A note on the index bundle over the moduli space of monopoles

Donaldson has shown that the moduli space of monopoles $M_k$ is diffeomorphic to the space \Rat_k of based rational maps from the two-sphere to itself. We use this diffeomorphism to give an explicit description of the bundle on \Rat_k obtained by pushing out the index bundle from $M_k$. This gives an alternative and more explicit proof of some earlier results of Cohen and Jones.Comment: 9 page

First-principles study of (BiScO3){1-x}-(PbTiO3){x} piezoelectric alloys

We report a first-principles study of a class of (BiScO3)_{1-x}-(PbTiO3)_x (BS-PT) alloys recently proposed by Eitel et al. as promising materials for piezoelectric actuator applications. We show that (i) BS-PT displays very large structural distortions and polarizations at the morphotropic phase boundary (MPB) (we obtain a c/a of ~1.05-1.08 and P_tet of ~1.1 C/m^2); (ii) the ferroelectric and piezoelectric properties of BS-PT are dominated by the onset of hybridization between Bi/Pb-6p and O-2p orbitals, a mechanism that is enhanced upon substitution of Pb by Bi; and (iii) the piezoelectric responses of BS-PT and Pb(Zr_{1-x}Ti_x)O3 (PZT) at the MPB are comparable, at least as far as the computed values of the piezoelectric coefficient d_15 are concerned. While our results are generally consistent with experiment, they also suggest that certain intrinsic properties of BS-PT may be even better than has been indicated by experiments to date. We also discuss results for PZT that demonstrate the prominent role played by Pb displacements in its piezoelectric properties.Comment: 6 pages, with 3 postscript figures embedded. Uses REVTEX and epsf macros. Also available at http://www.physics.rutgers.edu/~dhv/preprints/ji_bi/index.htm

Correction to: The relevance of the interpersonal theory of suicide for predicting past-year and lifetime suicidality in autistic adults (Molecular Autism, (2022), 13, 1, (14), 10.1186/s13229-022-00495-5)

Following publication of the original article [1], the authors reported missing information in the ‘Acknowledgements’ section. The corrected ‘Acknowledgements’ section reads: We thank our participants for their generosity in taking part in the present research and for their helpful feedback towards this and future research. We would like to thank the ACORN panel at Bournemouth University for the funding this research, and our supportive colleagues. Special thanks goes to Rebecca Ellis for her patience in assisting with participant payments. We thank our colleagues at the Autism Research Centre who helped us recruit through their participant panel; the staff at Autistica who allowed us to advertise to their research network; moderators and owners of Facebook groups who were willing to let us advertise our study. Dr. Moseley thanks Dr. Sarah George, Dr. Helen Bolderston, and Dr. Cécile Bardon for their advice around ensuring the safety of participants, with especial thanks to Dr. Bardon for her warm encouragement. Finally, the authors remember all autistic people whose lives were lost to suicide, both within our participant cohort and the broader autistic community. The original article [1] has been updated

On a diffuse interface model for tumour growth with non-local interactions and degenerate mobilities

We study a non-local variant of a diffuse interface model proposed by Hawkins--Darrud et al. (2012) for tumour growth in the presence of a chemical species acting as nutrient. The system consists of a Cahn--Hilliard equation coupled to a reaction-diffusion equation. For non-degenerate mobilities and smooth potentials, we derive well-posedness results, which are the non-local analogue of those obtained in Frigeri et al. (European J. Appl. Math. 2015). Furthermore, we establish existence of weak solutions for the case of degenerate mobilities and singular potentials, which serves to confine the order parameter to its physically relevant interval. Due to the non-local nature of the equations, under additional assumptions continuous dependence on initial data can also be shown.Comment: 28 page

Description of the inelastic collision of two solitary waves for the BBM equation

We prove that the collision of two solitary waves of the BBM equation is inelastic but almost elastic in the case where one solitary wave is small in the energy space. We show precise estimates of the nonzero residue due to the collision. Moreover, we give a precise description of the collision phenomenon (change of size of the solitary waves).Comment: submitted for publication. Corrected typo in Theorem 1.

