Singular solutions of a modified two-component Camassa-Holm equation

The Camassa-Holm equation (CH) is a well known integrable equation describing the velocity dynamics of shallow water waves. This equation exhibits spontaneous emergence of singular solutions (peakons) from smooth initial conditions. The CH equation has been recently extended to a two-component integrable system (CH2), which includes both velocity and density variables in the dynamics. Although possessing peakon solutions in the velocity, the CH2 equation does not admit singular solutions in the density profile. We modify the CH2 system to allow dependence on average density as well as pointwise density. The modified CH2 system (MCH2) does admit peakon solutions in velocity and average density. We analytically identify the steepening mechanism that allows the singular solutions to emerge from smooth spatially-confined initial data. Numerical results for MCH2 are given and compared with the pure CH2 case. These numerics show that the modification in MCH2 to introduce average density has little short-time effect on the emergent dynamical properties. However, an analytical and numerical study of pairwise peakon interactions for MCH2 shows a new asymptotic feature. Namely, besides the expected soliton scattering behavior seen in overtaking and head-on peakon collisions, MCH2 also allows the phase shift of the peakon collision to diverge in certain parameter regimes.Comment: 25 pages, 11 figure

Capillary-gravity waves: The effect of viscosity on the wave resistance

The effect of viscosity on the wave resistance experienced by a 2d perturbation moving at uniform velocity over the free surface of a fluid is investigated. The analysis is based on Rayleigh's linearized theory of capillary-gravity waves. It is shown in particular that the wave resistance remains bounded as the velocity of the perturbation approches the minimun phase speed, unlike what is predicted by the inviscid theory.Comment: Europhysics Letters, in pres

Liquid drop splashing on smooth, rough and textured surfaces

Splashing occurs when a liquid drop hits a dry solid surface at high velocity. This paper reports experimental studies of how the splash depends on the roughness and the texture of the surfaces as well as the viscosity of the liquid. For smooth surfaces, there is a "corona" splash caused by the presence of air surrounding the drop. There are several regimes that occur as the velocity and liquid viscosity are varied. There is also a "prompt" splash that depends on the roughness and texture of the surfaces. A measurement of the size distribution of the ejected droplets is sensitive to the surface roughness. For a textured surface in which pillars are arranged in a square lattice, experiment shows that the splashing has a four-fold symmetry. The splash occurs predominantly along the diagonal directions. In this geometry, two factors affect splashing the most: the pillar height and spacing between pillars.Comment: 9 pages, 11 figure

A common neural substrate for language production and verbal working memory

Verbal working memory (VWM), the ability to maintain and manipulate representations of speech sounds over short periods, is held by some influential models to be independent from the systems responsible for language production and comprehension [e.g., Baddeley, A. D. Working memory, thought, and action. New York, NY: Oxford University Press, 2007]. We explore the alternative hypothesis that maintenance in VWM is subserved by temporary activation of the language production system [Acheson, D. J., & MacDonald, M. C. Verbal working memory and language production: Common approaches to the serial ordering of verbal information. Psychological Bulletin, 135, 50–68, 2009b]. Specifically, we hypothesized that for stimuli lacking a semantic representation (e.g., nonwords such as mun), maintenance in VWM can be achieved by cycling information back and forth between the stages of phonological encoding and articulatory planning. First, fMRI was used to identify regions associated with two different stages of language production planning: the posterior superior temporal gyrus (pSTG) for phonological encoding (critical for VWM of nonwords) and the middle temporal gyrus (MTG) for lexical–semantic retrieval (not critical for VWM of nonwords). Next, in the same subjects, these regions were targeted with repetitive transcranial magnetic stimulation (rTMS) during language production and VWM task performance. Results showed that rTMS to the pSTG, but not the MTG, increased error rates on paced reading (a language production task) and on delayed serial recall of nonwords (a test of VWM). Performance on a lexical–semantic retrieval task (picture naming), in contrast, was significantly sensitive to rTMS of the MTG. Because rTMS was guided by language production-related activity, these results provide the first causal evidence that maintenance in VWM directly depends on the long-term representations and processes used in speech production

