Nucleon Structure from Lattice QCD

Recent advances in lattice field theory, in computer technology and in chiral perturbation theory have enabled lattice QCD to emerge as a powerful quantitative tool in understanding hadron structure. I describe recent progress in the computation of the nucleon form factors and moments of parton distribution functions, before proceeding to describe lattice studies of the Generalized Parton Distributions (GPDs). In particular, I show how lattice studies of GPDs contribute to building a three-dimensional picture of the proton. I conclude by describing the prospects for studying the structure of resonances from lattice QCD.Comment: 6 pages, invited plenary talk at NSTAR 2007, 5-8 September 2007, Bonn, German

Ensemble decision tree models using RUSBoost for estimating risk of iron failure in drinking water distribution systems

Safe, trusted drinking water is fundamental to society. Discolouration is a key aesthetic indicator visible to customers. Investigations to understand discolouration and iron failures in water supply systems require assessment of large quantities of disparate, inconsistent, multidimensional data from multiple corporate systems. A comprehensive data matrix was assembled for a seven year period across the whole of a UK water company (serving three million people). From this a novel data driven tool for assessment of iron risk was developed based on a yearly update and ranking procedure, for a subset of the best quality data. To avoid a ‘black box’ output, and provide an element of explanatory (human readable) interpretation, classification decision trees were utilised. Due to the very limited number of iron failures, results from many weak learners were melded into one high-quality ensemble predictor using the RUSBoost algorithm which is designed for class imbalance. Results, exploring simplicity vs predictive power, indicate enough discrimination between variable relationships in the matrix to produce ensemble decision tree classification models with good accuracy for iron failure estimation at District Management Area (DMA) scale. Two model variants were explored: ‘Nowcast’ (situation at end of calendar year) and ‘Futurecast’ (predict end of next year situation from this year’s data). The Nowcast 2014 model achieved 100% True Positive Rate (TPR) and 95.3% True Negative Rate (TNR), with 3.3% of DMAs classified High Risk for un-sampled instances. The Futurecast 2014 achieved 60.5% TPR and 75.9% TNR, with 25.7% of DMAs classified High Risk for un-sampled instances. The output can be used to focus preventive measures to improve iron compliance

Ensemble decision tree models using RUSBoost for estimating risk of iron failure in drinking water distribution systems

Safe, trusted drinking water is fundamental to society. Discolouration is a key aesthetic indicator visible to customers. Investigations to understand discolouration and iron failures in water supply systems require assessment of large quantities of disparate, inconsistent, multidimensional data from multiple corporate systems. A comprehensive data matrix was assembled for a seven year period across the whole of a UK water company (serving three million people). From this a novel data driven tool for assessment of iron risk was developed based on a yearly update and ranking procedure, for a subset of the best quality data. To avoid a ‘black box’ output, and provide an element of explanatory (human readable) interpretation, classification decision trees were utilised. Due to the very limited number of iron failures, results from many weak learners were melded into one high-quality ensemble predictor using the RUSBoost algorithm which is designed for class imbalance. Results, exploring simplicity vs predictive power, indicate enough discrimination between variable relationships in the matrix to produce ensemble decision tree classification models with good accuracy for iron failure estimation at District Management Area (DMA) scale. Two model variants were explored: ‘Nowcast’ (situation at end of calendar year) and ‘Futurecast’ (predict end of next year situation from this year’s data). The Nowcast 2014 model achieved 100% True Positive Rate (TPR) and 95.3% True Negative Rate (TNR), with 3.3% of DMAs classified High Risk for un-sampled instances. The Futurecast 2014 achieved 60.5% TPR and 75.9% TNR, with 25.7% of DMAs classified High Risk for un-sampled instances. The output can be used to focus preventive measures to improve iron compliance