The Fermi-Pasta-Ulam problem revisited: stochasticity thresholds in nonlinear Hamiltonian systems

The Fermi-Pasta-Ulam $\alpha$-model of harmonic oscillators with cubic anharmonic interactions is studied from a statistical mechanical point of view. Systems of N= 32 to 128 oscillators appear to be large enough to suggest statistical mechanical behavior. A key element has been a comparison of the maximum Lyapounov coefficient $\lambda_{max}$ of the FPU $\alpha$-model and that of the Toda lattice. For generic initial conditions, $\lambda_{max}(t)$ is indistinguishable for the two models up to times that increase with decreasing energy (at fixed N). Then suddenly a bifurcation appears, which can be discussed in relation to the breakup of regular, soliton-like structures. After this bifurcation, the $\lambda_{max}$ of the FPU model appears to approach a constant, while the $\lambda_{max}$ of the Toda lattice appears to approach zero, consistent with its integrability. This suggests that for generic initial conditions the FPU $\alpha$-model is chaotic and will therefore approach equilibrium and equipartition of energy. There is, however, a threshold energy density $\epsilon_c(N)\sim 1/N^2$, below which trapping occurs; here the dynamics appears to be regular, soliton-like and the approach to equilibrium - if any - takes longer than observable on any available computer. Above this threshold the system appears to behave in accordance with statistical mechanics, exhibiting an approach to equilibrium in physically reasonable times. The initial conditions chosen by Fermi, Pasta and Ulam were not generic and below threshold and would have required possibly an infinite time to reach equilibrium.Comment: 24 pages, REVTeX, 8 PostScript figures. Published versio

The Stroop revisited: a meta-analysis of interference control in AD/HD

Background: An inhibition deficit, including poor interference control, has been implicated as one of the core deficits in AD/HD. Interference control is clinically measured by the Stroop Colour-Word Task. The aim of this meta-analysis was to investigate the strength of an interference deficit in AD/HD as measured by the Stroop Colour-Word Task and to assess the role of moderating variables that could explain the results. These moderating variables included: methods of calculating the interference score, comorbid reading and psychiatric disorders, AD/HD-subtypes, gender, age, intellectual functioning, medication, and sample size. Methods: Seventeen independent studies were located including 1395 children, adolescents, and young adults, in the age range of 6-27 years. A meta-analysis was conducted to assess the effect sizes for the scores on the word and the colour card as well as the interference score. Results: Children with AD/HD performed more poorly on all three dependent variables. The effect sizes for word reading (d = .49) and colour naming (d = .58) were larger and more homogeneous than the effect size for the interference score (d = .35). The method used to calculate the interference score strongly influenced the findings for this measure. When interference control was calculated as the difference between the score on the colour card minus the score on the colour-word card, no differences were found between AD/HD groups and normal control groups. Discussion: The Stroop Colour-Word Task, in standard form, does not provide strong evidence for a deficit in interference control in AD/HD. However, the Stroop Colour-Word Task may not be a valid measure of interference control in AD/HD and alternative methodologies may be needed to test this aspect of the inhibitory deficit model in AD/HD. © Association for Child Psychology Psychiatry, 2004

Counterfactual Thinking and Entrepreneurial Self‐Efficacy: The Moderating Role of Self‐Esteem and Dispositional Affect

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/97291/1/etap472.pd

Advances in ab-initio theory of Multiferroics. Materials and mechanisms: modelling and understanding

Within the broad class of multiferroics (compounds showing a coexistence of magnetism and ferroelectricity), we focus on the subclass of "improper electronic ferroelectrics", i.e. correlated materials where electronic degrees of freedom (such as spin, charge or orbital) drive ferroelectricity. In particular, in spin-induced ferroelectrics, there is not only a {\em coexistence} of the two intriguing magnetic and dipolar orders; rather, there is such an intimate link that one drives the other, suggesting a giant magnetoelectric coupling. Via first-principles approaches based on density functional theory, we review the microscopic mechanisms at the basis of multiferroicity in several compounds, ranging from transition metal oxides to organic multiferroics (MFs) to organic-inorganic hybrids (i.e. metal-organic frameworks, MOFs)Comment: 22 pages, 9 figure

A joint geochemical–geophysical record of time-dependent mantle convection south of Iceland

The North Atlantic V-Shaped Ridges (VSRs) provide a spatially extensive and clear record of unsteady mantle convective circulation over >40 My>40 My. VSRs are diachronous ridges of thick crust formed with a periodicity of ∼5 My∼5 My along the Mid Atlantic Ridge, south of Iceland. We present data from a set of dredged basalt samples that shows chemical variation associated with two complete VSR crustal thickness cycles where they intersect the Mid Atlantic Ridge. The new dataset also records chemical variation associated with a VSR crustal thickness cycle along a plate spreading flow-line. Inverse correlations between crustal thickness and both incompatible trace element concentrations and incompatible element ratios such as Nb/Y and La/Sm are observed. Geochemical and crustal thickness observations can be matched using a time-dependent mid-ocean ridge melting model with a basal boundary condition of sinusoidally varying potential temperature. Our observations and models suggest that VSRs are generated when hot patches are carried up the plume stem beneath SE Iceland and spread radially outward within the asthenosphere. These patches are then drawn upward into the melting region when passing beneath the Mid Atlantic Ridge. The geometry of the VSRs and the size of the dynamically supported swell suggest that the Iceland Plume is the strongest plume in the Earth at present, with a volume flux of View the MathML source49±14 km3yr−1