Centrifugal quantum states of neutrons

We propose a method for observation of the quasi-stationary states of neutrons, localized near the curved mirror surface. The bounding effective well is formed by the centrifugal potential and the mirror Fermi-potential. This phenomenon is an example of an exactly solvable "quantum bouncer" problem that could be studied experimentally. It could provide a promising tool for studying fundamental neutron-matter interactions, as well as quantum neutron optics and surface physics effects. We develop formalism, which describes quantitatively the neutron motion near the mirror surface. The effects of mirror roughness are taken into account.Comment: 13 pages, 10 figure

Fractional Klein-Kramers equation for superdiffusive transport: normal versus anomalous time evolution in a differential L{\'e}vy walk model

We introduce a fractional Klein-Kramers equation which describes sub-ballistic superdiffusion in phase space in the presence of a space-dependent external force field. This equation defines the differential L{\'e}vy walk model whose solution is shown to be non-negative. In the velocity coordinate, the probability density relaxes in Mittag-Leffler fashion towards the Maxwell distribution whereas in the space coordinate, no stationary solution exists and the temporal evolution of moments exhibits a competition between Brownian and anomalous contributions.Comment: 4 pages, REVTe

Calculation of atomic spontaneous emission rate in 1D finite photonic crystal with defects

We derive the expression for spontaneous emission rate in finite one-dimensional photonic crystal with arbitrary defects using the effective resonator model to describe electromagnetic field distributions in the structure. We obtain explicit formulas for contributions of different types of modes, i.e. radiation, substrate and guided modes. Formal calculations are illustrated with a few numerical examples, which demonstrate that the application of effective resonator model simplifies interpretation of results.Comment: Cent. Eur. J. Phys, in pres

Facile access to a heterocyclic, sp3-rich chemical scaffold via a tandem condensation/intramolecular nitrone–alkene [3+2] cycloaddition strategy

A heterocyclic, sp3-rich chemical scaffold was synthesised in just 6 steps via a highly regio- and diastereo-selective tandem nitrone formation/intramolecular nitrone–alkene [3+2] cycloaddition reaction. A library of 543 lead-like compounds based on the scaffold core has been produced

Wnt signalling and cancer stem cells

[Abstract] Intracellular signalling mediated by secreted Wnt proteins is essential for the establishment of cell fates and proper tissue patterning during embryo development and for the regulation of tissue homeostasis and stem cell function in adult tissues. Aberrant activation of Wnt signalling pathways has been directly linked to the genesis of different tumours. Here, the components and molecular mechanisms implicated in the transduction of Wnt signal, along with important results supporting a central role for this signalling pathway in stem cell function regulation and carcinogenesis will be briefly reviewed.Ministerio de Ciencia e Innovación; SAF2008-0060

Geometry-preserving expansion microscopy microplates enable high-fidelity nanoscale distortion mapping

Expansion microscopy (ExM) is a versatile super-resolution microscopy pipeline, leveraging nanoscale biomolecular crosslinking and osmotically driven swelling of hydrogels. Currently, ExM is a laborious and skill-intensive technique, involving manual handling of the hydrogels that can compromise the integrity of the gels and capacity to track gel isotropy, hence diminishing reproducibility. We have developed a 3D-printable microplate system to contain the entire ExM workflow within each well, enabling in situ image acquisition and eliminating the need for direct handling of the hydrogels. The preservation of the gel geometry and orientation of the microplate wells enables convenient tracking of gel expansion, pre- and post-ExM image acquisition, and distortion mapping of every cell or region of interest. We demonstrate the utility of this approach with both single-color and multiplexed ExM of cultured HeLa cells and dissected pupal Drosophila melanogaster wing tissue to reveal distortion-prone structures ranging from sub-cellular organelles to micron-scale tissue regions