Slow relaxation in granular compaction

Experimental studies show that the density of a vibrated granular material evolves from a low density initial state into a higher density final steady state. The relaxation towards the final density value follows an inverse logarithmic law. We propose a simple stochastic adsorption-desorption process which captures the essential mechanism underlying this remarkably slow relaxation. As the system approaches its final state, a growing number of beads have to be rearranged to enable a local density increase. In one dimension, this number grows as $N=\rho/(1-\rho)$, and the density increase rate is drastically reduced by a factor $e^{-N}$. Consequently, a logarithmically slow approach to the final state is found $\rho_{\infty}-\rho(t)\cong 1/\ln t$.Comment: revtex, 4 pages, 3 figures, also available from http://arnold.uchicago.edu/~ebn

Friedel oscillations in a two-band Hubbard model for CuO chains

Friedel oscillations induced by open boundary conditions in a two-band Hubbard model for CuO chains are numerically studied. We find that for physically realistic parameters and close to quarter filling, these oscillations have a 2k_F modulation according with experimental results on YBa_2Cu_3O_{7-delta}. In addition, we predict that, for the same parameters, as hole doping is reduced from quarter filling to half filling, Friedel oscillations would acquire a 4k_F modulation, typical of a strongly correlated electrons regime. The 4k_F modulation dominates also in the electron doped region. The range of parameters varied is very broad, and hence the results reported could apply to other cuprates and other strongly correlated compounds with quasi-one dimensional structures. On a more theoretical side, we stress the fact that the copper and oxygen subsystems should be described by two different Luttinger liquid exponents.Comment: 7 pages, 7 eps figure

Chiral Analysis of Quenched Baryon Masses

We extend to quenched QCD an earlier investigation of the chiral structure of the masses of the nucleon and the delta in lattice simulations of full QCD. Even after including the meson-loop self-energies which give rise to the leading and next-to-leading non-analytic behaviour (and hence the most rapid variation in the region of light quark mass), we find surprisingly little curvature in the quenched case. Replacing these meson-loop self-energies by the corresponding terms in full QCD yields a remarkable level of agreement with the results of the full QCD simulations. This comparison leads to a very good understanding of the origins of the mass splitting between these baryons.Comment: 23 pages, 6 figure

Organic and conventional tomato cropping systems.

Among several alternative agricultural systems have been developed, organic agriculture has deserved increasing interest from. The objective of this paper was comparing both organic (OS) and conventional (CS) tomato cropping systems for varieties Débora and Santa Clara, through an interdisciplinary study. The experiment was set up in a randomized blocks design with six replicates, in a dystrophic Ultisol plots measuring 25 ´ 17 m. Cropping procedures followed by either local conventional or organic growers practices recommendations. Fertilization in the OS was done with organic compost, single superphosphate, dolomitic limes (5L, 60 g, and 60 g per pit), and sprayed twice a week with biofertilizer. Fertilization in the CS was done with 200 g 4-14-8 (NPK) per pit and, after planting, 30 g N, 33 g K and 10.5 g P per pit; from 52 days after planting forth, plants were sprayed once a week with foliar fertilizer. In the CS, a blend of insecticides, fungicides and miticides was sprayed twice a week, after planting. In the OS, extracts of black pepper, garlic, and Eucalyptus; Bordeaux mixture, and biofertilizer, were applied twice a week to control diseases and pests. Tomato spotted wilt was the most important disease in the OS, resulting in smaller plant development, number of flower clusters and yield. In the CS, the disease was kept under control, and the population of thrips, the virus vector, occurred at lower levels than in the OS. Variety Santa Clara presented greater incidence of the viral disease, and for this reason had a poorer performance than 'Débora', especially in the OS. Occurrence of Liriomyza spp. was significantly smaller in the OS, possibly because of the greater frequency of Chrysoperla. The CS had smaller incidence of leaf spots caused by Septoria lycopersici and Xanthomonas vesicatoria. However, early blight and fruit rot caused by Alternaria solani occurred in larger numbers. No differences were observed with regard to the communities of fungi and bacteria in the phylloplane, and to the occurrence of weeds

Giant magnetothermopower of magnon-assisted transport in ferromagnetic tunnel junctions

