Superconducting Correlations in Metallic Nanoparticles: Exact Solution of the BCS Model by the Algebraic Bethe Ansatz

Superconducting pairing of electrons in nanoscale metallic particles with discrete energy levels and a fixed number of electrons is described by the reduced Bardeen, Cooper, and Schrieffer model Hamiltonian. We show that this model is integrable by the algebraic Bethe ansatz. The eigenstates, spectrum, conserved operators, integrals of motion, and norms of wave functions are obtained. Furthermore, the quantum inverse problem is solved, meaning that form factors and correlation functions can be explicitly evaluated. Closed form expressions are given for the form factors and correlation functions that describe superconducting pairing.

A demonstration of artificial dissipation effects in some finite volume solution methods for the Navier-Stokes equations

The artificial dissipation effects in some solutions obtained with a Navier-Stokes flow solver are demonstrated. The solvers were used to calculate the flow of an artificially dissipative fluid, which is a fluid having dissipative properties which arise entirely from the solution method itself. This was done by setting the viscosity and heat conduction coefficients in the Navier-Stokes solvers to zero everywhere inside the flow, while at the same time applying the usual no-slip and thermal conducting boundary conditions at solid boundaries. An artificially dissipative flow solution is found where the dissipation depends entirely on the solver itself. If the difference between the solutions obtained with the viscosity and thermal conductivity set to zero and their correct values is small, it is clear that the artificial dissipation is dominating and the solutions are unreliable.

Using the level set method to model endogenous lava dome growth

Modeling volcanic phenomena is complicated by free-surfaces often supporting large rheological gradients. Analytical solutions and analogue models provide explanations for fundamental characteristics of lava flows. But more sophisticated models are needed, incorporating improved physics and rheology to capture realistic events. To advance our understanding of the flow dynamics of highly viscous lava in Peléean lava dome formation, axi-symmetrical Finite Element Method (FEM) models of generic endogenous dome growth have been developed. We use a novel technique, the level-set method, which tracks a moving interface, leaving the mesh unaltered. The model equations are formulated in an Eulerian framework. In this paper we test the quality of this technique in our numerical scheme by considering existing analytical and experimental models of lava dome growth which assume a constant Newtonian viscosity. We then compare our model against analytical solutions for real lava domes extruded on Soufrière, St. Vincent, W.I. in 1979 and Mount St. Helens, USA in October 1980 using an effective viscosity. The level-set method is found to be computationally light and robust enough to model the free-surface of a growing lava dome. Also, by modeling the extruded lava with a constant pressure head this naturally results in a drop in extrusion rate with increasing dome height, which can explain lava dome growth observables more appropriately than when using a fixed extrusion rate. From the modeling point of view, the level-set method will ultimately provide an opportunity to capture more of the physics while benefiting from the numerical robustness of regular grids.

Effect of Mn deficiency and legume inoculation on rhizosphere pH in highly alkaline soils

Although plant growth is often limited at high pH, little is known about root-induced changes in the rhizospheres of plants growing in alkaline soils. The effect of Mn deficiency in Rhodes grass (Chloris gayana cv. Pioneer) and of legume inoculation in lucerne (Medicago sativa L. cv. Hunter River), on the rhizosphere pH of plants grown in highly alkaline bauxite residue was investigated. Rhizosphere pH was measured quantitatively, with a micro pH electrode, and qualitatively, with an agar/pH indicator solution. Manganese deficiency in Rhodes grass increased root-induced acidification of the rhizosphere in a soil profile in which N was supplied entirely as NO3-. Rhizosphere pH in the Mn deficient plants was up to 1.22 pH units lower than that of the bulk soil, while only 0.90 to 0.62 pH units lower in plants supplied with adequate Mn. When soil N was supplied entirely as NO3-, rhizosphere acidification was more efficient in inoculated lucerne (1.75 pH unit decrease) than in non-inoculated lucerne (1.16 pH unit decrease). This difference in capacity to lower rhizosphere pH is attributable to the ability of the inoculated lucerne to fix atmospheric N2 rather than relying on the soil N (NO3 ) reserves as the non-inoculated plants. Rhizosphere acidification in both Rhodes grass and lucerne was greatest in the meristematic root zone and least in the maturation root zone.

Control of nutrient solutions for studies at high pH

Little is known about factors effecting plant growth at high pH, with research often limited by the inability to separate nutritional deficiencies and HCO3- toxicity from the direct limitations imposed under high pH conditions. Various methods of controlling dilute nutrient solutions for studies at high pH were investigated. For short-term studies, it was found that a solution without Cu, Fe, Mn and Zn and aerated with CO2 depleted air, greatly reduced nutrient precipitation at high pH, thus eliminating nutritional differences between treatments. Manual pH adjustment and the use of ion exchange resins as pH buffers were unsuitable methods of pH control. However, pH control by automated titration had little effect on solution composition while maintaining constant pH. The system described is suitable for studies in which the pH of the bulk nutrient solution must be maintained. The system was used to examine OH- toxicity in mungbeans (Vigna radiata (L.) Wilczek cv. Emerald), with root length reduced at a bulk solution pH of 8.5 and greater.

