Lines pinning lines

A line g is a transversal to a family F of convex polytopes in 3-dimensional space if it intersects every member of F. If, in addition, g is an isolated point of the space of line transversals to F, we say that F is a pinning of g. We show that any minimal pinning of a line by convex polytopes such that no face of a polytope is coplanar with the line has size at most eight. If, in addition, the polytopes are disjoint, then it has size at most six. We completely characterize configurations of disjoint polytopes that form minimal pinnings of a line.Comment: 27 pages, 10 figure

Stability of homogeneous magnetic phases in a generalized t-J model

We study the stability of homogeneous magnetic phases in a generalized t-J model including a same-sublattice hopping t' and nearest-neighbor repulsion V by means of the slave fermion-Schwinger boson representation of spin operators. At mean-field order we find, in agreement with other authors, that the inclusion of further-neighbor hopping and Coulomb repulsion makes the compressibility positive, thereby stabilizing at this level the spiral and Neel orders against phase separation. However, the consideration of Gaussian fluctuation of order parameters around these mean-field solutions produces unstable modes in the dynamical matrix for all relevant parameter values, leaving only reduced stability regions for the Neel phase. We have computed the one-loop corrections to the energy in these regions, and have also briefly considered the effects of the correlated hopping term that is obtained in the reduction from the Hubbard to the t-J model.Comment: 5 pages, 5 figures, Revte

Phonon thermal conductivity in doped La2CuO4\rm\bf La_2CuO_4: Relevant scattering mechanisms

Results of in-plane and out-of-plane thermal conductivity measurements on $\rm La_{1.8-x}Eu_{0.2}Sr_xCuO_4$ ($0\leq x\leq0.2$) single crystals are presented. The most characteristic features of the temperature dependence are a pronounced phonon peak at low temperatures and a steplike anomaly at $T_{LT}$, i.e., at the transition to the low temperature tetragonal phase (LTT-phase), which gradually decrease with increasing Sr-content. Comparison of these findings with the thermal conductivity of $\rm La_{2-x}Sr_xCuO_4$ and $\rm La_2NiO_4$ clearly reveals that in $\rm La_{2-x}Sr_xCuO_4$ the most effective mechanism for phonon scattering is impurity-scattering (dopants), as well as scattering by soft phonons that are associated with the lattice instability in the low temperature orthorhombic phase (LTO-phase). There is no evidence that stripe correlations play a major role in suppressing the phonon peak in the thermal conductivity of $\rm La_{2-x}Sr_xCuO_4$.Comment: 7 pages, 4 figure

Upper critical field for underdoped high-T_c superconductors. Pseudogap and stripe--phase

We investigate the upper critical field in a stripe--phase and in the presence of a phenomenological pseudogap. Our results indicate that the formation of stripes affects the Landau orbits and results in an enhancement of $H_{c2}$. On the other hand, phenomenologically introduced pseudogap leads to a reduction of the upper critical field. This effect is of particular importance when the magnitude of the gap is of the order of the superconducting transition temperature. We have found that a suppression of the upper critical field takes place also for the gap that originates from the charge--density waves.Comment: 7 pages, 5 figure

Long-term development of white matter fibre density and morphology up to 13 years after preterm birth: a fixel-based analysis

Background It is well documented that infants born very preterm (VP) are at risk of brain injury and altered brain development in the neonatal period, however there is a lack of long-term, longitudinal studies on the effects of VP birth on white matter development over childhood. Most previous studies were based on voxel-averaged, non-fibre-specific diffusion magnetic resonance imaging (MRI) measures, such as fractional anisotropy. In contrast, the novel diffusion MRI analysis framework, fixel-based analysis (FBA), enables whole-brain analysis of microstructural and macrostructural properties of individual fibre populations at a sub-voxel level. We applied FBA to investigate the long-term implications of VP birth and associated perinatal risk factors on fibre development in childhood and adolescence. Methods Diffusion images were acquired for a cohort of VP (born <30 weeks' gestation) and full-term (FT, ≥37 weeks' gestation) children at two timepoints: mean (SD) 7.6 (0.2) years (n ​= ​138 VP and 32 FT children) and 13.3 (0.4) years (n ​= ​130 VP and 45 FT children). 103 VP and 21 FT children had images at both ages for longitudinal analysis. At every fixel (individual fibre population within an image voxel) across the white matter, we compared FBA metrics (fibre density (FD), cross-section (FC) and a combination of these properties (FDC)) between VP and FT groups cross-sectionally at each timepoint, and longitudinally between timepoints. We also examined associations between known perinatal risk factors and FBA metrics in the VP group. Results Compared with FT children, VP children had lower FD, FC and FDC throughout the white matter, particularly in the corpus callosum, tapetum, inferior fronto-occipital fasciculus, fornix and cingulum at ages 7 and 13 years, as well as the corticospinal tract and anterior limb of the internal capsule at age 13 years. VP children also had slower FDC development in the corpus callosum and corticospinal tract between ages 7 and 13 years compared with FT children. Within VP children, earlier gestational age at birth, lower birth weight z-score, and neonatal brain abnormalities were associated with lower FD, FC and FDC throughout the white matter at both ages. Conclusions VP birth and concomitant perinatal risk factors are associated with fibre tract-specific alterations to axonal development in childhood and adolescence.Claire E.Kelly, Deanne K.Thompson, Sila Genc, Jian Chen, Joseph YM.Yang, Chris Adamson ... et al

Brain tissue microstructural and free-water composition 13 years after very preterm birth

