ice ages.

A graph is called radially maximal if it is not complete and the addition of any new edge decreases its radius. Harary and Thomassen [‘Anticritical graphs’, Math. Proc. Cambridge Philos. Soc.79(1) (1976), 11–18] proved that the radius r and diameter d of any radially maximal graph satisfy $r\le d\le 2r-2.$ Dutton et al. [‘Changing and unchanging of the radius of a graph’, Linear Algebra Appl.217 (1995), 67–82] rediscovered this result with a different proof and conjectured that the converse is true, that is, if r and d are positive integers satisfying $r\le d\le 2r-2,$ then there exists a radially maximal graph with radius r and diameter $d.$ We prove this conjecture and a little more.

In the East African Rift, the western margin of Lake Turkana (northern Kenya) exposes Mio-Plio-Pleistocene lake sediments with dated volcanic horizons constraining basin dynamics at the astronomical time scale. Since the late Pliocene, coastal archaeological sites have formed within the lacustrine dynamics. Here, lake levels are reconstructed from 2.4 to 1.7 Ma using sedimentary facies and water/depth-controlled sediment association. The lacustrine stratigraphy is measured with a total station, and cyclostratigraphy is derived from tephrochronology. The water depths are evaluated from paleochemical properties of lake sediments analyzed by inductively coupled plasma optical emission spectrometry and inductively coupled plasma mass spectrometry. Our reconstruction highlights that Lake Turkana rose during 100 ka insolation/eccentricity maxima periods in response to higher monsoonal inputs of the Omo River. However, Lake Turkana also expanded through an insolation minimum at 2.17–1.95 Ma. This asynchronous lake phase coincides with volcanic closure of the Omo River and Lake Turkana outflow sill to the east and the Indian Ocean. An archaeological hiatus occurs during this endorheic lake phase, and alkalinity increases at the beginning of the hiatus. The lake rose again during insolation/eccentricity maxima at 1.9–1.7 Ma, and a new outflow sill opened to the west and the Nile basin. Hominin coastal occupations return during this exorheic/freshwater lake phase.

Dense retinotopy data sets were obtained by microelectrode visual receptive field mapping in dorsal and lateral visual cortex of anesthetized owl monkeys. The cortex was then physically flatmounted and stained for myelin or cytochrome oxidase. Retinotopic mapping data were digitized, interpolated to a uniform grid, analyzed using the visual field sign technique—which locally distinguishes mirror image from nonmirror image visual field representations—and correlated with the myelin or cytochrome oxidase patterns. The region between V2 (nonmirror) and MT (nonmirror) contains three areas—DLp (mirror), DLi (nonmirror), and DLa/MTc (mirror). DM (mirror) was thin anteroposteriorly, and its reduced upper field bent somewhat anteriorly away from V2. DI (nonmirror) directly adjoined V2 (nonmirror) and contained only an upper field representation that also adjoined upper field DM (mirror). Retinotopy was used to define area VPP (nonmirror), which adjoins DM anteriorly, area FSTd (mirror), which adjoins MT ventrolaterally, and TP (mirror), which adjoins MT and DLa/MTc dorsoanteriorly. There was additional retinotopic and architectonic evidence for five more subdivisions of dorsal and lateral extrastriate cortex—TA (nonmirror), MSTd (mirror), MSTv (nonmirror), FSTv (nonmirror), and PP (mirror). Our data appear quite similar to data from marmosets, though our field sign-based areal subdivisions are slightly different. The region immediately anterior to the superiorly located central lower visual field V2 varied substantially between individuals, but always contained upper fields immediately touching lower visual field V2. This region appears to vary even more between species. Though we provide a summary diagram, given within- and between-species variation, it should be regarded as a guide to parsing complex retinotopy rather than a literal representation of any individual, or as the only way to agglomerate the complex mosaic of partial upper and lower field, mirror- and nonmirror-image patches into areas.

