Some Recent Results on Pair Correlation Functions and Susceptibilities in Exactly Solvable Models

Using detailed exact results on pair-correlation functions of Z-invariant Ising models, we can write and run algorithms of polynomial complexity to obtain wavevector-dependent susceptibilities for a variety of Ising systems. Reviewing recent work we compare various periodic and quasiperiodic models, where the couplings and/or the lattice may be aperiodic, and where the Ising couplings may be either ferromagnetic, or antiferromagnetic, or of mixed sign. We present some of our results on the square-lattice fully-frustrated Ising model. Finally, we make a few remarks on our recent works on the pentagrid Ising model and on overlapping unit cells in three dimensions and how these works can be utilized once more detailed results for pair correlations in, e.g., the eight-vertex model or the chiral Potts model or even three-dimensional Yang-Baxter integrable models become available.Comment: LaTeX2e using iopart.cls, 10 pages, 5 figures (5 eps files), Dunk Island conference in honor of 60th birthday of A.J. Guttman

aFold – using polynomial uncertainty modelling for differential gene expression estimation from RNA sequencing data

Data normalization and identification of significant differential expression represent crucial steps in RNA-Seq analysis. Many available tools rely on assumptions that are often not met by real data, including the common assumption of symmetrical distribution of up- and down-regulated genes, the presence of only few differentially expressed genes and/or few outliers. Moreover, the cut-off for selecting significantly differentially expressed genes for further downstream analysis often depend on arbitrary choices

Effective models for gapped phases of strongly correlated quantum lattice models

We present a robust scheme to derive effective models non-perturbatively for quantum lattice models when at least one degree of freedom is gapped. A combination of graph theory and the method of continuous unitary transformations (gCUTs) is shown to efficiently capture all zero-temperature fluctuations in a controlled spatial range. The gCUT can be used either for effective quasi-particle descriptions or for effective low-energy descriptions in case of infinitely degenerate subspaces. We illustrate the method for 1d and 2d lattice models yielding convincing results in the thermodynamic limit. We find that the recently discovered spin liquid in the Hubbard model on the honeycomb lattice lies outside the perturbative strong-coupling regime. Various extensions and perspectives of the gCUT are discussed.Comment: 6 pages, 5 figures, extended discussion on J2/J1 for the honeycomb Hubbard model and on the properties of different generators for the continuous unitary transformatio

New structural approach for determining load carrying capability of filament wound composite materials

Metal lined boron and graphite composites exhibit high strength and minimum weight, making them superior to aluminum cylindrical shell structures and to steel or aluminum constructed pressure vessels. S glass filament-epoxy resin matrix with aluminum liner is suitable for cryogenic tanks

Cluster magnetic fields from active galactic nuclei

Active galactic nuclei (AGN) found at the centers of clusters of galaxies are a possible source for weak cluster-wide magnetic fields. To evaluate this scenario, we present 3D adaptive mesh refinement MHD simulations of a cool-core cluster that include injection of kinetic, thermal, and magnetic energy via an AGN-powered jet. Using the MHD solver in FLASH 2, we compare several sub-resolution approaches that link the estimated accretion rate as measured on the simulation mesh to the accretion rate onto the central black hole and the resulting feedback. We examine the effects of magnetized outflows on the accretion history of the black hole and discuss the ability of these models to magnetize the cluster medium.Comment: 4 pages, 2 figures, submitted to conference proceedings "The Monster's Fiery Breath: Feedback in Groups, Galaxies, and Clusters

The Influence of AGN Feedback on Galaxy Cluster Observables

Galaxy clusters are valuable cosmological probes. However, cluster mass estimates rely on observable quantities that are affected by complicated baryonic physics in the intracluster medium (ICM), including feedback from active galactic nuclei (AGN). Cosmological simulations have started to include AGN feedback using subgrid models. In order to make robust predictions, the systematics of different implementations and parametrizations need to be understood. We have developed an AGN subgrid model in FLASH that supports a few different black hole accretion models and feedback models. We use this model to study the effect of AGN on X-ray cluster observables and its dependence on model variations.Comment: minor error corrected, to appear in proceedings of the conference "The Monster's Fiery Breath: Feedback in Galaxies, Groups, and Clusters", June 2009, Madison, Wisconsi

Optical properties of 4 A single-walled carbon nanotubes inside the zeolite channels studied from first principles calculations

The structural, electronic, and optical properties of 4 A single-walled carbon nanotubes (SWNTs) contained inside the zeolite channels have been studied based upon the density-functional theory in the local-density approximation (LDA). Our calculated results indicate that the relaxed geometrical structures for the smallest SWNTs in the zeolite channels are much different from those of the ideal isolated SWNTs, producing a great effect on their physical properties. It is found that all three kinds of 4 A SWNTs can possibly exist inside the Zeolite channels. Especially, as an example, we have also studied the coupling effect between the ALPO_4-5 zeolite and the tube (5,0) inside it, and found that the zeolite has real effects on the electronic structure and optical properties of the inside (5,0) tube.Comment: 9 pages, 6figure

Coronal magnetic fields produced by photospheric shear

The magneto-frictional method is used for computing force free fields to examine the evolution of the magnetic field of a line dipole, when there is relative shearing motion between the two polarities. It found that the energy of the sheared field can be arbitrarily large compared with the potential field. It is also found that it is possible to fit the magnetic energy, as a function of shear, by a simple functional form