Fermi Surface of Alpha-Uranium at Ambient Pressure

We have performed de Haas-van Alphen measurements of the Fermi surface of alpha-uranium single crystals at ambient pressure within the alpha-3 charge density wave (CDW) state from 0.020 K - 10 K and magnetic fields to 35 T using torque magnetometry. The angular dependence of the resulting frequencies is described. Effective masses were measured and the Dingle temperature was determined to be 0.74 K +/- 0.04 K. The observation of quantum oscillations within the alpha-3 CDW state gives new insight into the effect of the charge density waves on the Fermi surface. In addition we observed no signature of superconductivity in either transport or magnetization down to 0.020 K indicating the possibility of a pressure-induced quantum critical point that separates the superconducting dome from the normal CDW phase.Comment: 11 pages, 4 figures, 3 table

On two problems in graph Ramsey theory

We study two classical problems in graph Ramsey theory, that of determining the Ramsey number of bounded-degree graphs and that of estimating the induced Ramsey number for a graph with a given number of vertices. The Ramsey number r(H) of a graph H is the least positive integer N such that every two-coloring of the edges of the complete graph $K_N$ contains a monochromatic copy of H. A famous result of Chv\'atal, R\"{o}dl, Szemer\'edi and Trotter states that there exists a constant c(\Delta) such that r(H) \leq c(\Delta) n for every graph H with n vertices and maximum degree \Delta. The important open question is to determine the constant c(\Delta). The best results, both due to Graham, R\"{o}dl and Ruci\'nski, state that there are constants c and c' such that 2^{c' \Delta} \leq c(\Delta) \leq 2^{c \Delta \log^2 \Delta}. We improve this upper bound, showing that there is a constant c for which c(\Delta) \leq 2^{c \Delta \log \Delta}. The induced Ramsey number r_{ind}(H) of a graph H is the least positive integer N for which there exists a graph G on N vertices such that every two-coloring of the edges of G contains an induced monochromatic copy of H. Erd\H{o}s conjectured the existence of a constant c such that, for any graph H on n vertices, r_{ind}(H) \leq 2^{c n}. We move a step closer to proving this conjecture, showing that r_{ind} (H) \leq 2^{c n \log n}. This improves upon an earlier result of Kohayakawa, Pr\"{o}mel and R\"{o}dl by a factor of \log n in the exponent.Comment: 18 page

Spinal degeneration is associated with lumbar multifidus morphology in secondary care patients with low back or leg pain

Associations between multifidus muscle morphology and degenerative pathologies have been implied in patients with non-specific low back pain, but it is unknown how these are influenced by pathology severity, number, or distribution. MRI measures of pure multifidus muscle cross-sectional area (CSA) were acquired from 522 patients presenting with low back and/or leg symptoms in an outpatient clinic. We explored cross-sectional associations between the presence, distribution, and/or severity of lumbar degenerative pathologies (individually and in aggregate) and muscle outcomes in multivariable analyses (beta coefficients [95% CI]). We identified associations between lower pure multifidus muscle CSA and disc degeneration (at two or more levels): − 4.51 [− 6.72; − 2.3], Modic 2 changes: − 4.06 [− 6.09; − 2.04], endplate defects: − 2.74 [− 4.58; − 0.91], facet arthrosis: − 4.02 [− 6.26; − 1.78], disc herniations: − 3.66 [− 5.8; − 1.52], and when > 5 pathologies were present: − 6.77 [− 9.76; − 3.77], with the last supporting a potential dose–response relationship between number of spinal pathologies and multifidus morphology. Our findings could hypothetically indicate that these spinal and muscle findings: (1) are part of the same degenerative process, (2) result from prior injury or other common antecedent events, or (3) have a directional relationship. Future longitudinal studies are needed to further examine the complex nature of these relationships

Non-stationarity in peaks-over-threshold river flows:a regional random effects model

