Cohomogeneity one actions on noncompact symmetric spaces of rank one

We classify, up to orbit equivalence, all cohomogeneity one actions on the hyperbolic planes over the complex, quaternionic and Cayley numbers, and on the complex hyperbolic spaces , . For the quaternionic hyperbolic spaces , , we reduce the classification problem to a problem in quaternionic linear algebra and obtain partial results. For real hyperbolic spaces, this classification problem was essentially solved by Élie Cartan.

     

Conductance and Kondo effect in a controlled single-atom contact

The tip of a low-temperature scanning tunneling microscope is brought into contact with individual cobalt atoms adsorbed on Cu(100). A smooth transition from the tunneling regime to contact occurs at a conductance of G approximately G0. Spectroscopy in the contact regime, i.e., at currents in a muA range, was achieved and indicated a significant change of the Kondo temperature TK. Calculations indicate that the proximity of the tip shifts the cobalt d band and thus affects TK.     

Controlled contact to a C60 molecule

The tip of a low-temperature scanning tunneling microscope is approached towards a C60 molecule adsorbed at a pentagon-hexagon bond on Cu(100) to form a tip-molecule contact. The conductance rapidly increases to approximately 0.25 conductance quanta in the transition region from tunneling to contact. Ab-initio calculations within density functional theory and nonequilibrium Green's function techniques explain the experimental data in terms of the conductance of an essentially undeformed C60. The conductance in the transition region is affected by structural fluctuations which modulate the tip-molecule distance.     

Electronic superstructure of lead phthalocyanine on lead islands

Lead phthalocyanine (PbPc) deposited on lead islands on Ag(111) forms two-dimensional crystals of densely packed molecules. For particular orientations, the molecular arrays exhibit an electronic superstructure with an extraordinarily large unit cell. The molecules induce a shift of quantum well states, which are confined to the Pb islands. Patterns formed by PbPc on Ag(111) are drastically different.     

Influence of alkyl chain length and molecular weight on the surface functionalization via adsorption/entrapment with biocidal cationic block copolymers

Polysulfone (PSf) films were functionalized with block copolymers containing poly(n-butyl acrylate) (PBA) as anchor block which is able to firmly tether the biocidal quaternized poly(2-dimethylaminoethyl methacrylate) (PDMAEMAq) to the surface. Block copolymers were synthesized using sequential atom transfer radical polymerization (ATRP) and quaternization with methyl and/or octyl groups rendered the polymers biocidal. Upon reversible swelling of the PSf surface layer in the adsorption/entrapment process, incorporation of the block copolymer is anticipated to be stable; homopolymers, i.e., methyl- or octyl-quaternized PDMAEMAq, were investigated for comparison. The addition of salt to the functionalization solution containing the block copolymer induced a decrease in the critical micelle concentration and lead to higher functionalization efficiency. The impact of intra- or interchain interactions in these aggregates on adsorption and firm entrapment in PSf was determined by measuring contact angle, charge density and zeta potential.     

Two-step hybrid conservative remapping for multimaterial arbitrary Lagrangian–Eulerian methods

We present a new hybrid conservative remapping algorithm for multimaterial Arbitrary Lagrangian–Eulerian (ALE) methods. The hybrid remapping is performed in two steps. In the first step, only nodes of the grid that lie inside subdomains occupied by single materials are moved. At this stage, computationally cheap swept-region remapping is used. In the second step, nodes that are vertices of mixed cells (cells containing several materials) and vertices of some cells in a buffer zone around mixed cells are moved. At this stage, intersection-based remapping is used. The hybrid algorithm results in computational expense that lies between swept-region and intersection-based remapping We demonstrate the performance of our new method for both structured and unstructured polygonal grids in two dimensions, as well as for cell-centered and staggered discretizations.     

Parton energy loss in strongly coupled AdS/CFT

This is a brief review of the theory and phenomenology of parton energy loss in strongly coupled field theories with a gravity dual and its comparison with parton energy loss in QCD at weak coupling.     

Antimicrobial porous hybrids consisting of bacterial nanocellulose and silver nanoparticles

The increasing resistance of pathogens and bacteria is a serious problem in the medical treatment of wounds and injuries. Therefore, new therapeutic agents are not solely based on antibiotics, but also on the use of antimicrobial metal nanoparticles. In this paper we present an innovative method to prepare porous hybrids consisting of bacterial nanocellulose (BNC) and silver nanoparticles (AgNPs). The stepwise modification is based on fairly simple chemical reactions already described for two-dimensional cellulose films. We transferred this method to the three-dimensional, porous network of BNC leading to an antimicrobial activation of its surface. Compared to former approaches, the ultrafine network structure of BNC is less damaged by using mild chemicals. The amount and distribution of the AgNPs on the modified BNC was investigated using scanning electron microscopy. The AgNPs are firmly immobilized on the top and bottom surface of the BNC by chemical interactions. Their size and quantity increase with an increasing concentration of AgNO₃ and extended reaction time in the AgNO₃ solution. A strong antimicrobial activity of the BNC-AgNP hybrids against Escherichia coli was detected. Furthermore, agar diffusion tests confirmed that this activity is restricted to the modified dressing itself, avoiding a release of NPs into the wound. Therefore, the produced hybrids could be potentially suited as novel antimicrobial wound dressings.     

Weighted divisor sums and Bessel function series,II

On page 335 in his lost notebook, Ramanujan recorded without proofs two identities involving finite trigonometric sums and doubly infinite series of Bessel functions. In each case, there are three possible interpretations for the double series. In an earlier paper, two of the present authors proved the first identity under one possible interpretation. In the present paper, the second identity is proved under a similar interpretation, with one additional assumption. Moreover, under a second interpretation, entirely different proofs of both identities, depending on weighted (or twisted) divisor sums, are offered. The two identities are intimately connected with the classical circle and divisor problems, respectively.