Quantifying loopy network architectures

Biology presents many examples of planar distribution and structural networks having dense sets of closed loops. An archetype of this form of network organization is the vasculature of dicotyledonous leaves, which showcases a hierarchically-nested architecture containing closed loops at many different levels. Although a number of methods have been proposed to measure aspects of the structure of such networks, a robust metric to quantify their hierarchical organization is still lacking. We present an algorithmic framework, the hierarchical loop decomposition, that allows mapping loopy networks to binary trees, preserving in the connectivity of the trees the architecture of the original graph. We apply this framework to investigate computer generated graphs, such as artificial models and optimal distribution networks, as well as natural graphs extracted from digitized images of dicotyledonous leaves and vasculature of rat cerebral neocortex. We calculate various metrics based on the Asymmetry, the cumulative size distribution and the Strahler bifurcation ratios of the corresponding trees and discuss the relationship of these quantities to the architectural organization of the original graphs. This algorithmic framework decouples the geometric information (exact location of edges and nodes) from the metric topology (connectivity and edge weight) and it ultimately allows us to perform a quantitative statistical comparison between predictions of theoretical models and naturally occurring loopy graphs.Comment: 17 pages, 8 figures. During preparation of this manuscript the authors became aware of the work of Mileyko at al., concurrently submitted for publicatio

Interplay between spin-density-wave and superconducting states in quasi-one-dimensional conductors

The interference between spin-density-wave and superconducting instabilities in quasi-one-dimensional correlated metals is analyzed using the renormalization group method. At the one-loop level, we show how the interference leads to a continuous crossover from a spin-density-wave state to unconventional superconductivity when deviations from perfect nesting of the Fermi surface exceed a critical value. Singlet pairing between electrons on neighboring stacks is found to be the most favorable symmetry for superconductivity. The consequences of non uniform spin-density-wave pairing on the structure of phase diagram within the crossover region is also discussed.Comment: 10 pages RevTex,4 Figures, submitted to EPJ

Proceedings for the ICASE Workshop on Heterogeneous Boundary Conditions

Domain Decomposition is a complex problem with many interesting aspects. The choice of decomposition can be made based on many different criteria, and the choice of interface of internal boundary conditions are numerous. The various regions under study may have different dynamical balances, indicating that different physical processes are dominating the flow in these regions. This conference was called in recognition of the need to more clearly define the nature of these complex problems. This proceedings is a collection of the presentations and the discussion groups

Fermi Surface Nesting and the Origin of the Charge Density Wave in NbSe2_2

We use highly accurate density functional calculations to study the band structure and Fermi surfaces of NbSe2. We calculate the real part of the non-interacting susceptibility, Re chi_0(q), which is the relevant quantity for a charge density wave (CDW) instability and the imaginary part, Im chi_0(q), which directly shows Fermi surface (FS) nesting. We show that there are very weak peaks in Re chi_0(q) near the CDW wave vector, but that no such peaks are visible in Im chi_0(q), definitively eliminating FS nesting as a factor in CDW formation. Because the peak in Re chi_0(q) is broad and shallow, it is unlikely to be the direct cause of the CDW instability. We briefly address the possibility that electron-electron interactions (local field effects) produce additional structure in the total (renormalized) susceptibility, and we discuss the role of electron-ion matrix elements.Comment: Replacement of Table II values, minor changes to tex

A Quantum Monte Carlo Method and Its Applications to Multi-Orbital Hubbard Models

We present a framework of an auxiliary field quantum Monte Carlo (QMC) method for multi-orbital Hubbard models. Our formulation can be applied to a Hamiltonian which includes terms for on-site Coulomb interaction for both intra- and inter-orbitals, intra-site exchange interaction and energy differences between orbitals. Based on our framework, we point out possible ways to investigate various phase transitions such as metal-insulator, magnetic and orbital order-disorder transitions without the minus sign problem. As an application, a two-band model is investigated by the projection QMC method and the ground state properties of this model are presented.Comment: 10 pages LaTeX including 2 PS figures, to appear in J.Phys.Soc.Jp

Role of multiorbital effects in the magnetic phase diagram of iron-pnictides

We elucidate the pivotal role of the bandstructure's orbital content in deciding the type of commensurate magnetic order stabilized within the itinerant scenario of iron-pnictides. Recent experimental findings in the tetragonal magnetic phase attest to the existence of the so-called charge and spin ordered density wave over the spin-vortex crystal phase, the latter of which tends to be favored in simplified band models of itinerant magnetism. Here we show that employing a multiorbital itinerant Landau approach based on realistic bandstructures can account for the experimentally observed magnetic phase, and thus shed light on the importance of the orbital content in deciding the magnetic order. In addition, we remark that the presence of a hole pocket centered at the Brillouin zone's ${\rm M}$-point favors a magnetic stripe rather than a tetragonal magnetic phase. For inferring the symmetry properties of the different magnetic phases, we formulate our theory in terms of magnetic order parameters transforming according to irreducible representations of the ensuing D$_{\rm 4h}$ point group. The latter method not only provides transparent understanding of the symmetry breaking schemes but also reveals that the leading instabilities always belong to the $\{A_{1g},B_{1g}\}$ subset of irreducible representations, independent of their C$_2$ or C$_4$ nature.Comment: 11 pages, 6 figure