Generalized DPW method and an application to isometric immersions of space forms

Let $G$ be a complex Lie group and $\Lambda G$ denote the group of maps from the unit circle ${\mathbb S}^1$ into $G$, of a suitable class. A differentiable map $F$ from a manifold $M$ into $\Lambda G$, is said to be of \emph{connection order $(_a^b)$} if the Fourier expansion in the loop parameter $\lambda$ of the ${\mathbb S}^1$-family of Maurer-Cartan forms for $F$, namely F_\lambda^{-1} \dd F_\lambda, is of the form $\sum_{i=a}^b \alpha_i \lambda^i$. Most integrable systems in geometry are associated to such a map. Roughly speaking, the DPW method used a Birkhoff type splitting to reduce a harmonic map into a symmetric space, which can be represented by a certain order $(_{-1}^1)$ map, into a pair of simpler maps of order $(_{-1}^{-1})$ and $(_1^1)$ respectively. Conversely, one could construct such a harmonic map from any pair of $(_{-1}^{-1})$ and $(_1^1)$ maps. This allowed a Weierstrass type description of harmonic maps into symmetric spaces. We extend this method to show that, for a large class of loop groups, a connection order $(_a^b)$ map, for $a<0<b$, splits uniquely into a pair of $(_a^{-1})$ and $(_1^b)$ maps. As an application, we show that constant non-zero curvature submanifolds with flat normal bundle of a sphere or hyperbolic space split into pairs of flat submanifolds, reducing the problem (at least locally) to the flat case. To extend the DPW method sufficiently to handle this problem requires a more general Iwasawa type splitting of the loop group, which we prove always holds at least locally.Comment: Some typographical correction

Moving lattice kinks and pulses: an inverse method

We develop a general mapping from given kink or pulse shaped travelling-wave solutions including their velocity to the equations of motion on one-dimensional lattices which support these solutions. We apply this mapping - by definition an inverse method - to acoustic solitons in chains with nonlinear intersite interactions, to nonlinear Klein-Gordon chains, to reaction-diffusion equations and to discrete nonlinear Schr\"odinger systems. Potential functions can be found in at least a unique way provided the pulse shape is reflection symmetric and pulse and kink shapes are at least $C^2$ functions. For kinks we discuss the relation of our results to the problem of a Peierls-Nabarro potential and continuous symmetries. We then generalize our method to higher dimensional lattices for reaction-diffusion systems. We find that increasing also the number of components easily allows for moving solutions.Comment: 15 pages, 5 figure

On the algebraic K-theory of the complex K-theory spectrum

Let p>3 be a prime, let ku be the connective complex K-theory spectrum, and let K(ku) be the algebraic K-theory spectrum of ku. We study the p-primary homotopy type of the spectrum K(ku) by computing its mod (p,v_1) homotopy groups. We show that up to a finite summand, these groups form a finitely generated free module over a polynomial algebra F_p[b], where b is a class of degree 2p+2 defined as a higher Bott element.Comment: Revised and expanded version, 42 pages

High-tech composites to ancient metals

Neutron diffraction methods offer a direct measure of the elastic component of strain deep within crystalline materials through precise characterisation of the interplanar crystal lattice spacing. The unique non-destructive nature of this measurement technique is particularly beneficial in the context of engineering design and archaeological materials science, since it allows the evaluation of a variety of structural and deformational parameters inside real components without material removal, or at worst with minimal interference. We review a wide range of recent experimental studies using the Engin-X materials engineering instrument at the ISIS neutron source and show how the technique provides the basis for developing improved insight into materials of great importance to applications and industry. © 2009 Elsevier Ltd. All rights reserved

Anisotropy in mechanical properties and fracture behavior of an oxide dispersion Fe20Cr5Al alloy

