Parity-breaking bifurcation and global oscillation in patterns of ion channels

Stationary spatiotemporal pattern formation emerging from the electric activity of biological membranes is widespread in cells and tissues. A known key instability comes from the self-aggregation of membrane channels. In a two-dimensional geometry, we show that the primary pattern undergoes four secondary instabilities: Eckhaus-like, period-halving, drift instabilities, and a global oscillation. The stability diagram is determined. The parity-breaking (drift) bifurcation of channel density is characterized analytically and numerically.     

On the Topology of Real Algebraic Plane Curves

We revisit the problem of computing the topology and geometry of a real algebraic plane curve. The topology is of prime interest but geometric information, such as the position of singular and critical points, is also relevant. A challenge is to compute efficiently this information for the given coordinate system even if the curve is not in generic position. Previous methods based on the cylindrical algebraic decomposition use sub-resultant sequences and computations with polynomials with algebraic coefficients. A novelty of our approach is to replace these tools by Gröbner basis computations and isolation with rational univariate representations. This has the advantage of avoiding computations with polynomials with algebraic coefficients, even in non-generic positions. Our algorithm isolates critical points in boxes and computes a decomposition of the plane by rectangular boxes. This decomposition also induces a new approach for computing an arrangement of polylines isotopic to the input curve. We also present an analysis of the complexity of our algorithm. An implementation of our algorithm demonstrates its efficiency, in particular on high-degree non-generic curves.     

A profile decomposition approach to the L^\infty _t(L^{3}_x) Navier–Stokes regularity criterion

In this paper we continue to develop an alternative viewpoint on recent studies of Navier–Stokes regularity in critical spaces, a program which was started in the recent work by Kenig and Koch (Ann Inst H Poincaré Anal Non Linéaire 28(2):159–187, 2011). Specifically, we prove that strong solutions which remain bounded in the space ${L^3(\mathbb R ^3)}$ do not become singular in finite time, a known result established by Escauriaza et al. (Uspekhi Mat Nauk 58(2(350)):3–44, 2003) in the context of suitable weak solutions. Here, we use the method of “critical elements” which was recently developed by Kenig and Merle to treat critical dispersive equations. Our main tool is a “profile decomposition” for the Navier–Stokes equations in critical Besov spaces which we develop here. As a byproduct of this tool, assuming a singularity-producing initial datum for Navier–Stokes exists in a critical Lebesgue or Besov space, we show there is one with minimal norm, generalizing a result of Rusin and Sverak (J Funct Anal 260(3):879–891, 2011).     

Radiative processes as a condensation phenomenon and the physical meaning of deformed canonical structures

We study the radiative corrections of QED₃ from the dual point of view and show that this process is the exact dual to the Julia–Toulouse mechanism introduced by Quevedo and Trugenberger [F. Quevedo, C.A. Trugenberger, Nucl. Phys. B 501 (1997) 143] some years ago. We discuss the physics behind this mechanism that involves condensation of topological defects. It is shown that the dual Stuckelberg mechanism is responsible for the “rank-jump” phenomenon that transforms the scalar field (dual to Maxwell in this dimensionality) into the vectorial self-dual field. This phenomenon is studied using the ideas of noncommutative fields theory that examines possible deformations of the canonical structure of some well-known models in (2+1)D$(2+1)\mathrm{D}$. A deformation is constructed linking the massless scalar field theory with the self-dual theory. This is the exact dual of the known deformation connecting the Maxwell theory with the Maxwell–Chern–Simons theory. Duality, radiative corrections, the Julia–Toulouse mechanism and canonical deformations are then used to establish a web of relations between the mentioned theories and to propose a physical picture of the deformation procedure adopted.     

Photoluminescence asymmetry with quantum state preparation

We show that the number of photons in a strongly coupled exciton–photon system is asymmetric with the detuning of the modes when, in the spontaneous emission regime, the two modes are entangled. As changing the detuning is easy in semiconductor microcavities–where on the other hand the nature of the strong-coupling in terms of single-particle effects is not yet resolved–we propose this effect as a test of the quantum character of microcavity polaritons.     

Structured Hybrid Nanoparticles via Surface‐Initiated ATRP of Methyl Methacrylate from Ordered Mesoporous Silica

Structured hybrid nanoparticles were synthesized via surface‐initiated atom transfer radical polymerization of MMA from ordered mesoporous silica (OMS) nanoparticles with various morphologies. The design of the OMS particles was adjusted to target either spherical core‐shell or cylindrical morphologies with a mean diameter below 400 nm. The polymer growth via ATRP from the silica surface was well‐controlled as demonstrated by the macromolecular characteristics of the grafted chains. Original hybrid multilayered nanoparticles composed of either a dense silica core or hollow core; an inner OMS shell showing radial orientation of the mesopores and an outer PMMA shell with controlled thickness were successfully prepared.

     

Radical Cyclisation of α‐Halo Aluminium Acetals: A Mechanistic Study

α‐Bromo aluminium acetals are suitable substrates for Ueno–Stork‐like radical cyclisations affording γ‐lactols and acid‐sensitive methylene‐γ‐lactols in high yields. The mechanistic study herein sets the scope and limitation of this reaction. The influence of the halide (or chalcogenide) atom X (X=Cl, Br, I, SPh, SePh) in the precursors α‐haloesters, as well as influence of the solvent and temperature was studied. The structure of the aluminium acetal intermediates resulting from the reduction of the corresponding α‐haloesters has been investigated by low‐temperature ¹³C‐INEPT diffusion‐ordered NMR spectroscopy (DOSY) experiments and quantum calculations, providing new insights into the structures of these thermally labile intermediates. Oxygen‐bridged dimeric structures with a planar Al₂O₂ ring are proposed for the least hindered aluminium acetals, while monomeric structures seem to prevail for the most hindered species. A comparison against the radical cyclisation of aluminium acetals derived from allyl and propargyl alcohols with the parent Ueno–Stork has been made at the BHandHLYP/6‐311++G(d,p) level of theory, highlighting mechanistic similarities and differences.     

Influence of the PVOH molar mass on the morphology and functional properties of EVOH/PVOH films prepared by melt blending

The influences of the molar mass (low, medium, and high) and content of poly(vinyl alcohol) (PVOH) dispersed by melt-blending in an ethylene vinyl alcohol (EVOH) copolymer on the morphology, microstructure, thermal, mechanical, and oxygen barrier properties were investigated. Multilayer films with external low-density polyethylene layers and inner EVOH/PVOH blend layer and respective monolayer films were elaborated and characterized. EVOH/PVOH blends exhibited a good compatibility because of the initial presence of PVOH segments in EVOH. The detailed quantitative analysis of the morphology performed for all blends showed that the finest dispersion was obtained with the PVOH with the lowest molar mass. The properties of the films as a function of the PVOH content and its molar mass were determined herein. Significant improvement of barrier properties was obtained at moderated water activities (up to a_w = 0.6) by using the PVOH with the lowest molar mass. Compared to the neat EVOH material, the oxygen permeability coefficients decreased by a factor 2 by adding 15 vol% PVOH while the thermal and mechanical properties remained similar.