We present a theoretical description of the thermopower due to magnon-assisted tunneling in a mesoscopic tunnel junction between two ferromagnetic metals. The thermopower is generated in the course of thermal equilibration between two baths of magnons, mediated by electrons. For a junction between two ferromagnets with antiparallel polarizations, the ability of magnon-assisted tunneling to create thermopower $S_{AP}$ depends on the difference between the size $\Pi_{\uparrow, \downarrow}$ of the majority and minority band Fermi surfaces and it is proportional to a temperature dependent factor $(k_{B}T/\omega_{D})^{3/2}$ where $\omega_{D}$ is the magnon Debye energy. The latter factor reflects the fractional change in the net magnetization of the reservoirs due to thermal magnons at temperature $T$ (Bloch's $T^{3/2}$ law). In contrast, the contribution of magnon-assisted tunneling to the thermopower $S_P$ of a junction with parallel polarizations is negligible. As the relative polarizations of ferromagnetic layers can be manipulated by an external magnetic field, a large difference $\Delta S = S_{AP} - S_P \approx S_{AP} \sim - (k_B/e) f (\Pi_{\uparrow},\Pi_{\downarrow}) (k_BT/\omega_{D})^{3/2}$ results in a magnetothermopower effect. This magnetothermopower effect becomes giant in the extreme case of a junction between two half-metallic ferromagnets, $\Delta S \sim - k_B/e$.Comment: 9 pages, 4 eps figure

Quenched chiral logarithms in lattice QCD with exact chiral symmetry

We examine quenched chiral logarithms in lattice QCD with overlap Dirac quark. For 100 gauge configurations generated with the Wilson gauge action at $\beta = 5.8$ on the $8^3 \times 24$ lattice, we compute quenched quark propagators for 12 bare quark masses. The pion decay constant is extracted from the pion propagator, and from which the lattice spacing is determined to be 0.147 fm. The presence of quenched chiral logarithm in the pion mass is confirmed, and its coefficient is determined to be $\delta = 0.203 \pm 0.014$, in agreement with the theoretical estimate in quenched chiral perturbation theory. Further, we obtain the topological susceptibility of these 100 gauge configurations by measuring the index of the overlap Dirac operator. Using a formula due to exact chiral symmetry, we obtain the $\eta'$ mass in quenched chiral perturbation theory, $m_{\eta'} = (901 \pm 64)$ Mev, and an estimate of $\delta = 0.197 \pm 0.027$, which is in good agreement with that determined from the pion mass.Comment: 24 pages, 6 EPS figures; v2: some clarifications added, to appear in Physical Review

Quenched Lattice QCD with Domain Wall Fermions and the Chiral Limit

Quenched QCD simulations on three volumes, $8^3 \times$, $12^3 \times$ and $16^3 \times 32$ and three couplings, $\beta=5.7$, 5.85 and 6.0 using domain wall fermions provide a consistent picture of quenched QCD. We demonstrate that the small induced effects of chiral symmetry breaking inherent in this formulation can be described by a residual mass (\mres) whose size decreases as the separation between the domain walls ($L_s$) is increased. However, at stronger couplings much larger values of $L_s$ are required to achieve a given physical value of \mres. For $\beta=6.0$ and $L_s=16$, we find \mres/m_s=0.033(3), while for $\beta=5.7$, and $L_s=48$, \mres/m_s=0.074(5), where $m_s$ is the strange quark mass. These values are significantly smaller than those obtained from a more naive determination in our earlier studies. Important effects of topological near zero modes which should afflict an accurate quenched calculation are easily visible in both the chiral condensate and the pion propagator. These effects can be controlled by working at an appropriately large volume. A non-linear behavior of $m_\pi^2$ in the limit of small quark mass suggests the presence of additional infrared subtlety in the quenched approximation. Good scaling is seen both in masses and in $f_\pi$ over our entire range, with inverse lattice spacing varying between 1 and 2 GeV.Comment: 91 pages, 34 figure