Well-posed boundary value problems for integrable evolution equations on a finite interval

We consider boundary value problems posed on an interval [0,L] for an arbitrary linear evolution equation in one space dimension with spatial derivatives of order n. We characterize a class of such problems that admit a unique solution and are well posed in this sense. Such well-posed boundary value problems are obtained by prescribing N conditions at x=0 and n–N conditions at x=L, where N depends on n and on the sign of the highest-degree coefficient n in the dispersion relation of the equation. For the problems in this class, we give a spectrally decomposed integral representation of the solution; moreover, we show that these are the only problems that admit such a representation. These results can be used to establish the well-posedness, at least locally in time, of some physically relevant nonlinear evolution equations in one space dimension.

Initial boundary value problems for the nonlinear Schrödinger equation

A new spectral method for solving initial boundary value problems for linear and integrable nonlinear partial differential equations in two independent variables is applied to the nonlinear Schrödinger equation and to its linearized version in the domain {x≥l(t), t≥0}. We show that there exist two cases: (a) if l″(t)<0, then the solution of the linear or nonlinear equations can be obtained by solving the respective scalar or matrix Riemann-Hilbert problem, which is defined on a time-dependent contour; (b) if l″(t)>0, then the Riemann-Hilbert problem is replaced by a respective scalar or matrix problem on a time-independent domain. In both cases, the solution is expressed in a spectrally decomposed form.

Synoptic controls on boundary-layer characteristics

We report the characteristics of the three-dimensional, time evolving, atmospheric boundary layer that develops beneath an idealised, dry, baroclinic weather system. The boundary-layer structure is forced by thermal advection associated with the weather system. Large positive heat fluxes behind the cold front drive a vigorous convective boundary layer, whereas moderate negative heat fluxes in the warm sector between the cold and warm fronts generate shallow, stably stratified or neutral boundary layers. The forcing of the boundary-layer structure is quantified by forming an Eulerian mass budget integrated over the depth of the boundary layer. The mass budget indicates that tropospheric air is entrained into the boundary layer both in the vicinity of the high-pressure centre, and behind the cold front. It is then transported horizontally within the boundary layer and converges towards the cyclone's warm sector, whence it is ventilated out into the troposphere. This cycling of air is likely to be important for the ventilation of pollution out of the boundary layer, and for the transformation of the properties of large-scale air masses.

Controls on boundary layer ventilation: Boundary layer processes and large-scale dynamics

Midlatitude cyclones are important contributors to boundary layer ventilation. However, it is uncertain how efficient such systems are at transporting pollutants out of the boundary layer, and variations between cyclones are unexplained. In this study 15 idealized baroclinic life cycles, with a passive tracer included, are simulated to identify the relative importance of two transport processes: horizontal divergence and convergence within the boundary layer and large-scale advection by the warm conveyor belt. Results show that the amount of ventilation is insensitive to surface drag over a realistic range of values. This indicates that although boundary layer processes are necessary for ventilation they do not control the magnitude of ventilation. A diagnostic for the mass flux out of the boundary layer has been developed to identify the synoptic-scale variables controlling the strength of ascent in the warm conveyor belt. A very high level of correlation (R-2 values exceeding 0.98) is found between the diagnostic and the actual mass flux computed from the simulations. This demonstrates that the large-scale dynamics control the amount of ventilation, and the efficiency of midlatitude cyclones to ventilate the boundary layer can be estimated using the new mass flux diagnostic. We conclude that meteorological analyses, such as ERA-40, are sufficient to quantify boundary layer ventilation by the large-scale dynamics.