Effects of auditory feedback consistency on vowel production

In investigations of feedback control during speech production, researchers have focused on two different kinds of responses to erroneous or unexpected auditory feedback. Compensation refers to online, feedback-based corrections of articulations. In contrast, adaptation refers to long-term changes in the speech production system after exposure to erroneous/unexpected feedback, which may last even after feedback is normal again. In the current study, we aimed to compare both types of feedback responses by investigating the conditions under which the system starts adapting in addition to merely compensating. Participants vocalized long vowels while they were exposed to either consistently altered auditory feedback, or to feedback that was unpredictably either altered or normal. Participants were not aware of the manipulation of auditory feedback. We predicted that both conditions would elicit compensation, whereas adaptation would be stronger when the altered feedback was consistent across trials. The results show that although there seems to be somewhat more adaptation for the consistently altered feedback condition, a substantial amount of individual variability led to statistically unreliable effects at the group level. The results stress the importance of taking into account individual differences and show that people vary widely in how they respond to altered auditory feedback

Hydrodynamic and magnetohydrodynamic computations inside a rotating sphere

Numerical solutions of the incompressible magnetohydrodynamic (MHD) equations are reported for the interior of a rotating, perfectly-conducting, rigid spherical shell that is insulator-coated on the inside. A previously-reported spectral method is used which relies on a Galerkin expansion in Chandrasekhar-Kendall vector eigenfunctions of the curl. The new ingredient in this set of computations is the rigid rotation of the sphere. After a few purely hydrodynamic examples are sampled (spin down, Ekman pumping, inertial waves), attention is focused on selective decay and the MHD dynamo problem. In dynamo runs, prescribed mechanical forcing excites a persistent velocity field, usually turbulent at modest Reynolds numbers, which in turn amplifies a small seed magnetic field that is introduced. A wide variety of dynamo activity is observed, all at unit magnetic Prandtl number. The code lacks the resolution to probe high Reynolds numbers, but nevertheless interesting dynamo regimes turn out to be plentiful in those parts of parameter space in which the code is accurate. The key control parameters seem to be mechanical and magnetic Reynolds numbers, the Rossby and Ekman numbers (which in our computations are varied mostly by varying the rate of rotation of the sphere) and the amount of mechanical helicity injected. Magnetic energy levels and magnetic dipole behavior are exhibited which fluctuate strongly on a time scale of a few eddy turnover times. These seem to stabilize as the rotation rate is increased until the limit of the code resolution is reached.Comment: 26 pages, 17 figures, submitted to New Journal of Physic

Two-component {CH} system: Inverse Scattering, Peakons and Geometry

An inverse scattering transform method corresponding to a Riemann-Hilbert problem is formulated for CH2, the two-component generalization of the Camassa-Holm (CH) equation. As an illustration of the method, the multi - soliton solutions corresponding to the reflectionless potentials are constructed in terms of the scattering data for CH2.Comment: 22 pages, 3 figures, draft, please send comment

New and updated tests of print exposure and reading abilities in college students

The relationship between print exposure and measures of reading skill was examined in college students (N=99, 58 female; mean age=20.3 years). Print exposure was measured with several new self-reports of reading and writing habits, as well as updated versions of the Author Recognition Test and the Magazine Recognition Test (Stanovich & West, 1989). Participants completed a sentence comprehension task with syntactically complex sentences, and reading times and comprehension accuracy were measured. An additional measure of reading skill was provided by participants’ scores on the verbal portions of the ACT, a standardized achievement test. Higher levels of print exposure were associated with higher sentence processing abilities and superior verbal ACT performance. The relative merits of different print exposure assessments are discussed

Sport, physical activity and the establishment of Health and Wellbeing Boards in Nottingham and Nottinghamshire

This paper will examine the emergence of Health and Wellbeing Boards in Nottinghamshire and the City of Nottingham and explore the implications for sport and physical activity. At the time of writing the transfer of responsibilities for Public Health and the establishment of Health and Wellbeing Boards in both the City of Nottingham and within Nottinghamshire County Council are considered to be relatively advanced by the Strategic Health Authorities, the respective local authorities and by the boards of the two Primary Care Trusts. "Shadow"� Health and Well being Board have been established in both authorities and they have been meeting regularly for s everal months. Public health and commissioning staff have also been successfully relocated and new strategies and priorities are starting to emerge. Nottingham and Nottinghamshire have traditionally acknowledged the role of sport and physical activity to the wider determinants of public health and given a relatively high priority to the contribution that sport and physical activity can make to the ir preventative health and early intervention agendas. This paper will look at the transition to Health and Wellbeing boards to assess how the role of sport and physical activity may be changing and to identify opportunities for its contribution to policy and practise in the future. It will examine both the theory and practise behind the emerging governance arr angements, the strategic objectives and priorities, and the developing evidential base for future policy and delivery within the two areas