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.

Solute transport by surface runoff from low-angle slopes: theory and application

The removal of chemicals in solution by overland how from agricultural land has the potential to be a significant source of chemical loss where chemicals are applied to the soil surface, as in zero tillage and surface-mulched farming systems. Currently, we lack detailed understanding of the transfer mechanism between the soil solution and overland flow, particularly under field conditions. A model of solute transfer from soil solution to overland flow was developed. The model is based on the hypothesis that a solute is initially distributed uniformly throughout the soil pore space in a thin layer at the soil surface. A fundamental assumption of the model is that at the time runoff commences, any solute at the soil surface that could be transported into the soil with the infiltrating water will already have been convected away from the area of potential exchange. Solute remaining at the soil surface is therefore not subject to further infiltration and may be approximated as a layer of tracer on a plane impermeable surface. The model fitted experimental data very well in all but one trial. The model in its present form focuses on the exchange of solute between the soil solution and surface water after the commencement of runoff. Future model development requires the relationship between the mass transfer parameters of the model and the time to runoff: to be defined. This would enable the model to be used for extrapolation beyond the specific experimental results of this study. The close agreement between experimental results and model simulations shows that the simple transfer equation proposed in this study has promise for estimating solute loss to surface runoff. Copyright (C) 2000 John Wiley & Sons, Ltd.

In vivo protein cyclization promoted by a circularly permuted Synechocystis sp PCC6803 DnaB mini-intein

A synthetic Synechocystis sp. PCC6803 DnaB split mini-intein gene was constructed for the in vivo cyclization of recombinant proteins expressed in Escherichia coli. The system was used to cyclize the NH2-terminal domain of E. coli DnaB, the structure of which had been determined previously by NMR spectroscopy. Cyclization was found to proceed efficiently, with little accumulation of precursor, and the product was purified in high yield. The solution structure of cyclic DnaB-N is not significantly different from that of linear DnaB-N and it unfolds reversibly at temperatures similar to14 degreesC higher. Improved hydrogen bonding was observed in the first and last helices, and the length of the last helix was increased, while the 9-amino acid linker used to join the NH2 and COOH termini was found to be highly mobile. The measured thermodynamic stabilization of the structure (DeltaDeltaG approximate to 2 kcal/mol) agrees well with the value estimated from the reduced conformational entropy in the unfolded form. Simple polymer theory can be used to predict likely free energy changes resulting from protein cyclization and how the stabilization depends on the size of the protein and the length of the linker used to connect the termini.

A director theory for visco-elastic folding instabilities in multilayered rock

A model for finely layered visco-elastic rock proposed by us in previous papers is revisited and generalized to include couple stresses. We begin with an outline of the governing equations for the standard continuum case and apply a computational simulation scheme suitable for problems involving very large deformations. We then consider buckling instabilities in a finite, rectangular domain. Embedded within this domain, parallel to the longer dimension we consider a stiff, layered beam under compression. We analyse folding up to 40% shortening. The standard continuum solution becomes unstable for extreme values of the shear/normal viscosity ratio. The instability is a consequence of the neglect of the bending stiffness/viscosity in the standard continuum model. We suggest considering these effects within the framework of a couple stress theory. Couple stress theories involve second order spatial derivatives of the velocities/displacements in the virtual work principle. To avoid C-1 continuity in the finite element formulation we introduce the spin of the cross sections of the individual layers as an independent variable and enforce equality to the spin of the unit normal vector to the layers (-the director of the layer system-) by means of a penalty method. We illustrate the convergence of the penalty method by means of numerical solutions of simple shears of an infinite layer for increasing values of the penalty parameter. For the shear problem we present solutions assuming that the internal layering is oriented orthogonal to the surfaces of the shear layer initially. For high values of the ratio of the normal-to the shear viscosity the deformation concentrates in thin bands around to the layer surfaces. The effect of couple stresses on the evolution of folds in layered structures is also investigated. (C) 2002 Elsevier Science Ltd. All rights reserved.