Using a runway paradigm to assess the relative strength of rats' motivations for enrichment objects

Laboratory animals should be provided with enrichment objects in their cages; however, it is first necessary to test whether the proposed enrichment objects provide benefits that increase the animals’ welfare. The two main paradigms currently used to assess proposed enrichment objects are the choice test, which is limited to determining relative frequency of choice, and consumer demand studies, which can indicate the strength of a preference but are complex to design. Here, we propose a third methodology: a runway paradigm, which can be used to assess the strength of an animal’s motivation for enrichment objects, is simpler to use than consumer demand studies, and is faster to complete than typical choice tests. Time spent with objects in a standard choice test was used to rank several enrichment objects in order to compare with the ranking found in our runway paradigm. The rats ran significantly more times, ran faster, and interacted longer with objects with which they had previously spent the most time. It was concluded that this simple methodology is suitable for measuring rats’ motivation to reach enrichment objects. This can be used to assess the preference for different types of enrichment objects or to measure reward system processes.

A Nyström method for a boundary value problem arising in unsteady water wave problems

This paper is concerned with solving numerically the Dirichlet boundary value problem for Laplace’s equation in a nonlocally perturbed half-plane. This problem arises in the simulation of classical unsteady water wave problems. The starting point for the numerical scheme is the boundary integral equation reformulation of this problem as an integral equation of the second kind on the real line in Preston et al. (2008, J. Int. Equ. Appl., 20, 121–152). We present a Nystr¨om method for numerical solution of this integral equation and show stability and convergence, and we present and analyse a numerical scheme for computing the Dirichlet-to-Neumann map, i.e., for deducing the instantaneous fluid surface velocity from the velocity potential on the surface, a key computational step in unsteady water wave simulations. In particular, we show that our numerical schemes are superalgebraically convergent if the fluid surface is infinitely smooth. The theoretical results are illustrated by numerical experiments.

Black carbon measurements in the boundary layer over western and northern Europe

Europe is a densely populated region that is a significant global source of black carbon (BC) aerosol, but there is a lack of information regarding the physical properties and spatial/vertical distribution of rBC in the region. We present the first aircraft observations of sub-micron refractory BC (rBC) aerosol concentrations and physical properties measured by a single particle soot photometer (SP2) in the lower troposphere over Europe. The observations spanned a region roughly bounded by 50° to 60° N and from 15° W to 30° E. The measurements, made between April and September 2008, showed that average rBC mass concentrations ranged from about 300 ng m−3 near urban areas to approximately 50 ng m−3 in remote continental regions, lower than previous surface-based measurements. rBC represented between 0.5 and 3% of the sub-micron aerosol mass. Black carbon mass size distributions were log-normally distributed and peaked at approximately 180 nm, but shifted to smaller diameters (~160 nm) near source regions. rBC was correlated with carbon monoxide (CO) but had different ratios to CO depending on location and air mass. Light absorption coefficients were measured by particle soot absorption photometers on two separate aircraft and showed similar geographic patterns to rBC mass measured by the SP2. We summarize the rBC and light absorption measurements as a function of longitude and air mass age and also provide profiles of rBC mass concentrations and size distribution statistics. Our results will help evaluate model-predicted regional rBC concentrations and properties and determine regional and global climate impacts from rBC due to atmospheric heating and surface dimming.

Visual practices and the objects of design

Recent interest in material objects - the things of everyday interaction - has led to articulations of their role in the literature on organizational knowledge and learning. What is missing is a sense of how the use of these 'things' is patterned across both industrial settings and time. This research addresses this gap with a particular emphasis on visual materials. Practices are analysed in two contrasting design settings: a capital goods manufacturer and an architectural firm. Materials are observed to be treated both as frozen, and hence unavailable for change; and as fluid, open and dynamic. In each setting temporal patterns of unfreezing and refreezing are associated with the different types of materials used. The research suggests that these differing patterns or rhythms of visual practice are important in the evolution of knowledge and in structuring social relations for delivery. Hence, to improve their performance practitioners should not only consider the types of media they use, but also reflect on the pace and style of their interactions.

