N=8 Supergravity on the Light Cone

We construct the generating functional for the light-cone superfield amplitudes in a chiral momentum superspace. It generates the n-point particle amplitudes which on shell are equivalent to the covariant ones. Based on the action depending on unconstrained light-cone chiral scalar superfield, this functional provides a regular d=4 QFT path integral derivation of the Nair-type amplitude constructions. By performing a Fourier transform into the light-cone chiral coordinate superspace we find that the quantum corrections to the superfield amplitudes with n legs are non-local in transverse directions for the diagrams with the number of loops smaller than n(n-1)/2 +1. This suggests the reason why UV infinities, which are proportional to local vertices, cannot appear at least before 7 loops in the light-cone supergraph computations. By combining the E7 symmetry with the supersymmetric recursion relations we argue that the light-cone supergraphs predict all loop finiteness of d=4 N=8 supergravity.Comment: 38

Load-depth sensing of isotropic, linear viscoelastic materials using rigid axisymmetric indenters

An indentation experiment involves five variables: indenter shape, material behavior of the substrate, contact size, applied load and indentation depth. Only three variable are known afterwards, namely, indenter shape, plus load and depth as function of time. As the contact size is not measured and the determination of the material properties is the very aim of the test; two equations are needed to obtain a mathematically solvable system. For elastic materials, the contact size can always be eliminated once and for all in favor of the depth; a single relation between load, depth and material properties remains with the latter variable as unknown. For viscoelastic materials where hereditary integrals model the constitutive behavior, the relation between depth and contact size usually depends also on the (time-dependent) properties of the material. Solving the inverse problem, i.e., determining the material properties from the experimental data, therefore needs both equations. Extending Sneddon's analysis of the indentation problem for elastic materials to include viscoelastic materials, the two equations mentioned above are derived. To find the time dependence of the material properties the feasibility of Golden and Graham's method of decomposing hereditary integrals (J.M. Golden and G.A.C. Graham. Boundary value problems in linear viscoelasticity, Springer, 1988) is investigated and applied to a single load-unload process and to sinusoidally driven stationary state indentation processes.Comment: 116 pages, 29 figure

Understanding the central kinematics of globular clusters with simulated integrated-light IFU observations

The detection of intermediate mass black holes in the centres of globular clusters is highly controversial, as complementary observational methods often deliver significantly different results. In order to understand these discrepancies, we develop a procedure to simulate integral field unit (IFU) observations of globular clusters: Simulating IFU Star Cluster Observations (SISCO). The input of our software are realistic dynamical models of globular clusters that are then converted in a spectral data cube. We apply SISCO to Monte Carlo cluster simulations from Downing et al. (2010), with a realistic number of stars and concentrations. Using independent realisations of a given simulation we are able to quantify the stochasticity intrinsic to the problem of observing a partially resolved stellar population with integrated-light spectroscopy. We show that the luminosity-weighted IFU observations can be strongly biased by the presence of a few bright stars that introduce a scatter in the velocity dispersion measurements up to $\simeq$40% around the expected value, preventing any sound assessment of the central kinematic and a sensible interpretation of the presence/absence of an intermediate mass black hole. Moreover, we illustrate that, in our mock IFU observations, the average kinematic tracer has a mass of $\simeq$0.75 solar masses, only slightly lower than the mass of the typical stars examined in studies of resolved line-of-sight velocities of giant stars. Finally, in order to recover unbiased kinematic measurements we test different masking techniques that allow us to remove the spaxels dominated by bright stars, bringing the scatter down to a level of only a few percent. The application of SISCO will allow to investigate state-of-the-art simulations as realistic observations.Comment: 13 pages, 9 figures, 1 table. Accepted for publication in MNRA

Three flow regimes of viscous jet falling onto a moving surface

A stationary viscous jet falling from an oriented nozzle onto a moving surface is studied, both theoretically and experimentally. We distinguish three flow regimes and classify them by the convexity of the jet shape (concave, vertical and convex). The fluid is modeled as a Newtonian fluid, and the model for the flow includes viscous effects, inertia and gravity. By studying the characteristics of the conservation of momentum for a dynamic jet, the boundary conditions for each flow regime are derived, and the flow regimes are characterized in terms of the process and material parameters. The model is solved by a transformation into an algebraic equation. We make a comparison between the model and experiments, and obtain qualitative agreement

Some remarks concerning rank 2 bundles and Chow groups

[No abstract available

Falling of a viscous jet onto a moving surface

We analyze the stationary flow of a jet of Newtonian fluid that is drawn by gravity onto a moving surface. The situation is modeled by a third-order ODE on a domain of unknown length and with an additional integral condition; by solving part of the equation explicitly we can reformulate the problem as a first-order ODE, again with an integral constraint. We show that there are two flow regimes, and characterize the associated regions in the three-dimensional parameter space in terms of an easily calculable quantity. In a qualitative sense the results from the model are found to correspond with experimental observations.Comment: 16 pages, 11 figure

Optimal Tradeoff Between Exposed and Hidden Nodes in Large Wireless Networks

Wireless networks equipped with the CSMA protocol are subject to collisions due to interference. For a given interference range we investigate the tradeoff between collisions (hidden nodes) and unused capacity (exposed nodes). We show that the sensing range that maximizes throughput critically depends on the activation rate of nodes. For infinite line networks, we prove the existence of a threshold: When the activation rate is below this threshold the optimal sensing range is small (to maximize spatial reuse). When the activation rate is above the threshold the optimal sensing range is just large enough to preclude all collisions. Simulations suggest that this threshold policy extends to more complex linear and non-linear topologies