6,523 research outputs found
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
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