A homomorphism between link and XXZ modules over the periodic Temperley-Lieb algebra

We study finite loop models on a lattice wrapped around a cylinder. A section of the cylinder has N sites. We use a family of link modules over the periodic Temperley-Lieb algebra EPTL_N(\beta, \alpha) introduced by Martin and Saleur, and Graham and Lehrer. These are labeled by the numbers of sites N and of defects d, and extend the standard modules of the original Temperley-Lieb algebra. Beside the defining parameters \beta=u^2+u^{-2} with u=e^{i\lambda/2} (weight of contractible loops) and \alpha (weight of non-contractible loops), this family also depends on a twist parameter v that keeps track of how the defects wind around the cylinder. The transfer matrix T_N(\lambda, \nu) depends on the anisotropy \nu and the spectral parameter \lambda that fixes the model. (The thermodynamic limit of T_N is believed to describe a conformal field theory of central charge c=1-6\lambda^2/(\pi(\lambda-\pi)).) The family of periodic XXZ Hamiltonians is extended to depend on this new parameter v and the relationship between this family and the loop models is established. The Gram determinant for the natural bilinear form on these link modules is shown to factorize in terms of an intertwiner i_N^d between these link representations and the eigenspaces of S^z of the XXZ models. This map is shown to be an isomorphism for generic values of u and v and the critical curves in the plane of these parameters for which i_N^d fails to be an isomorphism are given.Comment: Replacement of "The Gram matrix as a connection between periodic loop models and XXZ Hamiltonians", 31 page

Donor Electron Wave Functions for Phosphorus in Silicon: Beyond Effective Mass Theory

We calculate the electronic wave-function for a phosphorus donor in silicon by numerical diagonalisation of the donor Hamiltonian in the basis of the pure crystal Bloch functions. The Hamiltonian is calculated at discrete points localised around the conduction band minima in the reciprocal lattice space. Such a technique goes beyond the approximations inherent in the effective-mass theory, and can be modified to include the effects of altered donor impurity potentials, externally applied electro-static potentials, as well as the effects of lattice strain. Modification of the donor impurity potential allows the experimentally known low-lying energy spectrum to be reproduced with good agreement, as well as the calculation of the donor wavefunction, which can then be used to calculate parameters important to quantum computing applications.Comment: 10 pages, 5 figure

Refined conformal spectra in the dimer model

Working with Lieb's transfer matrix for the dimer model, we point out that the full set of dimer configurations may be partitioned into disjoint subsets (sectors) closed under the action of the transfer matrix. These sectors are labelled by an integer or half-integer quantum number we call the variation index. In the continuum scaling limit, each sector gives rise to a representation of the Virasoro algebra. We determine the corresponding conformal partition functions and their finitizations, and observe an intriguing link to the Ramond and Neveu-Schwarz sectors of the critical dense polymer model as described by a conformal field theory with central charge c=-2.Comment: 44 page

A Computational Study of the Weak Galerkin Method for Second-Order Elliptic Equations

The weak Galerkin finite element method is a novel numerical method that was first proposed and analyzed by Wang and Ye for general second order elliptic problems on triangular meshes. The goal of this paper is to conduct a computational investigation for the weak Galerkin method for various model problems with more general finite element partitions. The numerical results confirm the theory established by Wang and Ye. The results also indicate that the weak Galerkin method is efficient, robust, and reliable in scientific computing.Comment: 19 page

Surfaces containing a family of plane curves not forming a fibration

We complete the classification of smooth surfaces swept out by a 1-dimensional family of plane curves that do not form a fibration. As a consequence, we characterize manifolds swept out by a 1-dimensional family of hypersurfaces that do not form a fibration.Comment: Author's post-print, final version published online in Collect. Mat