There have been many studies demonstrating children born very preterm exhibit brain white matter microstruc- tural alterations, which have been related to neurodevelopmental difficulties. These prior studies have often been based on diffusion MRI modelling and analysis techniques, which commonly focussed on white matter microstructural properties in children born very preterm. However, there have been relatively fewer studies investigating the free-water content of the white matter, and also the microstructure and free-water content of the cortical grey matter, in children born very preterm. These biophysical properties of the brain change rapidly during fetal and neonatal brain development, and therefore such properties are likely also adversely affected by very preterm birth. In this study, we investigated the relationship of very preterm birth (<30 weeks’ gestation) to both white matter and cortical grey matter microstructure and free-water content in childhood using advanced diffusion MRI analyses. A total of 130 very preterm participants and 45 full-term control participants underwent diffusion MRI at age 13 years. Diffusion tissue signal fractions derived by Single-Shell 3-Tissue Constrained Spherical Deconvolution were used to investigate brain tissue microstructural and free-water composition. The tissue microstructural and free-water composition metrics were analysed using a voxel-based analysis and cortical region-of-interest analysis approach. Very preterm 13-year-olds exhibited reduced white matter microstructural density and in- creased free-water content across widespread regions of the white matter compared with controls. Additionally, very preterm 13-year-olds exhibited reduced microstructural density and increased free-water content in specific temporal, frontal, occipital and cingulate cortical regions. These brain tissue composition alterations were strongly associated with cerebral white matter abnormalities identified in the neonatal period, and concurrent adverse cognitive and motor outcomes in very preterm children. The findings demonstrate brain microstructural and free-water alterations up to thirteen years from neonatal brain abnormalities in very preterm children that relate to adverse neurodevelopmental outcomes.Claire Kelly, Thijs Dhollander, Ian H Harding, Wasim Khan, Richard Beare, Jeanie LY Cheong, Lex W Doyle, Marc Seal, Deanne K Thompson, Terrie E Inder, Peter J Anderso

Magnetic Properties of YBa_2Cu_3O_{7-\delta} in a self-consistent approach: Comparison with Quantum-Monte-Carlo Simulations and Experiments

We analyze single-particle electronic and two-particle magnetic properties of the Hubbard model in the underdoped and optimally-doped regime of \YBCO by means of a modified version of the fluctuation-exchange approximation, which only includes particle-hole fluctuations. Comparison of our results with Quantum-Monte Carlo (QMC) calculations at relatively high temperatures ($T\sim 1000 K$) suggests to introduce a temperature renormalization in order to improve the agreement between the two methods at intermediate and large values of the interaction $U$. We evaluate the temperature dependence of the spin-lattice relaxation time $T_1$ and of the spin-echo decay time $T_{2G}$ and compare it with the results of NMR measurements on an underdoped and an optimally doped \YBCO sample. For $U/t=4.5$ it is possible to consistently adjust the parameters of the Hubbard model in order to have a good {\it semi-quantitative} description of this temperature dependence for temperatures larger than the spin gap as obtained from NMR measurements. We also discuss the case $U/t\sim 8$, which is more appropriate to describe magnetic and single-particle properties close to half-filling. However, for this larger value of $U/t$ the agreement with QMC as well as with experiments at finite doping is less satisfactory.Comment: Final version, to appear in Phys. Rev. B (sched. Feb. 99

Dispersion of Ordered Stripe Phases in the Cuprates

A phase separation model is presented for the stripe phase of the cuprates, which allows the doping dependence of the photoemission spectra to be calculated. The idealized limit of a well-ordered array of magnetic and charged stripes is analyzed, including effects of long-range Coulomb repulsion. Remarkably, down to the limit of two-cell wide stripes, the dispersion can be interpreted as essentially a superposition of the two end-phase dispersions, with superposed minigaps associated with the lattice periodicity. The largest minigap falls near the Fermi level; it can be enhanced by proximity to a (bulk) Van Hove singularity. The calculated spectra are dominated by two features -- this charge stripe minigap plus the magnetic stripe Hubbard gap. There is a strong correlation between these two features and the experimental photoemission results of a two-peak dispersion in La$_{2-x}$Sr$_x$CuO$_4$, and the peak-dip-hump spectra in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. The differences are suggestive of the role of increasing stripe fluctuations. The 1/8 anomaly is associated with a quantum critical point, here expressed as a percolation-like crossover. A model is proposed for the limiting minority magnetic phase as an isolated two-leg ladder.Comment: 24 pages, 26 PS figure

Magnetotransport in the Normal State of La1.85Sr0.15Cu(1-y)Zn(y)O4 Films

We have studied the magnetotransport properties in the normal state for a series of La1.85Sr0.15Cu(1-y)Zn(y)O4 films with values of y, between 0 and 0.12. A variable degree of compressive or tensile strain results from the lattice mismatch between the substrate and the film, and affects the transport properties differently from the influence of the zinc impurities. In particular, the orbital magnetoresistance (OMR) varies with y but is strain-independent. The relations for the resistivity and the Hall angle and the proportionality between the OMR and tan^2 theta are followed about 70 K. We have been able to separate the strain and impurity effects by rewriting the above relations, where each term is strain-independent and depends on y only. We also find that changes in the lattice constants give rise to closely the same fractional changes in other terms of the equation.The OMR is more strongly supressed by the addition of impurities than tan^2 theta. We conclude that the relaxation ratethat governs Hall effect is not the same as for the magnetoresistance. We also suggest a correspondence between the transport properties and the opening of the pseudogap at a temperature which changes when the La-sr ratio changes, but does not change with the addition of the zinc impurities