Stability property of matchings is a natural solution concept in coalitional market games

Stability of matchings was proved to be a new cooperative equilibrium concept in Sotomayor (Dynamics and equilibrium: essays in honor to D. Gale, 1992). That paper introduces the innovation of treating as multi-dimensional the payoff of a player with a quota greater than one. This is done for the many-to-many matching model with additively separable utilities, for which the stability concept is defined. It is then proved, via linear programming, that the set of stable outcomes is nonempty and it may be strictly bigger than the set of dual solutions and strictly smaller than the core. The present paper defines a general concept of stability and shows that this concept is a natural solution concept, stronger than the core concept, for a much more general coalitional game than a matching game. Instead of mutual agreements inside partnerships, the players are allowed to make collective agreements inside coalitions of any size and to distribute his labor among them. A collective agreement determines the level of labor at which the coalition operates and the division, among its members, of the income generated by the coalition. An allocation specifies a set of collective agreements for each player.

The pareto-stability concept is a natural solution concept for discrete matching markets with indifferences

In a decentralized setting the game-theoretical predictions are that only strong blockings are allowed to rupture the structure of a matching. This paper argues that, under indifferences, also weak blockings should be considered when these blockings come from the grand coalition. This solution concept requires stability plus Pareto optimality. A characterization of the set of Pareto-stable matchings for the roommate and the marriage models is provided in terms of individually rational matchings whose blocking pairs, if any, are formed with unmatched agents. These matchings always exist and give an economic intuition on how blocking can be done by non-trading agents, so that the transactions need not be undone as agents reach the set of stable matchings. Some properties of the Pareto-stable matchings shared by the Marriage and Roommate models are obtained.

On recent developments in the theory of abstract differential equations with fractional derivatives

This note is motivated from some recent papers treating the problem of the existence of a solution for abstract differential equations with fractional derivatives. We show that the existence results in [Agarwal et al. (2009) [1], Belmekki and Benchohra (2010) [2], Darwish et al. (2009) [3], Hu et al. (2009) [4], Mophou and N`Guerekata (2009) [6,7], Mophou (2010) [8,9], Muslim (2009) [10], Pandey et al. (2009) [11], Rashid and El-Qaderi (2009) [12] and Tai and Wang (2009) [13]] are incorrect since the considered variation of constant formulas is not appropriate. In this note, we also consider a different approach to treat a general class of abstract fractional differential equations. (C) 2010 Elsevier Ltd. All rights reserved.

Odorant-induced currents in intact patches from rat olfactory receptor neurons: Theory and experiment

Odorant-induced currents in mammalian olfactory receptor neurons have proved difficult to obtain reliably using conventional whole-cell recording. By using a mathematical model of the electrical circuit of the patch and rest-of-cell, we demonstrate how cell-attached patch measurements can be used to quantitatively analyze responses to odorants or a high (100 mM) K+ solution. High K+ induced an immediate current flux from cell to pipette, which was modeled as a depolarization of similar to 52 mV, close to that expected from the Nernst equation (56 mV), and no change in the patch conductance. By contrast, a cocktail of cAMP-stimulating odorants induced a current flux from pipette into cell following a significant (4-10 s) delay. This was modeled as an average patch conductance increase of 36 pS and a depolarization of 13 mV, Odorant-induced single channels had a conductance of 16 pS. In cells bathed with no Mg2+ and 0.25 mM Ca2+, odorants induced a current flow from cell to pipette, which was modeled as a patch conductance increase of similar to 115 pS and depolarization of similar to 32 mV, All these results are consistent with cAMP-gated cation channels dominating the odorant response, This approach, which provides useful estimates of odorant-induced voltage and conductance changes, is applicable to similar measurements in any small cells.

Self-defocusing effects in an ethanol solution of chlorophyll

The thermally induced optical nonlinearity in a chlorophyll ethanol solution is examined. A theory is presented which shows good agreement with experiment. The theory models an optically thick but physically thin medium whose only heat transport mechanism is conduction. An average nz was found for the medium which corresponds well with previous results but the thermal medium is shown to be fundamentally different from a Kerr medium.