Memory-encoding vibrations in a disconnecting air bubble

Many nonlinear processes, such as the propagation of waves over an ocean or the transmission of light pulses down an optical fibre1, are integrable in the sense that the dynamics has as many conserved quantities as there are independent variables. The result is a time evolution that retains a complete memory of the initial state. In contrast, the nonlinear dynamics near a finite-time singularity, in which physical quantities such as pressure or velocity diverge at a point in time, is believed to evolve towards a universal form, one independent of the initial state2. The break-up of a water drop in air3 or a viscous liquid inside an immiscible oil4,5 are processes that conform to this second scenario. These opposing scenarios collide in the nonlinearity produced by the formation of a finite-time singularity that is also integrable. We demonstrate here that the result is a novel dynamics with a dual character

Theory and Computation of the Spheroidal Wave Functions

In this paper we report on a package, written in the Mathematica computer algebra system, which has been developed to compute the spheroidal wave functions of Meixner [J. Meixner and R.W. Schaefke, Mathieusche Funktionen und Sphaeroidfunktionen, 1954] and is available online (www.physics.uwa.edu.au/~falloon/spheroidal/spheroidal.html). This package represents a substantial contribution to the existing software, since it computes the spheroidal wave functions to arbitrary precision for general complex parameters mu, nu, gamma and argument z; existing software can only handle integer mu, nu and does not give arbitrary precision. The package also incorporates various special cases and computes analytic power series and asymptotic expansions in the parameter gamma. The spheroidal wave functions of Flammer [C. Flammer, Spheroidal Wave Functions, 1957] are included as a special case of Meixner's more general functions. This paper presents a concise review of the general theory of spheroidal wave functions and a description of the formulas and algorithms used in their computation, and gives high-precision numerical examples.Comment: 26 pages, 4 Appendices, 5 Table

Specialized ommatidia of the polarization-sensitive dorsal rim area in the eye of monarch butterflies have non-functional reflecting tapeta

Many insects exploit sky light polarization for navigation or cruising-course control. The detection of polarized sky light is mediated by the ommatidia of a small specialized part of the compound eye: the dorsal rim area (DRA). We describe the morphology and fine structure of the DRA in monarch butterflies (Danaus plexippus). The DRA consists of approximately 100 ommatidia forming a narrow ribbon along the dorsal eye margin. Each ommatidium contains two types of photoreceptor with mutually orthogonal microvilli orientations occurring in a 2:6 ratio. Within each rhabdomere, the microvilli are well aligned. Rhabdom structure and orientation remain constant at all retinal levels, but the rhabdom profiles, as seen in tangential sections through the DRA, change their orientations in a fan-like fashion from the frontal to the caudal end of the DRA. Whereas these properties (two microvillar orientations per rhabdom, microvillar alignment along rhabdomeres, ommatidial fan array) are typical for insect DRAs in general, we also report and discuss here a novel feature. The ommatidia of monarch butterflies are equipped with reflecting tapeta, which are directly connected to the proximal ends of the rhabdoms. Although tapeta are also present in the DRA, they are separated from the rhabdoms by a space of approximately 55 μm effectively inactivating them. This reduces self-screening effects, keeping polarization sensitivity of all photoreceptors of the DRA ommatidia both high and approximately equal

Order and Stochastic Dynamics in Drosophila Planar Cell Polarity

Cells in the wing blade of Drosophila melanogaster exhibit an in-plane polarization causing distal orientation of hairs. Establishment of the Planar Cell Polarity (PCP) involves intercellular interactions as well as a global orienting signal. Many of the genetic and molecular components underlying this process have been experimentally identified and a recently advanced system-level model has suggested that the observed mutant phenotypes can be understood in terms of intercellular interactions involving asymmetric localization of membrane bound proteins. Among key open questions in understanding the emergence of ordered polarization is the effect of stochasticity and the role of the global orienting signal. These issues relate closely to our understanding of ferromagnetism in physical systems. Here we pursue this analogy to understand the emergence of PCP order. To this end we develop a semi-phenomenological representation of the underlying molecular processes and define a “phase diagram” of the model which provides a global view of the dependence of the phenotype on parameters. We show that the dynamics of PCP has two regimes: rapid growth in the amplitude of local polarization followed by a slower process of alignment which progresses from small to large scales. We discuss the response of the tissue to various types of orienting signals and show that global PCP order can be achieved with a weak orienting signal provided that it acts during the early phase of the process. Finally we define and discuss some of the experimental predictions of the model