On the solution of integral equations with a generalized cauchy kernal

A certain class of singular integral equations that may arise from the mixed boundary value problems in nonhonogeneous materials is considered. The distinguishing feature of these equations is that in addition to the Cauchy singularity, the kernels contain terms that are singular only at the end points. In the form of the singular integral equations adopted, the density function is a potential or a displacement and consequently the kernal has strong singularities of the form (t-x)(-2), x(n-2) (t+x)(n), (n is = or 2, 0 x, t b). The complex function theory is used to determine the fundamental function of the problem for the general case and a simple numerical technique is described to solve the integral equation. Two examples from the theory of elasticity are then considered to show the application of the technique

On the solution of integral equations with a generalized cauchy kernel

In this paper a certain class of singular integral equations that may arise from the mixed boundary value problems in nonhomogeneous materials is considered. The distinguishing feature of these equations is that in addition to the Cauchy singularity, the kernels contain terms that are singular only at the end points. In the form of the singular integral equations adopted, the density function is a potential or a displacement and consequently the kernel has strong singularities of the form (t-x) sup-2, x sup n-2 (t+x) sup n, (n or = 2, 0x,tb). The complex function theory is used to determine the fundamental function of the problem for the general case and a simple numerical technique is described to solve the integral equation. Two examples from the theory of elasticity are then considered to show the application of the technique

On the solution of integral equations with strongly singular kernels

Some useful formulas are developed to evaluate integrals having a singularity of the form (t-x) sup-m ,m greater than or equal 1. Interpreting the integrals with strong singularities in Hadamard sense, the results are used to obtain approximate solutions of singular integral equations. A mixed boundary value problem from the theory of elasticity is considered as an example. Particularly for integral equations where the kernel contains, in addition to the dominant term (t-x) sup -m , terms which become unbounded at the end points, the present technique appears to be extremely effective to obtain rapidly converging numerical results

On the solution of integral equations with strong ly singular kernels

In this paper some useful formulas are developed to evaluate integrals having a singularity of the form (t-x) sup-m, m or = 1. Interpreting the integrals with strong singularities in Hadamard sense, the results are used to obtain approximate solutions of singular integral equations. A mixed boundary value problem from the theory of elasticity is considered as an example. Particularly for integral equations where the kernel contains, in addition to the dominant term (t,x) sup-m, terms which become unbounded at the end points, the present technique appears to be extremely effective to obtain rapidly converging numerical results

The mode 3 crack problem in bonded materials with a nonhomogeneous interfacial zone

The mode 3 crack problem for two bonded homogeneous half planes was considered. The interfacial zone was modelled by a nonhomogeneous strip in such a way that the shear modulus is a continuous function throughout the composite medium and has discontinuous derivatives along the boundaries of the interfacial zone. The problem was formulated for cracks perpendicular to the nominal interface and was solved for various crack locations in and around the interfacial region. The asymptotic stress field near the tip of a crack terminating at an interface was examined and it was shown that, unlike the corresponding stress field in piecewise homogeneous materials, in this case the stresses have the standard square root singularity and their angular variation was identical to that of a crack in a homogeneous medium. With application to the subcritical crack growth process in mind, the results given include mostly the stress intensity factors for some typical crack geometries and various material combinations

The crack problem in bonded nonhomogeneous materials

The plane elasticity problem for two bonded half planes containing a crack perpendicular to the interface was considered. The effect of very steep variations in the material properties near the diffusion plane on the singular behavior of the stresses and stress intensity factors were studied. The two materials were thus, assumed to have the shear moduli mu(o) and mu(o) exp (Beta x), x=0 being the diffusion plane. Of particular interest was the examination of the nature of stress singularity near a crack tip terminating at the interface where the shear modulus has a discontinuous derivative. The results show that, unlike the crack problem in piecewise homogeneous materials for which the singularity is of the form r/alpha, 0 less than alpha less than 1, in this problem the stresses have a standard square-root singularity regardless of the location of the crack tip. The nonhomogeneity constant Beta has, however, considerable influence on the stress intensity factors

Stabilization of Extra Dimensions at Tree Level

By considering the effects of string winding and momentum modes on a time dependent background, we find a method by which six compact dimensions become stabilized naturally at the self-dual radius while three dimensions grow large.Comment: 15 pages, 2 figures, minor typos correcte

SppC based energy frontier lepton-proton colliders: luminosity and physics

In this study, main parameters of Super proton-proton Collider (SppC) based lepton-proton colliders are estimated. For electron beam parameters, highest energy International Linear Collider (ILC) and Plasma Wake Field Accelerator-Linear Collider (PWFA-LC) options are taken into account. For muon beams, 1.5 TeV and 3 TeV center of mass energy Muon Collider parameters are used. In addition, ultimate $\mu$p collider which assumes construction of additional 50 TeV muon ring in the SppC tunnel is considered as well. It is shown that $L_{ep}$ $\sim$ $10^{32}$ $cm^{-2}s^{-1}$ can be achieved with moderate upgrade of the SppC proton beam parameters. Physics search potential of proposed lepton-proton colliders is illustrated by considering small Bjorken x region as an example of SM physics and resonant production of color octet leptons as an example of BSM physics.Comment: 11 pages, 3 figures, 8 table

Modeling Phase-resolved Observations of the Surfaces of Magnetic Neutron Stars

Recent observations by XMM-Newton detected rotational pulsations in the total brightness and spectrum of several neutron stars. To properly interpret the data, accurate modeling of neutron star emission is necessary. Detailed analysis of the shape and strength of the rotational variations allows a measurement of the surface composition and magnetic field, as well as constrains the nuclear equation of state. We discuss our models of the spectra and light curves of two of the most observed neutron stars, RX J1856.5-3754 and 1E 1207.4-5209, and discuss some implications of our results and the direction of future work.Comment: 5 pages, 6 figures; Proceedings of "40 Years of Pulsars", eds. C. Bassa, Z. Wang, A. Cumming, V. Kaspi, AIP, submitte

Effect of Ce substitution on the magnetoresistivity and flux pinning energy of the Bi2Sr2Ca1-x CexCu2O8+δ superconductors

In this study, the effect of Ce doping on the properties of Bi 2Sr2Ca1-x Ce x Cu2O 8+δ ceramic superconductors, with x=0.0, 0.01, 0.05, 0.1, and 0.25, has been investigated. Samples' precursors were prepared using the conventional solid state method and subsequently textured using the Laser Floating Zone technique. The magnetoresistance measurements were studied under various applied magnetic fields. The activation energies, irreversibility fields (H irr ), upper critical fields (H c2) and coherence lengths at 0 K (ξ(0)) were calculated from the resistivity versus temperature (ρ-T) curves, under DC magnetic fields up to 5 T. The thermally activated flux flow model has been applied in order to calculate the flux pinning energies. The results indicated that H c2(0) varied from 416.19 to 115 T and the flux pinning energies varied from 1.46 to 0.042 eV at 0 T. © 2013 Springer Science+Business Media New York.This work is supported by the Research Fund of Çukurova University, Adana, Turkey, under grant contracts No: FEF2011YL27 and FEF2013BAP11. A. Sotelo and M.A. Madre wish to thank the Gobierno de Aragón (Research Group T12), for financial support. M.A. Madre also acknowledges the MINECO-FEDER (Project MAT2011-22719) for funding.Peer Reviewe