On a fourth order nonlinear Helmholtz equation

In this paper, we study the mixed dispersion fourth order nonlinear Helmholtz equation $\Delta^2 u -\beta \Delta u + \alpha u= \Gamma|u|^{p-2} u$ in $\mathbb R^N$ for positive, bounded and $\mathbb Z^N$-periodic functions $\Gamma$. Using the dual method of Evequoz and Weth, we find solutions to this equation and establish some of their qualitative properties

Local real-space view of the achiral 1T\text{\ensuremath{-}}{\mathrm{TiSe}}_{2} 2×2×22\times2\times2 charge density wave

The transition metal dichalcogenide 1T−TiSe2-two-dimensional layered material undergoing a commensurate 2×2×2 charge density wave (CDW) transition with a weak periodic lattice distortion (PLD) below ≈200 K. Scanning tunneling microscopy (STM) combined with intentionally introduced interstitial Ti atoms allows us to go beyond the usual spatial resolution of STM and to intimately probe the three- dimensional character of the PLD. Furthermore, the inversion-symmetric achiral nature of the CDW in the z direction is revealed, contradicting the claimed existence of helical CDW stacking and associated chiral order. This study paves the way to a simultaneous real-space probing of both charge and structural reconstructions in CDW compounds

Fluctuation spectrum of fluid membranes coupled to an elastic meshwork: jump of the effective surface tension at the mesh size

We identify a class of composite membranes: fluid bilayers coupled to an elastic meshwork, that are such that the meshwork's energy is a function $F_\mathrm{el}[A_\xi]$ \textit{not} of the real microscopic membrane area $A$, but of a \textit{smoothed} membrane's area $A_\xi$, which corresponds to the area of the membrane coarse-grained at the mesh size $\xi$. We show that the meshwork modifies the membrane tension $\sigma$ both below and above the scale $\xi$, inducing a tension-jump $\Delta\sigma=dF_\mathrm{el}/dA_\xi$. The predictions of our model account for the fluctuation spectrum of red blood cells membranes coupled to their cytoskeleton. Our results indicate that the cytoskeleton might be under extensional stress, which would provide a means to regulate available membrane area. We also predict an observable tension jump for membranes decorated with polymer "brushes"

Microwave Assisted Synthesis of Py-Im Polyamides

Microwave synthesis was utilized to rapidly build Py-Im polyamides in high yields and purity using Boc-protection chemistry on Kaiser oxime resin. A representative polyamide targeting the 5′-WGWWCW-3′ (W = A or T) subset of the consensus Androgen and Glucocorticoid Response Elements was synthesized in 56% yield after 20 linear steps and HPLC purification. It was confirmed by Mosher amide derivatization of the polyamide that a chiral α-amino acid does not racemize after several additional coupling steps

Shear-banding in a lyotropic lamellar phase, Part 2: Temporal fluctuations

We analyze the temporal fluctuations of the flow field associated to a shear-induced transition in a lyotropic lamellar phase: the layering transition of the onion texture. In the first part of this work [Salmon et al., submitted to Phys. Rev. E], we have evidenced banded flows at the onset of this shear-induced transition which are well accounted for by the classical picture of shear-banding. In the present paper, we focus on the temporal fluctuations of the flow field recorded in the coexistence domain. These striking dynamics are very slow (100--1000s) and cannot be due to external mechanical noise. Using velocimetry coupled to structural measurements, we show that these fluctuations are due to a motion of the interface separating the two differently sheared bands. Such a motion seems to be governed by the fluctuations of $\sigma^\star$, the local stress at the interface between the two bands. Our results thus provide more evidence for the relevance of the classical mechanical approach of shear-banding even if the mechanism leading to the fluctuations of $\sigma^\star$ remains unclear

Local resilience of the 1T\text{\ensuremath{-}}{\mathrm{TiSe}}_{2} charge density wave to Ti self-doping

