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

Cluster observations of flux rope structures in the near-tail

International audienceAn investigation of the 2003 Cluster tail season has revealed small flux ropes in the near-tail plasma sheet of Earth. These flux ropes manifest themselves as a bipolar magnetic field signature (usually predominantly in the Z-component) associated with a strong transient peak in one or more of the other components (usually the Y-component). These signatures are interpreted as the passage of a cylindrical magnetic structure with a strong axial magnetic field over the spacecraft position. On the 2 October 2003 all four Cluster spacecraft observed a flux rope in the plasma sheet at X (GSM) ~-17 RE. The flux rope was travelling Earthward and duskward at ~160 kms-1, as determined from multi-spacecraft timing. This is consistent with the observed south-then-north bipolar BZ signature and corresponds to a size of ~0.3 RE (a lower estimate, measuring between the inflection points of the bipolar signature). The axis direction, determined from multi-spacecraft timing and the direction of the strong core field, was close to the intermediate variance direction of the magnetic field. The current inside the flux rope, determined from the curlometer technique, was predominantly parallel to the magnetic field. However, throughout the flux rope, but more significant in the outer sections, a non-zero component of current perpendicular to the magnetic field existed. This shows that the flux rope was not in a "constant a" force-free configuration, i.e. the magnetic force, J×B was also non-zero. In the variance frame of the magnetic field, the components of J×B suggest that the magnetic pressure force was acting to expand the flux rope, i.e. directed away from the centre of the flux rope, whereas the smaller magnetic tension force was acting to compress the flux rope. The plasma pressure is reduced inside the flux rope. A simple estimate of the total force acting on the flux rope from the magnetic forces and surrounding plasma suggests that the flux rope was experiencing an expansive total force. On 13 August 2003 all four Cluster spacecraft observed a flux rope at X (GSM) ~-18 RE. This flux rope was travelling tailward at 200 kms-1, consistent with the observed north-then-south bipolar BZ signature. The bipolar signature corresponds to a size of ~0.3 RE (lower estimate). In this case, the axis, determined from multi-spacecraft timing and the direction of the strong core field, was directed close to the maximum variance direction of the magnetic field. The current had components both parallel and perpendicular to the magnetic field, and J×B was again larger in the outer sections of the flux rope than in the centre. This flux rope was also under expansive magnetic pressure forces from J×B, i.e. directed away from the centre of the flux rope, and had a reduced plasma pressure inside the flux rope. A simple total force calculation suggests that this flux rope was experiencing a large expansive total force. The observations of a larger J×B signature in the outer sections of the flux ropes when compared to the centre may be explained if the flux ropes are observed at an intermediate stage of their evolution after creation by reconnection at multiple X lines near the Cluster apogee. It is suggested that these flux ropes are in the process of relaxing towards the force-free like configuration often observed further down the tail. The centre of the flux ropes may contain older reconnected flux at a later evolutionary stage and may therefore be more force-free

Spin physics with antiprotons

New possibilities arising from the availability at GSI of antiproton beams, possibly polarised, are discussed. The investigation of the nucleon structure can be boosted by accessing in Drell-Yan processes experimental asymmetries related to cross-sections in which the parton distribution functions (PDF) only appear, without any contribution from fragmentation functions; such processes are not affected by the chiral suppression of the transversity function $h_1(x)$. Spin asymmetries in hyperon production and Single Spin Asymmetries are discussed as well, together with further items like electric and magnetic nucleonic form factors and open charm production. Counting rates estimations are provided for each physical case. The sketch of a possible experimental apparatus is proposed.Comment: Presented for the proceedings of ASI "Spin and Symmetry", Prague, July 5-10, 2004, to be published in Czech. J. Phys. 55 (2005

A simply connected surface of general type with p_g=0 and K^2=2

In this paper we construct a simply connected, minimal, complex surface of general type with p_g=0 and K^2=2 using a rational blow-down surgery and Q-Gorenstein smoothing theory.Comment: 19 pages, 6 figures. To appear in Inventiones Mathematica

Thermal analysis of hadron multiplicities from relativistic quantum molecular dynamics