Rhizotoxicity of aluminate and polycationic aluminium at high pH

Although monomeric Al species are often toxic in acidic soils, the effects of the aluminate ion (Al(OH)4-) on roots grown in alkaline media are still unclear. Dilute, alkaline (pH 9.5) nutrient solutions were used to investigate the effects of Al(OH)4- on root growth of mungbean (Vigna radiata L.). Root growth was reduced by 13 % after 3 d growth in solutions with an Al(OH)4- activity of 16 μM and no detectable polycationic Al (Al13). This decrease in root growth was associated with the formation of lesions on the root tips (due to the rupturing of the epidermal and outer cortical cells) and a slight limitation to root hair growth (particularly on the lateral roots). When roots displaying these symptoms were transferred to fresh Al(OH)4- solutions for a further 12 h, no root tip lesions were observed and root hair growth on the lateral roots improved. The symptoms were similar to those induced by Al13 at concentrations as low as 0.50 μM Al which are below the detection limit of the ferron method. Thus, Al(OH)4- is considered to be non-toxic, with the observed reduction in root growth in solutions containing Al(OH)4- due to the gradual formation of toxic Al13 in the bulk nutrient solution resulting from the acidification of the alkaline nutrient solution by the plant roots.

Effect of pH on Na induced Ca deficiency

Although it is well known that high Na concentrations induce Ca deficiency in acidic conditions, the effect of high pH on this competitive mechanism is not so well understood. The effect of Ca activity ratio (CAR) and pH on the Ca uptake of mungbeans (Vigna radiata (L.) Wilczek cv. Emerald) and Rhodes grass (Chloris gayana cv. Pioneer) in Na dominated solution cultures and in soil was investigated. Changes in pH in the alkaline range were shown not to affect the critical CAR of 0.024 (corresponding to 90 % relative root length) for mungbeans grown in solution culture. Results from soil grown mungbeans confirmed those from solution culture, with a critical CAR of 0.025. A critical CAR of 0.034 was also established for soil grown Rhodes grass. The similarity of critical values established for mungbeans and Rhodes grass in solution culture and soil justifies the use of both solution culture and soil solution measurement as techniques for studying plant growth and limitations across plant species.

Solution structure of robustoxin, the lethal neurotoxin from the funnel-web spider Atrax robustus

The solution structure of robustoxin, the lethal neurotoxin from the Sydney funnel-web spider Atrax robustus, has been determined from 2D H-1 NMR data, Robustoxin is a polypeptide of 42 residues cross-linked by four disulphide bonds, the connectivities of which were determined from NMR data and trial structure calculations to be 1-15, 8-20, 14-31 and 16-42 (a 1-4/2-6/3-7/5-8 pattern), The structure consists of a small three-stranded, anti-parallel beta-sheet and a series of interlocking gamma-turns at the C-terminus. It also contains a cystine knot, thus placing it in the inhibitor cystine knot motif family of structures, which includes the omega-conotoxins and a number of plant and animal toxins and protease inhibitors. Robustoxin contains three distinct charged patches on its surface, and an extended loop that includes several aromatic and non-polar residues, Both of these structural features may play a role in its binding to the voltage-gated sodium channel. (C) 1997 Federation of European Biochemical Societies.

The expression of messenger RNAs coding for growth factors, their receptors, and eph-class receptor tyrosine kinases in normal and ototoxically damaged chick cochleae

Messenger RNAs coding for growth factors and receptor tyrosine kinases were measured by quantitative competitive and by semi-quantitative reverse-transcription polymerase chain reaction in whole and dissected chick inner ears. The fibroblast growth factor (FGF) receptor 1 chick embryonic kinase (CEK) 1 was expressed in all structures examined (otocyst, hatchling whole cochlea, cochlear nerve ganglion, and cochlear and vestibular sensory epithelia), although slightly more heavily in the otocyst. The related fibroblast growth factor receptors CEK 2 and 3 were preferentially expressed in the nerve ganglion and in the vestibular sensory epithelium, respectively. FGF 1 mRNA was low in early development, increasing to mature levels at around embryonic age 11 days, while FGF2, mRNA was expressed at constant levels at all ages. In response to ototoxic damage, FGF1 mRNA levels were increased in the early damaged cochlear sensory epithelium. Immunohistochemistry for CEK1 showed that normal hair cells expressed the receptor heavily on the hair cell stereocilia, while with early damage, CEK1 came to be expressed heavily on the apical surfaces of the supporting cells. In normal chicks, the CEK4 and CEK8 eph-class receptor tyrosine kinases were expressed relatively heavily by the cochlear nerve ganglion, and CEK10 was expressed relatively heavily by the cochlear hair cell sensory epithelium. The results suggest that the FGF system may be involved in the response of the cochlear epithelium to ototoxic damage. The eph-class receptor tyrosine kinase CEK10 may be involved in cell interactions in the cochlear sensory epithelium, while CEK4 and CEK8 may play a role in the cochlear innervation.