In Ti-intercalated self-doped 1T−TiSe2 crystals, the charge density wave (CDW) superstructure induces two nonequivalent sites for Ti dopants. Recently, it has been shown that increasing Ti doping dramatically influences the CDW by breaking it into phase-shifted domains. Here, we report scanning tunneling microscopy and spectroscopy experiments that reveal a dopant-site dependence of the CDW gap. Supported by density functional theory, we demonstrate that the loss of the long-range phase coherence introduces an imbalance in the intercalated-Ti site distribution and restrains the CDW gap closure. This local resilient behavior of the 1T−TiSe2 CDW reveals an entangled mechanism between CDW, periodic lattice distortion, and induced nonequivalent defects

Transgressive segregation reveals mechanisms of Arabidopsis immunity to Brassica-infecting races of white rust (Albugo candida)

Arabidopsis thaliana accessions are universally resistant at the adult leaf stage to white rust (Albugo candida) races that infect the crop species Brassica juncea and Brassica oleracea. We used transgressive segregation in recombinant inbred lines to test if this apparent species-wide (nonhost) resistance in A. thaliana is due to natural pyramiding of multiple Resistance (R) genes. We screened 593 inbred lines from an Arabidopsis multiparent advanced generation intercross (MAGIC) mapping population, derived from 19 resistant parental accessions, and identified two transgressive segregants that are susceptible to the pathogen. These were crossed to each MAGIC parent, and analysis of resulting F2 progeny followed by positional cloning showed that resistance to an isolate of A. candida race 2 (Ac2V) can be explained in each accession by at least one of four genes encoding nucleotide-binding, leucine-rich repeat (NLR) immune receptors. An additional gene was identified that confers resistance to an isolate of A. candida race 9 (AcBoT) that infects B. oleracea. Thus, effector-triggered immunity conferred by distinct NLR-encoding genes in multiple A. thaliana accessions provides species-wide resistance to these crop pathogens

Milli-arcsecond astrophysics with VSI, the VLTI spectro-imager in the ELT era

Nowadays, compact sources like surfaces of nearby stars, circumstellar environments of stars from early stages to the most evolved ones and surroundings of active galactic nuclei can be investigated at milli-arcsecond scales only with the VLT in its interferometric mode. We propose a spectro-imager, named VSI (VLTI spectro-imager), which is capable to probe these sources both over spatial and spectral scales in the near-infrared domain. This instrument will provide information complementary to what is obtained at the same time with ALMA at different wavelengths and the extreme large telescopes.Comment: 8 pages. To be published in the proceedings of the ESO workshop "Science with the VLT in the ELT Era", held in Garching (Germany) on 8-12 October 2007, A. Moorwood edito

Analytic Metaphysics versus Naturalized Metaphysics: The Relevance of Applied Ontology

The relevance of analytic metaphysics has come under criticism: Ladyman & Ross, for instance, have suggested do discontinue the field. French & McKenzie have argued in defense of analytic metaphysics that it develops tools that could turn out to be useful for philosophy of physics. In this article, we show first that this heuristic defense of metaphysics can be extended to the scientific field of applied ontology, which uses constructs from analytic metaphysics. Second, we elaborate on a parallel by French & McKenzie between mathematics and metaphysics to show that the whole field of analytic metaphysics, being useful not only for philosophy but also for science, should continue to exist as a largely autonomous field

Brunet-Derrida behavior of branching-selection particle systems on the line

We consider a class of branching-selection particle systems on $\R$ similar to the one considered by E. Brunet and B. Derrida in their 1997 paper "Shift in the velocity of a front due to a cutoff". Based on numerical simulations and heuristic arguments, Brunet and Derrida showed that, as the population size $N$ of the particle system goes to infinity, the asymptotic velocity of the system converges to a limiting value at the unexpectedly slow rate $(\log N)^{-2}$. In this paper, we give a rigorous mathematical proof of this fact, for the class of particle systems we consider. The proof makes use of ideas and results by R. Pemantle, and by N. Gantert, Y. Hu and Z. Shi, and relies on a comparison of the particle system with a family of $N$ independent branching random walks killed below a linear space-time barrier