Towards an Efficient Finite Element Method for the Integral Fractional Laplacian on Polygonal Domains

We explore the connection between fractional order partial differential equations in two or more spatial dimensions with boundary integral operators to develop techniques that enable one to efficiently tackle the integral fractional Laplacian. In particular, we develop techniques for the treatment of the dense stiffness matrix including the computation of the entries, the efficient assembly and storage of a sparse approximation and the efficient solution of the resulting equations. The main idea consists of generalising proven techniques for the treatment of boundary integral equations to general fractional orders. Importantly, the approximation does not make any strong assumptions on the shape of the underlying domain and does not rely on any special structure of the matrix that could be exploited by fast transforms. We demonstrate the flexibility and performance of this approach in a couple of two-dimensional numerical examples

Continuation for thin film hydrodynamics and related scalar problems

This chapter illustrates how to apply continuation techniques in the analysis of a particular class of nonlinear kinetic equations that describe the time evolution through transport equations for a single scalar field like a densities or interface profiles of various types. We first systematically introduce these equations as gradient dynamics combining mass-conserving and nonmass-conserving fluxes followed by a discussion of nonvariational amendmends and a brief introduction to their analysis by numerical continuation. The approach is first applied to a number of common examples of variational equations, namely, Allen-Cahn- and Cahn-Hilliard-type equations including certain thin-film equations for partially wetting liquids on homogeneous and heterogeneous substrates as well as Swift-Hohenberg and Phase-Field-Crystal equations. Second we consider nonvariational examples as the Kuramoto-Sivashinsky equation, convective Allen-Cahn and Cahn-Hilliard equations and thin-film equations describing stationary sliding drops and a transversal front instability in a dip-coating. Through the different examples we illustrate how to employ the numerical tools provided by the packages auto07p and pde2path to determine steady, stationary and time-periodic solutions in one and two dimensions and the resulting bifurcation diagrams. The incorporation of boundary conditions and integral side conditions is also discussed as well as problem-specific implementation issues

Measurement of ZZ production in leptonic final states at {\surd}s of 1.96 TeV at CDF

In this paper we present a precise measurement of the total ZZ production cross section in pp collisions at {\surd}s= 1.96 TeV, using data collected with the CDF II detector corresponding to an integrated luminosity of approximately 6 fb-1. The result is obtained by combining separate measurements in the four-charged (lll'l'), and two-charged-lepton and two-neutral-lepton (llvv) decay modes of the Z. The combined measured cross section for pp {\to} ZZ is 1.64^(+0.44)_(-0.38) pb. This is the most precise measurement of the ZZ production cross section in 1.96 TeV pp collisions to date.Comment: submitted to Phys. Rev. Let

Search for Gravitational Waves Associated with Gamma-Ray Bursts during the First Advanced LIGO Observing Run and Implications for the Origin of GRB 150906B

We present the results of the search for gravitational waves (GWs) associated with γ-ray bursts detected during the first observing run of the Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO). We find no evidence of a GW signal for any of the 41 γ-ray bursts for which LIGO data are available with sufficient duration. For all γ-ray bursts, we place lower bounds on the distance to the source using the optimistic assumption that GWs with an energy of ${10}^{-2}{M}_{\odot }{c}^{2}$ were emitted within the $16$–$500$ Hz band, and we find a median 90% confidence limit of 71 Mpc at 150 Hz. For the subset of 19 short/hard γ-ray bursts, we place lower bounds on distance with a median 90% confidence limit of 90 Mpc for binary neutron star (BNS) coalescences, and 150 and 139 Mpc for neutron star–black hole coalescences with spins aligned to the orbital angular momentum and in a generic configuration, respectively. These are the highest distance limits ever achieved by GW searches. We also discuss in detail the results of the search for GWs associated with GRB 150906B, an event that was localized by the InterPlanetary Network near the local galaxy NGC 3313, which is at a luminosity distance of $54$ Mpc (z = 0.0124). Assuming the γ-ray emission is beamed with a jet half-opening angle $\leqslant 30^\circ$, we exclude a BNS and a neutron star–black hole in NGC 3313 as the progenitor of this event with confidence >99%. Further, we exclude such progenitors up to a distance of 102 Mpc and 170 Mpc, respectively

SOME PECULIARITIES OF DUCTILE SHEAR FAILURE OF AMORPHOUS ALLOY RIBBONS

The kinetics of a shear crack propagation under ductile shear failure of amorphous alloys ribbons is studied experimentally. Some phenomena that accompany this failure are also studied: repeated alternation of the shear crack orientation, plastic corrugation of a ribbon, extreme local heating at the crack front, and the meniscus instability