Impact of biofilms in simulated drinking water and urban heat supply systems

Biofouling and biocorrosion were studied in drinking water and heating water systems by forming biofilms on steel and on polymethylmetacrylate. In the drinking water system, biofilm development was more significant on corroded surfaces, suggesting that in these conditions they were largely protected from disinfection, probably because of sheltering and chlorine demand by corrosion products. In the urban heat supply system, results suggest a higher biofilm activity at lower pH. Sulphate-reducing bacteria were detected in the urban heating biofilms, but little corrosion was observed on steel coupons. Results indicate that surface and bulk medium properties, as well as bacterial diversity are determinant parameters when studying biofouling and biocorrosion.Cirius – Danish Centre for International Cooperation and Mobility in Education and Trainin

The effect of dissolved stainless steel alloy elements on the activity and growth of SRB

Sulphate reducing bacteria have an important role in the sulphur cycle, and therefore in wastewater treatment systems. They are able to form biofilms on metallic surfaces, leading to fouling and corrosion problems. These bacteria are among the micro-organisms most frequently implicated in microbial corrosion of iron and ferrous alloys. Alloying elements added to steels for the improvement of their corrosion resistance such as molybdenum and nickel can be dissolved in bulk liquid during the corrosion processes and therefore available to the micro-organisms. That may affect bacterial metabolism and adhesion. In this study, suspended cultures of sulphate reducing bacteria (SRB) were subjected to several nickel concentrations in order to evaluate the effect of the dissolved metal on bacterial metabolism. Simultaneously, SRB biofilms were developed on stainless steel 304 and on polymethylmethacrylate (PMMA) in order to study surface effect on biofilm formation. Results showed that nickel (Ni) in all tested concentrations between 0.006 and 5 mg/L had a positive effect on the growth of Desuljovibrio desulfuricans. Additionally, biofilms formed on stainless steel presented higher metabolic activity, confirmed by sulphate removal and acetate concentration in the effluent stream. Metal elements present in stainless steel may affect SRB activity. This can be the case of nickel that represents around 8% of stainless steel 304 and that had a positive impact on suspended SRB cultures, under the tested concentrations

The influence of surface material on the development of Desulfovibrio desulfuricans biofilms

Sulphate reducing bacteria have an important role in the sulphur cycle, and therefore in wastewater treatment systems. They are able to form biofilms on metallic surfaces, leading to fouling and corrosion problems. Additionally, hydrogen sulphide that is a product of their metabolism can cause serious health risks. In this study, sulphate reducing bacteria (SRB) biofilms were developed on stainless steel 304 and on polycarbonate in order to evaluate surface effect on biofilm formation. Results showed that the biofilm formed on stainless steel presented higher metabolic activity, confirmed by lactate and sulfate removals. Metal elements present in stainless steel may affect SRB activity. This can be the case of nickel that represents around 8% of stainless steel 304. Studies performed with suspended cultures of Desulfovibrio desulfuricans also showed that the presence of nickel in the media had a positive impact on bacterial activity

The influence of nickel on the adhesion ability of Desulfovibrio desulfuricans

The build-up of biofilms on metals surfaces may lead to severe corrosion, especially in the presence of sulphate-reducing bacteria (SRB). To prevent the deterioration of material caused by biofilms it is necessary to understand the processes governing biofilm development including mechanisms of cell adhesion. Additionally, corrosion of metallic surfaces due to bacteria may lead to the dissolution of metallic elements that may further affect adhesion and biofilm development. A study was carried out to evaluate how the presence of nickel in the substrata affects the adhesion ability of Desulfovibrio desulfuricans. The substrata tested were stainless steel 304 (SS), metallic nickel (Ni) and polymethylmetacrylate (PMMA), a non-metallic material used as control. The influence of nickel on SRB growth and its relation to adhesion was also checked. A statistically significant difference in the number of adhered cells to the materials tested was detected, with higher bacterial number on nickel, followed by SS and finally by PMMA. The higher number of SRB adhered to steel compared with PMMA may be explained by differences in hydrophobicity, in roughness and in the electron-acceptor character of the substrata. Additionally, bacterial growth was found to be positively affected by the presence of nickel as revealed by a significant increase in the specific growth rate of SRB in the presence of increased nickel concentrations.Programme Praxis XXI