Signature of Spin Collective Mode in Local Tunneling Spectra of a d-wave Superconductor

We consider the influence of magnetic excitations on the local density of states in the d-wave superconductor. The magnetic susceptibility is calculated within the renormalized $t-t'-J$ model and its influence on the quasiparticle self-energy is considered using a minimal model originally proposed by Polkovnikov {\it et al.}[cond-mat/0203176]. We find the local density of states possess periodic components both along $(\pi,0)$ and $(\pi,\pi)$ directions with the associated wavevectors changing in magnitude as the quasiparticle energy is varied. Comparison with the STM experiment reveals that the calculated LDOS modulation is inconsistent with the measured data.Comment: Two figures separately attached as .jpg file

Defect and anisotropic gap induced quasi-one-dimensional modulation of local density of states in YBa2_2Cu3_3O7−δ_{7-\delta}

Motivated by recent angle-resolved photoemission spectroscopy (ARPES) measurement that superconducting YBa$_2$Cu$_3$O$_{7-\delta}$ (YBCO) exhibits a $d_{x^2-y^2} + s$-symmetry gap, we show possible quasi-one-dimensional modulations of local density of states in YBCO. These aniostropic gap and defect induced stripe structures are most conspicuous at higher biases and arise due to the nesting effect associated with a Fermi liquid. Observation of these spectra by scanning tunneling microscopy (STM) would unify the picture among STM, ARPES, and inelastic neutron scattering for YBCO.Comment: 4 pages, 4 figure

α-Domination

AbstractLet G=(V,E) be any graph with n vertices, m edges and no isolated vertices. For some α with 0<α⩽1 and a set S⊆V, we say that S is α-dominating if for all v∈V−S,|N(v)∩S|⩾α|N(v)|. The size of a smallest such S is called the α-domination number and is denoted by γα(G). In this paper, we introduce α-domination, discuss bounds for γ1/2(G) for the King's graph, and give bounds for γα(G) for a general α, 0<α⩽1. Furthermore, we show that the problem of deciding whether γα(G)⩽k is NP-complete

Seasonal Variation in Composition of Winery Wastewater in the Breede River Valley with Respect to Classical Water Quality Parameters

The annual wastewater quality dynamics of a winery from which wastewater was sourced for a fieldexperiment investigating the dilution of winery wastewater for vineyard irrigation were determined.Annual mean monthly pH ranged from 4.2 to 6.8 and was lower during grape harvest than in winter.Electrical conductivity (EC) increased from the start of harvest (February) and reached a maximumin May, followed by a decline to a minimum in August. The increase in EC probably originated fromcleaning agents used in the winery, as well as K+ in the grape lees and spillage from the grape fermentationprocess. With the exception of August, EC exceeded the critical value of 0.75 dS/m, which is the salinitythreshold for water used for grapevine irrigation. The mean monthly chemical oxygen demand (COD)level increased from January and was highest at peak harvest (March). The K+ and Na+ levels in the winerywastewater increased from February to May. The sodium adsorption ratio (SAR) ranged from 2.4 to 9.0and increased from January to June. Although COD concentration in winery wastewater is the preferredindicator of water quality for the South African wine industry, it did not provide a reliable indication ofsuitability for irrigation. However, EC was strongly determined by the K+ concentration. This was to beexpected, since K+ is usually the most abundant cation in winery wastewater. Therefore, EC would be amore reliable indicator of winery wastewater quality than COD concentration, particularly with regard tothe concentrations of cations such as K+ and Na+

An Assessment of Winery Wastewater Diluted for Irrigation of Grapevines in the Breede River Valley with Respect to Water Quality and Nutrient Load

Possible re-use of winery wastewater for irrigation was investigated in a field trial with micro-sprinklerirrigatedCabernet Sauvignon/99 Richter in the Breede River Valley region of South Africa. Irrigation withwinery wastewater diluted to 100, 250, 500, 1 000, 1 500, 2 000, 2 500 and 3 000 mg/L chemical oxygen demand(COD), respectively, was compared to irrigation with raw river water. Since the pH was lower than 6, thediluted wastewater could cause nutrient toxicity. The diluted winery wastewater did not pose any salinityhazard, as the electrical conductivity was well below 2 dS/m. For the given range of dilutions, the sodiumadsorption ratio never exceeded 10, which indicates that the water posed no sodicity hazard. Sodium andCl- never exceeded 115 and 150 mg/L, the respective upper thresholds for grapevines. With the exceptionof N, levels of H2PO4-, K+, Na+, Ca2+, Mg2+, HCO3-, SO42- and B3+ in the diluted wastewater increased with adecrease in dilution level. The N load in diluted winery wastewater appeared to be completely inadequateto supply the grapevine’s requirements. In contrast, the P load in the winery wastewater diluted to 2 500mg/L COD and higher would supply more than adequate P if the grape yield amounts to 10 t/ha. Likewise,the dilution of winery wastewater to 250 mg/L COD and higher would supply more than adequate K+ if thegrape yield amounts to 10 t/ha. However, K+ applied via the wastewater will only be beneficial if it is notleached from the root zone during winter

Effect of Irrigation Using Diluted Winery Wastewater on the Chemical Status of a Sandy Alluvial Soil, With Particular Reference to Potassium and Sodium

