A Cumulative Damage Model to Predict Load Duration Characteristics of Lumber

The exponential damage model dα/dt = exp[-a + bσs(t)/σs] is used in this paper to describe duration-of-load data on lumber tested in bending where dα/dt is rate of damage, σs is static strength, σ(t) represents applied load history, and a and b are parameters. A specially selected set of Douglas-fir 2 by 4s was divided into six 49-specimen groups having similar distributions of edge knot size and modulus of elasticity. Each group was randomly assigned to one of three rates of ramp loading or one of three levels of constant loading.The lognormal distribution σs = σoexp(wR) provided a reasonable description of static strength of the 2 by 4s where σo is the median static strength, w is a measure of variability, and R is a normal random variable. With b' = b/σo, the model used to fit the ramp and constant load experimental data by nonlinear least squares was dα/dt = exp[-a + b'σo(t)/exp(wR)]; thus a, b', and w were parameters that were estimated. The model fit some but not all of the ramp and constant load data reasonably well. The estimates of variability (w) were slightly greater under ramp loading than under constant loading. Residual strength of specimens surviving constant load was less than expected. A greater duration-of-load effect was observed for the edge knot 2 by 4 lumber than that previously indicated for small clear-wood specimens; however, the difference does not appear to be statistically significant

Decomposition of L2L^{2}-vector fields on Lipschitz surfaces: characterization via null-spaces of the scalar potential

For $\partial \Omega$ the boundary of a bounded and connected strongly Lipschitz domain in $\mathbb{R}^{d}$ with $d\geq3$, we prove that any field $f\in L^{2} (\partial \Omega ; \mathbb{R}^{d})$ decomposes, in an unique way, as the sum of three silent vector fields---fields whose magnetic potential vanishes in one or both components of $\mathbb{R}^d\setminus\partial \Omega$. Moreover, this decomposition is orthogonal if and only if $\partial \Omega$ is a sphere. We also show that any $f$ in $L^{2} (\partial \Omega ; \mathbb{R}^{d})$ is uniquely the sum of two silent fields and a Hardy function, in which case the sum is orthogonal regardless of $\partial \Omega$; we express the corresponding orthogonal projections in terms of layer potentials. When $\partial \Omega$ is a sphere, both decompositions coincide and match what has been called the Hardy-Hodge decomposition in the literature

Unique reconstruction of simple magnetizations from their magnetic potential

Inverse problems arising in (geo)magnetism are typically ill-posed, in particular {they exhibit non-uniqueness}. Nevertheless, there exist nontrivial model spaces on which the problem is uniquely solvable. Our goal is here to describe such spaces that accommodate constraints suited for applications. In this paper we treat the inverse magnetization problem on a Lipschitz domain with fairly general topology. We characterize the subspace of $L^{2}$-vector fields that causes non-uniqueness, and identify a subspace of harmonic gradients on which the inversion becomes unique. This classification has consequences for applications and we present some of them in the context of geo-sciences. In the second part of the paper, we discuss the space of piecewise constant vector fields. This vector space is too large to make the inversion unique. But as we show, it contains a dense subspace in $L^2$ on which the problem becomes uniquely solvable, i.e., magnetizations from this subspace are uniquely determined by their magnetic potential

Theory of Magneto--Acoustic Transport in Modulated Quantum Hall Systems Near ν=1/2\nu=1/2

Motivated by the experimental results of Willett et al [Phys.Rev. Lett., {\bf 78}, 4478 (1997)] we develop a magneto-transport theory for the response of a two dimensional electron gas (2DEG) in the Fractional Quantum Hall Regime near Landau level filling factor $\nu = 1/2$ to the surface acoustic wave (SAW) in the presence of an added periodic density modulation. We assume there exists a Composite Fermion Fermi Surface (CF-FS) at $\nu = 1/2$, and we show that the deformation of the (CF-FS) due to the density modulation can be at the origin of the observed transport anomalies for the experimental conditions. Our analysis is carried out particularly for the non-local case which corresponds to the SAW experiments. We introduce a new model of a deformed CF-FS. The model permits us to explain anomalous features of the response of the modulated 2DEG to the SAW near $\nu = 1/2:$ namely the nonlinear wave vector dependence of the electron conductivity, the appearance of peaks in the SAW velocity shift and attenuation and the anisotropy of the effect, all of which originate from contributions to the conductivity tensor due to the regions of the CF-FS which are flattened by the applied modulation.Comment: 13 pages, 4 figures, the published versio