Areas V3 and V4 are commonly thought of as individual entities in the primate visual system, based on definition criteria such as their representation of visual space, connectivity, functional response properties, and relative anatomical location in cortex. Yet, large-scale functional and anatomical organization patterns not only emphasize distinctions within each area, but also links across visual cortex. Specifically, the visuotopic organization of V3 and V4 appears to be part of a larger, supra-areal organization, clustering these areas with early visual areas V1 and V2. In addition, connectivity patterns across visual cortex appear to vary within these areas as a function of their supra-areal eccentricity organization. This complicates the traditional view of these regions as individual functional “areas.” Here, we will review the criteria for defining areas V3 and V4 and will discuss functional and anatomical studies in humans and monkeys that emphasize the integration of individual visual areas into broad, supra-areal clusters that work in concert for a common computational goal. Specifically, we propose that the visuotopic organization of V3 and V4, which provides the criteria for differentiating these areas, also unifies these areas into the supra-areal organization of early visual cortex. We propose that V3 and V4 play a critical role in this supra-areal organization by filtering information about the visual environment along parallel pathways across higher-order cortex.

The present theoretical study investigates turbulent film boiling on an elliptical tube with steam heating surface inside. The flow direction of the heating steam is opposite to the vapor film of the outer tube. Thus, the surface temperature is expressed by cosine function. The effect of temperature amplitude, eccentricity, nonlinear viscosity, nonlinear thermal conductivity, radiation and eddy diffusivity are all included in the present analysis. And the paper also discusses the vapor thickness, local Nusselt number and mean Nusselt number. The result shows, first, under the free convection turbulent film boiling with temperature variation, the bigger the temperature amplitude value is, the better the heat transfer efficiency is. Next, the increase of the eccentricity values will bring out the increase of the Nusselt number. Finally, a comparison between the results of the present study and those reported in a previous theoretical data is provided.

The modelling of the dynamic behaviour of three-dimensional model of two-stage gear system is formulated for general helical gears location. The excitation is induced by the periodic variation of the mesh stiffnesses. This case describes the real working of the gearings. First, the modal analysis of the system is treated. Then, the calculation of the dynamic response is performed by a step-by-step time integration method (Newmark method). Finally, two types of manufacturing defects on the gears are introduced in the model: eccentricity and profile defect. An analysis of the effects of these defects on the gear system dynamic behaviour is then treated.

The spatial region involved in vernier acuity (integration region) was behaviorally determined in cats and compared with published human data and cortical scaling parameters for the two species. Integration region was estimated from vernier thresholds obtained with: (1) gaps of various sizes between the contiguous ends of the offset contours (gap effects); and (2) irrelevant contours placed at various distances from the vernier offset (interference effects). The gap studies showed that thresholds decreased as the gap grew from 0 to 4–7 min but then increased progressively with separations greater than 7 min. In the interference studies, thresholds were increased 2–6 times when the irrelevant contours were located within 40 min of the offset. Comparing these data with available human measures showed large species differences. Converting the interference distances for both species into cortical distances using published estimates of cortical magnification factor did not resolve the discrepancy. However, a comparison of the cat data with published human data, taken at an eccentricity at which the estimated human cortical magnification factor equals that of the cat, i.e. 7 deg, showed the effects of gap size and interference distance on vernier thresholds to be remarkably similar between the two species. This similarity supports the hypothesis that positional acuity depends upon mechanisms in striate cortex, and also suggests that such acuity may be mediated by a generic neural mechanism common to mammals.

Human symmetry detection in dense patterns exhibits a spatial integration range that becomes narrower with distance of the symmetry axis from the fovea. This narrowing violates the general properties of eccentricity that have been found for all previous visual cortical areas, tasks, and assessment techniques. This reverse eccentricity scaling may, in conjunction with the long-range matching properties for symmetry described in Tyler and Hardage (1996), imply that symmetry is processed by a specialized cortical area with non-retinotopic neural architecture.