The re-use of winery wastewater for irrigation was investigated in a field trial with micro-sprinklerirrigated Cabernet Sauvignon/99 Richter in the Breede River Valley region of South Africa. Irrigation with winery wastewater diluted with river water to 100, 250, 500, 1 000, 1 500, 2 000, 2 500 and 3 000 mg/L chemical oxygen demand (COD) was compared to irrigation with river water. No trends were found in soil pH(KCl) and electrical conductivity of the saturated soil extract (ECe ) that were related to the different levels of dilution. However, ECe was considerably higher after the application of diluted winery wastewater irrigations compared to ECe at bud break. This suggests an accumulation of salts from the diluted winery wastewater. Under the prevailing conditions, soil K+ and Na+ increased with a decrease in the dilution of the winery wastewater. Increases in K+ could have a negative impact on wine colour stability should potassium be taken up by the grapevine in sufficient quantities, particularly if soil K+ accumulates to such an extent that it is luxuriously absorbed by grapevines. There were no consistent trends with regard to soil organic C, which indicates that there was too little organic material in the wastewater to have had a positive effect on soil fertility. Furthermore, organic material in the wastewater probably oxidised whenthe soil was aerated between irrigations. Although irrigation with diluted winery wastewater had almost no other effects, element accumulation, particularly with respect to K+ and Na+, might be more prominent in heavier soils or in regions with low winter rainfall

Irrigation of Agricultural Crops with Municipal Wastewater - A Review

Sustainable viticulture is important for socio-economic prosperity in the Western and Northern Cape provinces of South Africa. Limited natural water resources, as well as periodic droughts in these regions necessitate the need to find alternative sources of irrigation water to sustain yield and quality. The large volumes of treated municipal wastewater generated annually holds promise as an alternative water source. Despite various treatment procedures, municipal wastewater may contain high levels of Na+, B3+, Cl- and SO42-, as well as trace elements and heavy metals. However, it often contains essential plant nutrients, e.g. N, P and K+. If treated properly, municipal wastewater may be beneficial when reused for irrigating agricultural crops. Possible benefits include recycling of nutrients, fertiliser savings, the addition of organic material, a reduced pressure on fresh water sources and reduced environmental contamination. However, high salt loads, in particular Na+, can have detrimental effects on soil physical and chemical properties, as well as crop sustainability. Therefore, it is essential to implement measures that will limit damage caused by salinity and/or sodicity. The attenuation and accumulation of toxic substances should also be managed to a minimum. Most of the information regarding treated municipal wastewater has been generated through laboratory studies using simulated wastewater, or in some cases actual wastewater. No studies have yet investigated the impact of irrigation with treated municipal wastewater under the conditions that prevail in South African grape growing regions

Effect of Irrigation with Treated Municipal Wastewater on Vitis vinifera L. cvs. Cabernet Sauvignon and Sauvignon blanc in Commercial Vineyards in the Coastal Region of South Africa - Vegetative Growth, Yield and Juice Characteristics

A long-term trial was conducted in commercial vineyards in the Coastal region of South Africa to assess theimpact of treated municipal wastewater irrigation on vineyards. Cabernet Sauvignon and Sauvignon blancgrapevines were irrigated using treated municipal wastewater from the Potsdam wastewater treatmentworks for 11 years. Grapevines were either rainfed (RF), irrigated with treated municipal wastewater viaa single dripper line (SLD) or received twice the volume of wastewater via a double dripper line (DLD).Grapevine responses were measured from the 2013/14 to 2017/18 seasons. Although high amounts of K+,Na+ and Cl- were applied via wastewater irrigation, it did not result in excessive uptake by plants anddid not affect vegetative growth or yield negatively. Irrigation reduced water constraints throughout thegrowing season compared to RF conditions, particularly for Cabernet Sauvignon. Consequently, SLD andDLD grapevines produced stronger vegetative growth and higher yields compared to RF. Results showedthat the availability of irrigation water (albeit of relatively low quality) in regions where grapevines areusually grown under dryland conditions can increase grapevine productivity whilst maintaining goodfruit quality. However, the water can vary in its availability as well as its quality over a short period oftime. Plant and soil water status should be monitored regularly to avoid over-irrigation. Implementinglow frequency irrigation scheduling with a sufficient leaching fraction will allow adequate time betweenirrigation applications for soils to aerate and organic material to decompose. Irrigation water, soilsand grapevine leaves should be analysed to ensure that chemical parameters conform to recommendedthresholds and norms

The wave-vector power spectrum of the local tunnelling density of states: ripples in a d-wave sea

A weak scattering potential imposed on a $CuO_2$ layer of a cuprate superconductor modulates the local density of states $N(x,\omega)$. In recently reported experimental studies scanning-tunneling maps of $N(x,\omega)$ have been Fourier transformed to obtain a wave-vector power spectrum. Here, for the case of a weak scattering potential, we discuss the structure of this power spectrum and its relationship to the quasi-particle spectrum and the structure factor of the scattering potential. Examples of quasi-particle interferences in normal metals and $s$- and d-wave superconductors are discussed.Comment: 22 pages, 21 figures; enlarged discussion of the d-wave response, to be published in Physical Review

Expansion of Vortex Cores by Strong Electronic Correlation in La2−x_{2-x}Srx_xCuO4_4 at Low Magnetic Induction

The vortex core radius \rv, defined as the peak position of the supercurrent around the vortex, has been determined by muon spin rotation measurements in the mixed state of \lscox for $x=0.13$, 0.15, and 0.19. At lower doping (x=0.13 and 0.15), \rv(T) increases with decreasing temperature T, which is opposite to the behavior predicted by the conventional theory. Moreover, \rv(T\to0) is significantly larger than the Ginsburg-Landau coherence length determined by the upper critical field, and shows a clear tendency to decrease with increasing the doping x. These features can be qualitatively reproduced in a microscopic model involving antiferromagnetic electronic correlations.Comment: 6 pages, 4 figures, to be published in Phys. Rev.