Rigorous computation of smooth branches of equilibria for the three dimensional Cahn–Hilliard equation

In this paper, we propose a new general method to compute rigorously global smooth branches of equilibria of higher-dimensional partial differential equations. The theoretical framework is based on a combination of the theory introduced in Global smooth solution curves using rigorous branch following (van den Berg et al., Math. Comput. 79(271):1565–1584, 2010) and in Analytic estimates and rigorous continuation for equilibria of higher-dimensional PDEs (Gameiro and Lessard, J. Diff. Equ. 249(9):2237–2268, 2010). Using this method, one can obtain proofs of existence of global smooth solution curves of equilibria for large (continuous) parameter ranges and about local uniqueness of the solutions on the curve. As an application, we compute several smooth branches of equilibria for the three-dimensional Cahn–Hilliard equation.     

High fidelity neuronal networks formed by plasma masking with a bilayer membrane: analysis of neurodegenerative and neuroprotective processes

Spatially defined neuronal networks have great potential to be used in a wide spectrum of neurobiology assays. We present an original technique for the precise and reproducible formation of neuronal networks. A PDMS membrane comprising through-holes aligned with interconnecting microchannels was used during oxygen plasma etching to dry mask a protein rejecting poly(ethylene glycol) (PEG) adlayer. Patterns were faithfully replicated to produce an oxidized interconnected array pattern which supported protein adsorption. Differentiated human SH-SY5Y neuron-like cells adhered to the array nodes with the micron-scale interconnecting tracks guiding neurite outgrowth to produce neuronal connections and establish a network. A 2.0 μm track width was optimal for high-level network formation and node compliance. These spatially standardized neuronal networks were used to analyse the dynamics of acrylamide-induced neurite degeneration and the protective effects of co-treatment with calpeptin or brain derived neurotrophic factor (BDNF).     

First total synthesis of (−)-8-epi-9-deoxygoniopypyrone

The structure and absolute configuration of natural 8-epi-9-deoxygoniopypyrone have been confirmed by an efficient and highly diastereoselective synthesis in 15 steps from (S)-mandelic acid with an overall yield of 43%.     

Conservation laws for cosmological perturbations

We briefly recall the problem of defining conserved quantities such as energy in general relativity, and the solution given by introducing a symmetric background. We apply the general formalism to perturbed Robertson-Walker spacetimes with de Sitter geometry as background. We relate the obtained conserved quantities to Traschen's integral constraints and mention a few applications in cosmology.     

New measurement of the beta decay rate of the16N(0−)-16O(0+) transition

The beta decay rate of the¹⁶N(0^?; 120keV) →¹⁶O(0⁺, G.S.) transition has been remeasured. Our result (Λ _β =0.48±0.024 s^?1) is in excellent agreement with a previous measurement but strongly disagrees with another experimental value. The two agreeing results provide an experimental verification of the importance of meson exchange currents in 0⁺-0^? weak transitions. A value ofg _p/g _A～11–12 can be inferred from the correspondingΛ _μ rate.     

Measurement of the beta spectrum of the 0− (120 keV) state of16N

We have measured the beta spectrum of the 0^?(120 keV,t _1/2=5.25 μs) state of¹⁶N. The response function of our detector has been measured, parameterized and then fitted to known spectral shapes taken under conditions close to those in the actual experiment. Using this response function and subtracting a 56 μs half-life background due to neutron capture in the detector, the measured 0^? spectrum compares well with the allowed shape for the 0^?→0⁺ spectrum plus a small contribution from the allowed 0^?→1^? transition.     

Synthese et isomerisation de methoxycarbonyl-5 dihydropyrannones-2

Condensation of dimethyl 3-methylglutaconate with ketones provides a one pot route for the preparation of 5-methoxycarbonyl-4-methyldihydropyran-2-ones. The experimental conditions to give selectively pyran-2-ones isomers are discussed. The structure of the different products was established on the basis of ¹H and ¹³C nmr spectral data.     

Are defect models consistent with the entropy and specific heat of glass formers?

We show that pointlike defect model of glasses cannot explain the thermodynamic properties of glass formers, as for example, the excess specific heat close to the glass transition, contrary to the claim of Garrahan and Chandler [Proc. Natl. Acad. Sci. U.S.A. 100, 9710 (2003)]. More general models and approaches in terms of extended defects are also discussed.     

Imaging electron trajectories in a laser-wakefield cavity using betatron X-ray radiation

We demonstrate that betatron x-ray radiation accurately provides direct imaging of electrons trajectories accelerated in laser wakefields. Experimental far field x-ray beam profiles reveal that electrons can follow similar transverse trajectories with typical excursions of 1.5 microm+/-0.5 microm in the plane of laser polarization and 0.7 microm+/-0.2 microm in the plane perpendicular.