Features of MOG required for recognition by patients with MOG antibody-associated disorders

Antibodies to myelin oligodendrocyte glycoprotein (MOG-Abs) define a distinct disease entity. Here we aimed to understand essential structural features of MOG required for recognition by autoantibodies from patients. We produced the N-terminal part of MOG in a conformationally correct form; this domain was insufficient to identify patients with MOG-Abs by ELISA even after site-directed binding. This was neither due to a lack of lipid embedding nor to a missing putative epitope at the C-terminus, which we confirmed to be an intracellular domain. When MOG was displayed on transfected cells, patients with MOG-Abs recognized full-length MOG much better than its N-terminal part with the first hydrophobic domain (P < 0.0001). Even antibodies affinity-purified with the extracellular part of MOG recognized full-length MOG better than the extracellular part of MOG after transfection. The second hydrophobic domain of MOG enhanced the recognition of the extracellular part of MOG by antibodies from patients as seen with truncated variants of MOG. We confirmed the pivotal role of the second hydrophobic domain by fusing the intracellular part of MOG from the evolutionary distant opossum to the human extracellular part; the chimeric construct restored the antibody binding completely. Further, we found that in contrast to 8-18C5, MOG-Abs from patients bound preferentially as F(ab')(2) rather than Fab. It was previously found that bivalent binding of human IgG1, the prominent isotype of MOG-Abs, requires that its target antigen is displayed at a distance of 13-16 nm. We found that, upon transfection, molecules of MOG did not interact so closely to induce a Forster resonance energy transfer signal, indicating that they are more than 6 nm apart. We propose that the intracellular part of MOG holds the monomers apart at a suitable distance for bivalent binding; this could explain why a cell-based assay is needed to identify MOG-Abs. Our finding that MOG-Abs from most patients require bivalent binding has implications for understanding the pathogenesis of MOG-Ab associated disorders. Since bivalently bound antibodies have been reported to only poorly bind C1q, we speculate that the pathogenicity of MOG-Abs is mostly mediated by other mechanisms than complement activation. Therefore, therapeutic inhibition of complement activation should be less efficient in MOG-Ab associated disorders than in patients with antibodies to aquaporin-4

A Vanadium(III) Complex with Blue and NIR-II Spin-Flip Luminescence in Solution

Luminescence from Earth-abundant metal ions in solution at room temperature is a very challenging objective due to the intrinsically weak ligand field splitting of first-row transition metal ions, which leads to efficient nonradiative deactivation via metal-centered states. Only a handful of 3dn metal complexes (n ≠ 10) show sizable luminescence at room temperature. Luminescence in the near-infrared spectral region is even more difficult to achieve as further nonradiative pathways come into play. No Earth-abundant first-row transition metal complexes have displayed emission >1000 nm at room temperature in solution up to now. Here, we report the vanadium(III) complex mer-[V(ddpd)2][PF6]3 yielding phosphorescence around 1100 nm in valeronitrile glass at 77 K as well as at room temperature in acetonitrile with 1.8 × 10–4% quantum yield (ddpd = N,N′-dimethyl-N,N′-dipyridine-2-ylpyridine-2,6-diamine). In addition, mer-[V(ddpd)2][PF6]3 shows very strong blue fluorescence with 2% quantum yield in acetonitrile at room temperature. Our comprehensive study demonstrates that vanadium(III) complexes with d2 electron configuration constitute a new class of blue and NIR-II luminophores, which complement the classical established complexes of expensive precious metals and rare-earth elements