Exact parent Hamiltonian for the quantum Hall states in a lattice

We study lattice models of charged particles in uniform magnetic fields. We show how longer range hopping can be engineered to produce a massively degenerate manifold of single-particle ground states with wave functions identical to those making up the lowest Landau level of continuum electrons in a magnetic field. We find that in the presence of local interactions, and at the appropriate filling factors, Laughlin's fractional quantum Hall wave function is an exact many-body ground state of our lattice model. The hopping matrix elements in our model fall off as a Gaussian, and when the flux per plaquette is small compared to the fundamental flux quantum one only needs to include nearest and next-nearest neighbor hoppings. We suggest how to realize this model using atoms in optical lattices, and describe observable consequences of the resulting fractional quantum Hall physics.     

Closed Unstretchable Knotless Ribbons and the Wunderlich Functional

In 1962, Wunderlich published the article “On a developable Möbius band,” in which he attempted to determine the equilibrium shape of a free standing Möbius band. In line with Sadowsky’s pioneering works on Möbius bands of infinitesimal width, Wunderlich used an energy minimization principle, which asserts that the equilibrium shape of the Möbius band has the lowest bending energy among all possible shapes of the band. By using the developability of the band, Wunderlich reduced the bending energy from a surface integral to a line integral without assuming that the width of the band is small. Although Wunderlich did not completely succeed in determining the equilibrium shape of the Möbius band, his dimensionally reduced energy integral is arguably one of the most important developments in the field. In this work, we provide a rigorous justification of the validity of the Wunderlich integral and fully formulate the energy minimization problem associated with finding the equilibrium shapes of closed bands, including both orientable and nonorientable bands with arbitrary number of twists. This includes characterizing the function space of the energy functional, dealing with the isometry and local injectivity constraints, and deriving the Euler–Lagrange equations. Special attention is given to connecting edge conditions, regularity properties of the deformed bands, determination of the parameter space needed to ensure that the deformation is surjective, reduction in isometry constraints, and deriving matching conditions and jump conditions associated with the Euler–Lagrange equations.

     

A-priori testing of alpha regularisation models as subgrid-scale closures for large-eddy simulations

Alpha-type regularisation models provide theoretically attractive subgrid-scale closure approximations for large-eddy simulations of turbulent flow. We adopt the a-priori testing strategy to study three different alpha regularisation models, namely the Navier–Stokes-α model, the Leray-α model, and the Clark-α model. Specifically, we use high-resolution direct numerical simulation data of homogeneous isotropic turbulence to compute the mean subgrid-scale dissipation, the spatial distribution of the subgrid-scale dissipation, and the spatial distribution of elements of the subgrid-scale stress tensor. This is done for different filter parameters and different large-eddy simulation grid resolutions. Predictions of the three regularisation models are compared to the exact values of the subgrid-scale stress tensor, as defined in the filtered Navier–Stokes equations. The potential of the three regularisation models to provide good approximations is quantified using spatial correlation coefficients. Whereas the Clark-α model exhibits the highest spatial correlation coefficients for the subgrid-scale dissipation and the subgrid-scale stress tensor elements, the Leray-α model provides lower correlation coefficients, and the Navier–Stokes-α model exhibits the lowest correlation coefficients of the three models. Our results indicate the presence of an optimal choice of the filter parameter α depending on the large-eddy simulation grid resolution.     

Bacillus licheniformis peptidoglycan characterization by CZE–MS: Assessment with the benchmark RP‐HPLC‐MS method

Peptidoglycan or murein is an essential polymer found in bacterial cell wall. It is a dynamic structure that is continuously remodeled or modified during bacterial cell growth or in presence of cell wall stresses. These modifications are still poorly understood mainly due to the peptidoglycan, which is rather non‐soluble, and the difficulties to separate the hydrophilic glycopeptides (muropeptides) by reversed phase liquid chromatography, generated by the enzymatic digestion using mutanolysin, an N‐acetyl‐muramidase, cleaving the β_1→4 bound between N‐acetylglucosamine and N‐acetylmuramic acid. Here, we report the use of CZE–MS for an easy and fast screening of muropeptides generated by the action of muramidase on the Bacillus licheniformis cell wall. Electron transfer and CID–MS were also used to unambiguously identify and localize the presence or the absence of amidation and acetylation moieties on muropeptide variants. The reference method to analyse muropeptides by reversed phase chromatography was also tested and the advantages and disadvantages of both methods were evaluated.     

Crystal structure of an antiviral ankyrin targeting the HIV-1 capsid and molecular modeling of the ankyrin-capsid complex

Ankyrins are cellular repeat proteins, which can be genetically modified to randomize amino-acid residues located at defined positions in each repeat unit, and thus create a potential binding surface adaptable to macromolecular ligands. From a phage-display library of artificial ankyrins, we have isolated Ank^GAG1D4, a trimodular ankyrin which binds to the HIV-1 capsid protein N-terminal domain (NTD^CA) and has an antiviral effect at the late steps of the virus life cycle. In this study, the determinants of the Ank^GAG1D4-NTD^CA interaction were analyzed using peptide scanning in competition ELISA, capsid mutagenesis, ankyrin crystallography and molecular modeling. We determined the Ank^GAG1D4 structure at 2.2 Å resolution, and used the crystal structure in molecular docking with a homology model of HIV-1 capsid. Our results indicated that NTD^CA alpha-helices H1 and H7 could mediate the formation of the capsid-Ank^GAG1D4 binary complex, but the interaction involving H7 was predicted to be more stable than with H1. Arginine-18 (R18) in H1, and R132 and R143 in H7 were found to be the key players of the Ank^GAG1D4-NTD^CA interaction. This was confirmed by R-to-A mutagenesis of NTD^CA, and by sequence analysis of trimodular ankyrins negative for capsid binding. In Ank^GAG1D4, major interactors common to H1 and H7 were found to be S45, Y56, R89, K122 and K123. Collectively, our ankyrin-capsid binding analysis implied a significant degree of flexibility within the NTD^CA domain of the HIV-1 capsid protein, and provided some clues for the design of new antivirals targeting the capsid protein and viral assembly.     

Ab initio study of ladder-type polymers: Polythiophene and polypyrrole

An ab initio study of four polymers, polythiophene, polypyrrole, ladder-type polythiophene, and ladder-type polypyrrole is presented. Upon an analysis of the variation of the band gap when comparing the non-ladder and the ladder-type polymers, a discrepancy is found between the thiophene and the pyrrole polymer families. For polythiophene, the ladder-type polymer has a larger band gap than the non-ladder polymer whereas the opposite is found for the pyrrole polymers. This difference is explained in terms of the competition between the bond length alternation and the effect of the charge density distribution in the carbon backbone.