Anisotropy of fracture toughness and fracture behavior of Fe20Cr5Al oxide dispersion-strengthened alloy has been investigated by means of compression tests, hardness tests, and wedge splitting test. The results show a small effect of the compression direction on yield strength (YS) and strain hardening. The YS is minimum for longitudinal direction and maximum for the tangential direction. The transverse plastic strain ratio is similar for tangential and longitudinal directions but very different from that in normal direction. Hardness depends on the indentation plane; it is lower for any plane parallel to the L-T plane and of similar magnitude for the other orthogonal planes, i.e., the L-S and T-S planes. Macroscopically, two failure modes have been observed after wedge-splitting tests, those of LS and TS specimens in which fracture deviates along one or two branches normal to the notch plane, and those of LT, TL, SL, and ST specimens in which fracture propagates along the notch plane. Besides LT and TL specimens present delaminations parallel to L-T plane. Both, the fracture surface of branching cracks and that of the delaminations, show an intergranular brittle fracture appearance. It is proposed that the main cause of the delamination and crack branching is the alignment in the mesoscopic scale of the ultrafine grains structure which is enhanced by the 〈110〉- texture of the material and by the presence in the grain boundaries of both yttria dispersoids and impurity contaminations. An elastoplastic finite element analysis was performed to study what stress state is the cause of the branches and delaminations. It is concluded that the normal to the crack branches and/or the shear stress components could determine the crack bifurcation mechanism, whereas the delamination it seems that it is controlled by the magnitude of the stress component normal to the delamination plane. © The Minerals, Metals & Materials Society and ASM International 2014.Peer Reviewe

Single-fly genome assemblies fill major phylogenomic gaps across the Drosophilidae Tree of Life

Long-read sequencing is driving rapid progress in genome assembly : across all major groups of life, including species of the family Drosophilidae, a longtime model system for genetics, genomics, and evolution. We previously developed a cost-effective hybrid Oxford Nanopore (ONT) long-read and Illumina short-read sequencing approach and used it to assemble 101 drosophilid genomes from laboratory cultures, greatly increasing the number of genome assemblies for this taxonomic group. The next major challenge is to address the laboratory culture bias in taxon sampling by sequencing genomes of species that cannot easily be reared in the lab. Here, we build upon our previous methods to perform amplification-free ONT sequencing of single wild flies obtained either directly from the field or from ethanol-preserved specimens in museum collections, greatly improving the representation of lesser studied drosophilid taxa in whole-genome data. Using Illumina Novaseq X Plus and ONT P2 sequencers with R10.4.1 chemistry, we set a new benchmark for inexpensive hybrid genome assembly at US $150 per genome while assembling genomes from as little as 35 ng of genomic DNA from a single fly. We present 183 new genome assemblies for 179 species as a resource for drosophilid systematics, phylogenetics, and comparative genomics. Of these genomes, 62 are from pooled lab strains and 121 from single adult flies. Despite the sample limitations of working with small insects, most single-fly diploid assemblies are comparable in contiguity (>1 Mb contig N50), completeness (>98% complete dipteran BUSCOs), and accuracy (>QV40 genome-wide with ONT R10.4.1) to assemblies from inbred lines. We present a well-resolved multi-locus phylogeny for 360 drosophilid and 4 outgroup species encompassing all publicly available (as of August 2023) genomes for this group. Finally, we present a Progressive Cactus whole-genome, reference-free alignment built from a subset of 298 suitably high-quality drosophilid genomes. The new assemblies and alignment, along with updated laboratory protocols and computational pipelines, are released as an open resource and as a tool for studying evolution at the scale of an entire insect family

DISC1 genetics, biology and psychiatric illness

Psychiatric disorders are highly heritable, and in many individuals likely arise from the combined effects of genes and the environment. A substantial body of evidence points towards DISC1 being one of the genes that influence risk of schizophrenia, bipolar disorder and depression, and functional studies of DISC1 consequently have the potential to reveal much about the pathways that lead to major mental illness. Here, we review the evidence that DISC1 influences disease risk through effects upon multiple critical pathways in the developing and adult brain

Search for leptophobic Z ' bosons decaying into four-lepton final states in proton-proton collisions at root s=8 TeV

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Search for black holes and other new phenomena in high-multiplicity final states in proton-proton collisions at root s=13 TeV

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Search for heavy resonances decaying into a vector boson and a Higgs boson in final states with charged leptons, neutrinos, and b quarks

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