The effect of the functional attributes of objects within the caged environment on interaction time in laboratory rats

Determining rat preferences for, and behaviour towards, environmental enrichment objects allows us to provide evidence-based information about how the caged environment may be enriched. In recent years there have been many studies investigating the preferences of laboratory rodents for a wide variety of environmental enrichment objects and materials. While these have provided important information regarding the animals' perception of the items, very few studies have attempted to systematically investigate the precise attributes that constitute a preferred object and the behaviour that these objects afford. We have designed a research program to systematically study rats' motivation to interact with enrichment objects. Here we present the results from two experiments which examined the time rats spent with objects that only differed in size. This showed that rats spent longer with large objects rather than small ones, even though objects were presented individually. We also investigated the rats' behaviour with the objects in an open field and found that rats spent longer climbing on top of the large object. This behaviour continued when the large objects were laid on their sides instead of placed upright in the arena, suggesting that the rats were not simply climbing on the objects to investigate the top of the arena and thus an escape route, but instead were genuinely motivated to climb. This suggests that rat welfare could be enhanced by the addition to their cages of objects that permit climbing. (C) 2009 Elsevier B.V. All rights reserved.

Optokinetic stimulation induces illusory movement of both out-of-the-body and on-the-body hand-held visual objects

The coding of body part location may depend upon both visual and proprioceptive information, and allows targets to be localized with respect to the body. The present study investigates the interaction between visual and proprioceptive localization systems under conditions of multisensory conflict induced by optokinetic stimulation (OKS). Healthy subjects were asked to estimate the apparent motion speed of a visual target (LED) that could be located either in the extrapersonal space (visual encoding only, V), or at the same distance, but stuck on the subject's right index finger-tip (visual and proprioceptive encoding, V-P). Additionally, the multisensory condition was performed with the index finger kept in position both passively (V-P passive) and actively (V-P active). Results showed that the visual stimulus was always perceived to move, irrespective of its out- or on-the-body location. Moreover, this apparent motion speed varied consistently with the speed of the moving OKS background in all conditions. Surprisingly, no differences were found between V-P active and V-P passive conditions in the speed of apparent motion. The persistence of the visual illusion during the active posture maintenance reveals a novel condition in which vision totally dominates over proprioceptive information, suggesting that the hand-held visual stimulus was perceived as a purely visual, external object despite its contact with the hand.

Coding of visual space during motor preparation: approaching objects rapidly modulate corticospinal excitability in hand-centered coordinates

Defensive behaviors, such as withdrawing your hand to avoid potentially harmful approaching objects, rely on rapid sensorimotor transformations between visual and motor coordinates. We examined the reference frame for coding visual information about objects approaching the hand during motor preparation. Subjects performed a simple visuomanual task while a task-irrelevant distractor ball rapidly approached a location either near to or far from their hand. After the distractor ball appearance, single pulses of transcranial magnetic stimulation were delivered over the subject's primary motor cortex, eliciting motor evoked potentials (MEPs) in their responding hand. MEP amplitude was reduced when the ball approached near the responding hand, both when the hand was on the left and the right of the midline. Strikingly, this suppression occurred very early, at 70-80ms after ball appearance, and was not modified by visual fixation location. Furthermore, it was selective for approaching balls, since static visual distractors did not modulate MEP amplitude. Together with additional behavioral measurements, we provide converging evidence for automatic hand-centered coding of visual space in the human brain.

False recognition of abstract versus common objects in older and younger adults: testing the semantic categorization account

Older adults often demonstrate higher levels of false recognition than do younger adults. However, in experiments using novel shapes without preexisting semantic representations, this age-related elevation in false recognition was found to be greatly attenuated. Two experiments tested a semantic categorization account of these findings, examining whether older adults show especially heightened false recognition if the stimuli have preexisting semantic representations, such that semantic category information attenuates or truncates the encoding or retrieval of item-specific perceptual information. In Experiment 1, ambiguous shapes were presented with or without disambiguating semantic labels. Older adults showed higher false recognition when labels were present but not when labels were never presented. In Experiment 2, older adults showed higher false recognition for concrete but not abstract objects. The semantic categorization account was supported.