Enumeration of chord diagrams on many intervals and their non-orientable analogs

Two types of connected chord diagrams with chord endpoints lying in a collection of ordered and oriented real segments are considered here: the real segments may contain additional bivalent vertices in one model but not in the other. In the former case, we record in a generating function the number of fatgraph boundary cycles containing a fixed number of bivalent vertices while in the latter, we instead record the number of boundary cycles of each fixed length. Second order, non-linear, algebraic partial differential equations are derived which are satisfied by these generating functions in each case giving efficient enumerative schemes. Moreover, these generating functions provide multi-parameter families of solutions to the KP hierarchy. For each model, there is furthermore a non-orientable analog, and each such model likewise has its own associated differential equation. The enumerative problems we solve are interpreted in terms of certain polygon gluings. As specific applications, we discuss models of several interacting RNA molecules. We also study a matrix integral which computes numbers of chord diagrams in both orientable and non-orientable cases in the model with bivalent vertices, and the large-N limit is computed using techniques of free probability.Comment: 23 pages, 7 figures; revised and extended versio

Interdependence of magnetism and superconductivity in the borocarbide TmNi2B2C

We have discovered a new antiferromagnetic phase in TmNi2B2C by neutron diffraction. The ordering vector is Q_A = (0.48,0,0) and the phase appears above a critical in-plane magnetic field of 0.9 T. The field was applied in order to test the assumption that the zero-field magnetic structure at Q_F = (0.094,0.094,0) would change into a c-axis ferromagnet if superconductivity were destroyed. We present theoretical calculations which show that two effects are important: A suppression of the ferromagnetic component of the RKKY exchange interaction in the superconducting phase, and a reduction of the superconducting condensation energy due to the periodic modulation of the moments at the wave vector Q_A

Competing Ordered Phases in URu2Si2: Hydrostatic Pressure and Re-substitution

A persistent kink in the pressure dependence of the \hidden order" (HO) transition temperature of URu2-xRexSi2 is observed at a critical pressure Pc=15 kbar for 0 < x < 0.08. In URu2Si2, the kink at Pc is accompanied by the destruction of superconductivity; a change in the magnitude of a spin excitation gap, determined from electrical resistivity measurements; and a complete gapping of a portion of the Fermi surface (FS), inferred from a change in scattering and the competition between the HO state and superconductivity for FS fraction

Detecting and Characterizing Small Dense Bipartite-like Subgraphs by the Bipartiteness Ratio Measure

We study the problem of finding and characterizing subgraphs with small \textit{bipartiteness ratio}. We give a bicriteria approximation algorithm \verb|SwpDB| such that if there exists a subset $S$ of volume at most $k$ and bipartiteness ratio $\theta$, then for any $0<\epsilon<1/2$, it finds a set $S'$ of volume at most $2k^{1+\epsilon}$ and bipartiteness ratio at most $4\sqrt{\theta/\epsilon}$. By combining a truncation operation, we give a local algorithm \verb|LocDB|, which has asymptotically the same approximation guarantee as the algorithm \verb|SwpDB| on both the volume and bipartiteness ratio of the output set, and runs in time $O(\epsilon^2\theta^{-2}k^{1+\epsilon}\ln^3k)$, independent of the size of the graph. Finally, we give a spectral characterization of the small dense bipartite-like subgraphs by using the $k$th \textit{largest} eigenvalue of the Laplacian of the graph.Comment: 17 pages; ISAAC 201

Experimental investigation of the Landau-Pomeranchuk-Migdal effect in low-Z targets

In the CERN NA63 collaboration we have addressed the question of the potential inadequacy of the commonly used Migdal formulation of the Landau-Pomeranchuk-Migdal (LPM) effect by measuring the photon emission by 20 and 178 GeV electrons in the range 100 MeV - 4 GeV, in targets of LowDensityPolyEthylene (LDPE), C, Al, Ti, Fe, Cu, Mo and, as a reference target, Ta. For each target and energy, a comparison between simulated values based on the LPM suppression of incoherent bremsstrahlung is shown, taking multi-photon effects into account. For these targets and energies, we find that Migdal's theoretical formulation is adequate to a precision of better than about 5%, irrespective of the target substance.Comment: 8 pages, 13 figure

Band structure approach to the resonant x-ray scattering

We study the resonance behaviour of the forbidden 600 and 222 x-ray Bragg peaks in Ge using LDA band structure methods. These Bragg peaks remain forbidden in the resonant dipole scattering approximation even taking into account the non local nature of the band states. However they become allowed at resonance if the eigenstates of the unoccupied conduction band involve a hybridization of p like and d like atomic states. We show that the energy dependence of the resonant behaviour, including the phase of the scattering, is a direct measure of this p-d hybridization.and obtain quantitative agreement with experiment. A simple physical picture involving a product of dipole and quadrupolar transition matrix elements explains this behaviour and shows that it should be generally true for cases where the resonating atom is not at an inversion center. This has strong implications for the description of the resonance behavior of x-ray scattering in materials where the resonant atom is not at an inversion center such as V2O3 and in ferro and antiferro electric and piezo electric materials in general.Comment: 4 pages, 5figure

Modeling rhythmic patterns in the hippocampus

We investigate different dynamical regimes of neuronal network in the CA3 area of the hippocampus. The proposed neuronal circuit includes two fast- and two slowly-spiking cells which are interconnected by means of dynamical synapses. On the individual level, each neuron is modeled by FitzHugh-Nagumo equations. Three basic rhythmic patterns are observed: gamma-rhythm in which the fast neurons are uniformly spiking, theta-rhythm in which the individual spikes are separated by quiet epochs, and theta/gamma rhythm with repeated patches of spikes. We analyze the influence of asymmetry of synaptic strengths on the synchronization in the network and demonstrate that strong asymmetry reduces the variety of available dynamical states. The model network exhibits multistability; this results in occurrence of hysteresis in dependence on the conductances of individual connections. We show that switching between different rhythmic patterns in the network depends on the degree of synchronization between the slow cells.Comment: 10 pages, 9 figure

Fast recovery of the stripe magnetic order by Mn/Fe substitution in F-doped LaFeAsO superconductors

$^{75}$As Nuclear Magnetic (NMR) and Quadrupolar (NQR) Resonance were used, together with M\"{o}ssbauer spectroscopy, to investigate the magnetic state induced by Mn for Fe substitutions in F-doped LaFe$_{1-x}$Mn$_{x}$AsO superconductors. The results show that $0.5$% of Mn doping is enough to suppress the superconducting transition temperature $T_c$ from 27 K to zero and to recover the magnetic structure observed in the parent undoped LaFeAsO. Also the tetragonal to orthorhombic transition of the parent compound is recovered by introducing Mn, as evidenced by a sharp drop of the NQR frequency. The NQR spectra also show that a charge localization process is at play in the system. Theoretical calculations using a realistic five-band model show that correlation-enhanced RKKY exchange interactions between nearby Mn ions stabilize the observed magnetic order, dominated by $Q_1=(\pi,0)$ and $Q_2=(0,\pi)$ ordering vectors. These results give compelling evidence that F-doped LaFeAsO is a strongly correlated electron system at the verge of an electronic instability.Comment: 5 pages, 5 figures and 4 pages of supplemental materia