An effective mass theorem for the bidimensional electron gas in a strong magnetic field

We study the limiting behavior of a singularly perturbed Schr\"odinger-Poisson system describing a 3-dimensional electron gas strongly confined in the vicinity of a plane $(x,y)$ and subject to a strong uniform magnetic field in the plane of the gas. The coupled effects of the confinement and of the magnetic field induce fast oscillations in time that need to be averaged out. We obtain at the limit a system of 2-dimensional Schr\"odinger equations in the plane $(x,y)$, coupled through an effective selfconsistent electrical potential. In the direction perpendicular to the magnetic field, the electron mass is modified by the field, as the result of an averaging of the cyclotron motion. The main tools of the analysis are the adaptation of the second order long-time averaging theory of ODEs to our PDEs context, and the use of a Sobolev scale adapted to the confinement operator

Field theoretic description of charge regulation interaction

In order to find the exact form of the electrostatic interaction between two proteins with dissociable charge groups in aqueous solution, we have studied a model system composed of two macroscopic surfaces with charge dissociation sites immersed in a counterion-only ionic solution. Field-theoretic representation of the grand canonical partition function is derived and evaluated within the mean-field approximation, giving the Poisson-Boltzmann theory with the Ninham-Parsegian boundary condition. Gaussian fluctuations around the mean-field are then analyzed in the lowest order correction that we calculate analytically and exactly, using the path integral representation for the partition function of a harmonic oscillator with time-dependent frequency. The first order (one loop) free energy correction gives the interaction free energy that reduces to the zero-frequency van der Waals form in the appropriate limit but in general gives rise to a mono-polar fluctuation term due to charge fluctuation at the dissociation sites. Our formulation opens up the possibility to investigate the Kirkwood-Shumaker interaction in more general contexts where their original derivation fails.Comment: 12 pages, 9 figures, submitted to EPJ

Slow movement of a random walk on the range of a random walk in the presence of an external field

In this article, a localisation result is proved for the biased random walk on the range of a simple random walk in high dimensions (d \geq 5). This demonstrates that, unlike in the supercritical percolation setting, a slowdown effect occurs as soon a non-trivial bias is introduced. The proof applies a decomposition of the underlying simple random walk path at its cut-times to relate the associated biased random walk to a one-dimensional random walk in a random environment in Sinai's regime

Testing the psychometric properties of Kidscreen-27 with Irish children of low socio-economic status

BACKGROUND: Kidscreen-27 was developed as part of a cross-cultural European Union-funded project to standardise the measurement of children’s health-related quality of life. Yet, research has reported mixed evidence for the hypothesised 5-factor model, and no confirmatory factor analysis (CFA) has been conducted on the instrument with children of low socio-economic status (SES) across Ireland (Northern and Republic). METHOD: The data for this study were collected as part of a clustered randomised controlled trial. A total of 663 (347 male, 315 female) 8–9-year-old children (M = 8.74, SD = .50) of low SES took part. A 5- and modified 7-factor CFA models were specified using the maximum likelihood estimation. A nested Chi-square difference test was conducted to compare the fit of the models. Internal consistency and floor and ceiling effects were also examined. RESULTS: CFA found that the hypothesised 5-factor model was an unacceptable fit. However, the modified 7-factor model was supported. A nested Chi-square difference test confirmed that the fit of the 7-factor model was significantly better than that of the 5-factor model. Internal consistency was unacceptable for just one scale. Ceiling effects were present in all but one of the factors. CONCLUSIONS: Future research should apply the 7-factor model with children of low socio-economic status. Such efforts would help monitor the health status of the population

Disulfide-Mediated Reversible Polymerization toward Intrinsically Dynamic Smart Materials

The development of a dynamic chemistry toolbox to endow materials dynamic behavior has been key to the rational design of future smart materials. The rise of supramolecular and dynamic covalent chemistry offers many approaches to the construction of dynamic polymers and materials that can adapt, respond, repair, and recycle. Within this toolbox, the building blocks based on 1,2-dithiolanes have become an important scaffold, featuring their reversible polymerization mediated by dynamic covalent disulfide bonds, which enables a unique class of dynamic materials at the intersection of supramolecular polymers and adaptable covalent networks. This Perspective aims to explore the dynamic chemistry of 1,2-dithiolanes as a versatile structural unit for the design of smart materials by summarizing the state of the art as well as providing an overview of the fundamental challenges involved in this research area and its potential future directions

Exceptionally preserved early Cambrian bilaterian developmental stages from Mongolia

Fossilized invertebrate embryonic and later developmental stages are rare and restricted largely to the Ediacaran-Cambrian, providing direct insight into development during the emergence of animal bodyplans. Here we report a new assemblage of eggs, embryos and bilaterian post-embryonic developmental stages from the early Cambrian Salanygol Formation of Dzhabkan Microcontinent of Mongolia. The post-embryonic developmental stages of the bilaterian are preserved with cellular fidelity, possessing a series of bilaterally arranged ridges that compare to co-occurring camenellan sclerites in which the initial growth stages retain the cellular morphology of modified juveniles. In this work we identify these fossils as early post-embryonic developmental stages of camenellans, an early clade of stem-brachiopods, known previously only from isolated sclerites. This interpretation corroborates previous reconstructions of camenellan scleritomes with sclerites arranged in medial and peripheral concentric zones. It further supports the conjecture that molluscs and brachiopods are descended from an ancestral vermiform and slug-like bodyplan. The Cambrian is known as a period of rapid animal diversification, but the development of these animals is not well characterized. Here, Steiner et al. describe a new assemblage of Cambrian eggs, embryos and early postembryonic stages from Mongolia that provides insight into ancient bilaterian development and evolution

The Influence of Quadrature Errors on Isogeometric Mortar Methods

Mortar methods have recently been shown to be well suited for isogeometric analysis. We review the recent mathematical analysis and then investigate the variational crime introduced by quadrature formulas for the coupling integrals. Motivated by finite element observations, we consider a quadrature rule purely based on the slave mesh as well as a method using quadrature rules based on the slave mesh and on the master mesh, resulting in a non-symmetric saddle point problem. While in the first case reduced convergence rates can be observed, in the second case the influence of the variational crime is less significant