Time evolution in the unimolecular master equation at low temperatures: full spectral solution with scalable iterative methods and high precision

A new method is presented to determine an accurate eigendecomposition of difficult low temperature unimolecular master equation problems. Based on a generalisation of the Nesbet method, the new method is capable of achieving complete spectral resolution of the master equation matrix with relative accuracy in the eigenvectors. The method is applied to a test case of the decomposition of ethane at 300 K from a microcanonical initial population with energy transfer modelled by both Ergodic Collision Theory and the exponential-down model. The fact that quadruple precision (16-byte) arithmetic is required irrespective of the eigensolution method used is demonstrated. (C) 2001 Elsevier Science B.V. All rights reserved.

Theory and applications of fuzzy Volterra integral equations

Formulations of fuzzy integral equations in terms of the Aumann integral do not reflect the behavior of corresponding crisp models. Consequently, they are ill-adapted to describe physical phenomena, even when vagueness and uncertainty are present. A similar situation for fuzzy ODEs has been obviated by interpretation in terms of families of differential inclusions. The paper extends this formalism to fuzzy integral equations and shows that the resulting solution sets and attainability sets are fuzzy and far better descriptions of uncertain models involving integral equations. The investigation is restricted to Volterra type equations with mildly restrictive conditions, but the methods are capable of extensive generalization to other types and more general assumptions. The results are illustrated by integral equations relating to control models with fuzzy uncertainties.

Exact solution at integrable coupling of a model for the Josephson effect between small metallic grains

A model is introduced for two reduced BCS systems which are coupled through the transfer of Cooper pairs between the systems. The model may thus be used in the analysis of the Josephson effect arising from pair tunneling between two strongly coupled small metallic grains. At a particular coupling strength the model is integrable and explicit results are derived for the energy spectrum, conserved operators, integrals of motion, and wave function scalar products. It is also shown that form factors can be obtained for the calculation of correlation functions. Furthermore, a connection with perturbed conformal field theory is made.

Exact theory of sedimentation equilibrium made useful

The exact description of the thermodynamics of solutions has been used to describe, without approximation, the distribution of all the components of an incompressible solution in a centrifuge cell at sedimentation equilibrium. Thermodynamic parameters describing the interactions between solute components of known molar mass can be obtained by direct analysis of the experimental data. Interpretation of the measured thermodynamic parameters in terms of molecular interactions requires that an arbitrary distinction be made between nonassociative forces, like hard-sphere volume-exclusion and mean-field electrostatic repulsion or attraction, and specific short-range forces of association that give rise to the formation of molecular aggregates. Provided the former can be accounted for adequately, the effects of the latter can be elucidated in the form of good estimates of the equilibrium constants for the reactions of aggregation.

Applying complex network theory to the understanding of high-aspect-ratio carbon-filled composites

This work demonstrates that the theoretical framework of complex networks typically used to study systems such as social networks or the World Wide Web can be also applied to material science, allowing deeper understanding of fundamental physical relationships. In particular, through the application of the network theory to carbon nanotubes or vapour-grown carbon nanofiber composites, by mapping fillers to vertices and edges to the gap between fillers, the percolation threshold has been predicted and a formula that relates the composite conductance to the network disorder has been obtained. The theoretical arguments are validated by experimental results from the literature.

Mix design process of polyester polymer mortars modified with recycled GFRP waste materials

In this study, the effect of incorporation of recycled glass fibre reinforced plastics (GFRP) waste materials, obtained by means of shredding and milling processes, on mechanical behaviour of polyester polymer mortars (PM) was assessed. For this purpose, different contents of GFRP recyclates, between 4% up to 12% in weight, were incorporated into polyester PM materials as sand aggregates and filler replacements. The effect of the addition of a silane coupling agent to resin binder was also evaluated. Applied waste material was proceeding from the shredding of the leftovers resultant from the cutting and assembly processes of GFRP pultrusion profiles. Currently, these leftovers as well as non-conform products and scrap resulting from pultrusion manufacturing process are landfilled, with additional costs to producers and suppliers. Hence, besides the evident environmental benefits, a viable and feasible solution for these wastes would also conduct to significant economic advantages. Design of experiments and data treatment were accomplish by means of full factorial design approach and analysis of variance ANOVA. Experimental results were promising toward the recyclability of GFRP waste materials as partial replacement of aggregates and reinforcement for PM materials, with significant improvements on mechanical properties of resultant mortars with regards to waste-free formulations.