Some questions arising in the application of the thermal model to hadron production in heavy ion collisions are studied. We do so by applying the thermal model of hadron production to particle yields calculated by the microscopic transport model RQMD(v2.3). We study the bias of incomplete information about the final hadronic state on the extraction of thermal parameters.It is found that the subset of particles measured typically in the experiments looks more thermal than the complete set of stable particles. The hadrons which show the largest deviations from thermal behaviour in RQMD(v2.3) are the multistrange baryons and antibaryons. We also looked at the influence of rapidity cuts on the extraction of thermal parameters and found that they lead to different thermal parameters and larger disagreement between the RQMD yields and the thermal model.Comment: 12 pages, 2 figures, uses REVTEX, only misprint and stylistic corrections, to appear in Physical Review

The road to deterministic matrices with the restricted isometry property

The restricted isometry property (RIP) is a well-known matrix condition that provides state-of-the-art reconstruction guarantees for compressed sensing. While random matrices are known to satisfy this property with high probability, deterministic constructions have found less success. In this paper, we consider various techniques for demonstrating RIP deterministically, some popular and some novel, and we evaluate their performance. In evaluating some techniques, we apply random matrix theory and inadvertently find a simple alternative proof that certain random matrices are RIP. Later, we propose a particular class of matrices as candidates for being RIP, namely, equiangular tight frames (ETFs). Using the known correspondence between real ETFs and strongly regular graphs, we investigate certain combinatorial implications of a real ETF being RIP. Specifically, we give probabilistic intuition for a new bound on the clique number of Paley graphs of prime order, and we conjecture that the corresponding ETFs are RIP in a manner similar to random matrices.Comment: 24 page

A Rotating Collapsar and Possible Interpretation of the LSD Neutrino Signal from SN 1987A

We consider an improved rotational mechanism of the explosion of a collapsing supernova. We show that this mechanism leads to two-stage collapse with a phase difference of \sim 5 h. Based on this model, we attempt a new interpretation of the events in underground neutrino detectors on February 23, 1987, related to the supernova SN 1987A.Comment: 18 pages, 3 figures, 9 table

A model of force balance in Saturn's magnetodisc

We present calculations of magnetic potential associated with the perturbation of Saturn's magnetic field by a rotating, equatorially-situated disc of plasma. Such structures are central to the dynamics of the rapidly rotating magnetospheres of Saturn and Jupiter. They are `fed' internally by sources of plasma from moons such as Enceladus (Saturn) and Io (Jupiter). We use a scaled form of Euler potentials for the Jovian magnetodisc field (Caudal, 1986). In this formalism, the magnetic field is assumed to be azimuthally symmetric about the planet's axis of rotation, and plasma temperature is constant along a field line. We perturb the dipole potential by using simplified distributions of plasma pressure and angular velocity for both planets, based on observations by Cassini (Saturn) and Voyager (Jupiter). Our results quantify the degree of radial `stretching' exerted on the dipolar field lines through the plasma's rotational motion and pressure. A simplified version of the field model, the `homogeneous disc', can be used to easily estimate the distance of transition in the outer magnetosphere between pressure-dominated and centrifugally-dominated disc structure. We comment on the degree of equatorial confinement as represented by the scale height associated with disc ions of varying mass and temperature. For Saturn, we identify the principal forces which contribute to the magnetodisc current and make comparisons between the field structure predicted by the model and magnetic field measurements from Cassini. For Jupiter, we reproduce Caudal's original calculation in order to validate our model implementation. We also show that compared to Saturn, where plasma pressure gradient is, on average, weaker than centrifugal force, the outer plasmadisc of Jupiter is clearly a pressure-dominated structure.Comment: 24 pages, 15 figures, 2 tables; accepted for publication in MNRA

Search for associated Higgs boson production using like charge dilepton events in p(p)over-bar collisions at root s=1.96 TeV

We present a search for associated Higgs boson production in the process p (p) over bar -> W/ZH -> l(+/-)l'(+/-) + X in ee, e mu, and mu mu final states. The search is based on data collected by the D0 experiment at the Fermilab Tevatron Collider at root s = 1.96 TeV corresponding to 5.3 fb(-1) of integrated luminosity. We require two isolated leptons (electrons or muons) with the same electric charge and additional kinematic requirements. No significant excess above background is observed, and we set 95% C. L. observed (expected) upper limits on ratio of the production cross section to the standard model prediction of 6.4 (7.3) for a Higgs boson mass of 165 GeV and 13.5 (19.8) for a mass of 115 GeV