Under the influence of local- and large-scale climatological processes, extreme river flow events often show long-term trends, seasonality, inter-year variability and other characteristics of temporal non-stationarity. Properly accounting for this non-stationarity is vital for making accurate predictions of future floods. In this paper, a regional model based on the generalised Pareto distribution is developed for peaks-over-threshold river flow data sets when the event sizes are non-stationary. If observations are non-stationary and covariates are available then extreme value (semi-)parametric regression models may be used. Unfortunately the necessary covariates are rarely observed and, if they are, it is often not clear which process, or combination of processes, to include in the model. Within the statistical literature, latent process (or random effects) models are often used in such scenarios. We develop a regional time-varying random effects model which allows identification of temporal non-stationarity in event sizes by pooling information across all sites in a spatially homogeneous region. The proposed model, which is an instance of a Bayesian hierarchical model, can be used to predict both unconditional extreme events such as the m-year maximum, as well as extreme events that condition on being in a given year. The estimated random effects may also tell us about likely candidates for the climatological processes which cause non-stationarity in the flood process. The model is applied to UK flood data from 817 stations spread across 81 hydrometric regions

Magnetic polarons and magnetoresistance in EuB6

EuB6 is a low carrier density ferromagnet which exhibits large magnetoresistance, positive or negative depending on temperature. The formation of magnetic polarons just above the magnetic critical temperature has been suggested by spin-flip Raman scattering experiments. We find that the fact that EuB6 is a semimetal has to be taken into account to explain its electronic properties, including magnetic polarons and magnetoresistance.Comment: 6 pages, 1 figur

Magnetic field induced lattice anomaly inside the superconducting state of CeCoIn5_5: evidence of the proposed Fulde-Ferrell-Larkin-Ovchinnikov state

We report high magnetic field linear magnetostriction experiments on CeCoIn$_5$ single crystals. Two features are remarkable: (i) a sharp discontinuity in all the crystallographic axes associated with the upper superconducting critical field $B_{c2}$ that becomes less pronounced as the temperature increases; (ii) a distinctive second order-like feature observed only along the c-axis in the high field (10 T $\lesssim B \leq B_{c2}$) low temperature ($T \lesssim$ 0.35 K) region. This second order transition is observed only when the magnetic field lies within 20$^o$ of the ab-planes and there is no signature of it above $B_{c2}$, which raises questions regarding its interpretation as a field induced magnetically ordered phase. Good agreement with previous results suggests that this anomaly is related to the transition to the Fulde-Ferrel-Larkin-Ovchinnikov superconducting state.Comment: 3 figures, 5 page

A versatile and compact capacitive dilatometer

We describe the design, construction, calibration, and operation of a relatively simple differential capacitive dilatometer suitable for measurements of thermal expansion and magnetostriction from 300 K to below 1 K with a low-temperature resolution of about 0.05 angstroms. The design is characterized by an open architecture permitting measurements on small samples with a variety of shapes. Dilatometers of this design have operated successfully with a commercial physical property measurement system, with several types of cryogenic refrigeration systems, in vacuum, in helium exchange gas, and while immersed in liquid helium (magnetostriction only) to temperatures of 30 mK and in magnetic fields to 45 T.Comment: 8 pages, incorporating 6 figures, submitted to Rev. Sci. Instru

Long range order and two-fluid behavior in heavy electron materials

The heavy electron Kondo liquid is an emergent state of condensed matter that displays universal behavior independent of material details. Properties of the heavy electron liquid are best probed by NMR Knight shift measurements, which provide a direct measure of the behavior of the heavy electron liquid that emerges below the Kondo lattice coherence temperature as the lattice of local moments hybridizes with the background conduction electrons. Because the transfer of spectral weight between the localized and itinerant electronic degrees of freedom is gradual, the Kondo liquid typically coexists with the local moment component until the material orders at low temperatures. The two-fluid formula captures this behavior in a broad range of materials in the paramagnetic state. In order to investigate two-fluid behavior and the onset and physical origin of different long range ordered ground states in heavy electron materials, we have extended Knight shift measurements to URu$_2$Si$_2$, CeIrIn$_5$ and CeRhIn$_5$. In CeRhIn$_5$ we find that the antiferromagnetic order is preceded by a relocalization of the Kondo liquid, providing independent evidence for a local moment origin of antiferromagnetism. In URu$_2$Si$_2$ the hidden order is shown to emerge directly from the Kondo liquid and so is not associated with local moment physics. Our results imply that the nature of the ground state is strongly coupled with the hybridization in the Kondo lattice in agreement with phase diagram proposed by Yang and Pines.Comment: 9 pages, 13 figure