185,038 research outputs found

    Demarcating the Right to Gather News: A Sequential Interpretation of the First Amendment

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    In this paper we construct well-posed boundary conditions for the compressible Euler and Navier-Stokes equations in two space dimensions. When also considering the dual equations, we show how to construct the boundary conditions so that both the primal and dual problems are well-posed. By considering the primal and dual problems simultaneously, we construct energy stable and dual consistent finite difference schemes on summation-by-  parts form with weak imposition of the boundary conditions. According to linear theory, the stable and dual consistent discretization can be used to compute linear integral functionals from the solution at a superconvergent rate. Here we evaluate numerically the superconvergence property for the non-linear Euler and Navier{ Stokes equations with linear and non-linear integral functionals

    Explicit solutions to hyper-Bessel integral equations of second kind

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    AbstractIn earlier papers, the authors have used the transmutation method to find solutions to Volterra integral or differ-integral equations of second kind, involving Erdélyi-Kober fractional integration operators (see [1,2]), as well as to dual integral equations and some Bessel-type differential equations (see [3,4]). Here we consider the so-called hyper-Bessel integral equations whose kernel-function is a rather general special function (a Meijer's G-function). Such an equation can be written also in a form involving a product of arbitrary number of Erdélyi-Kober integrals. By means of a Poisson-type transmutation, we reduce its solution to the well-known solution of a simpler Volterra equation involving Riemann-Liouville integration only. In the general case, the solution is found as a series of integrals of G-functions, easily reducible to series of G-functions. For particular nonhomogeneous (right-hand side) parts, this solution reduces to some known special functions. The main techniques are based on the generalized fractional calculus

    Development of classical boundary element analysis of fracture mechanics in gradient materials

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    Over the last decade, the authors have extended the classical boundary element methods (BEM) for analysis of the fracture mechanics in functionally gradient materials. This paper introduces the dual boundary element method associated with the generalized Kelvin fundamental solutions of multilayered elastic solids (or Yue’s solution). This dual BEM uses a pair of the displacement and traction boundary integral equations. The former is collocated exclusively on the uncracked boundary, and the latter is collocated only on one side of the crack surface. All the singular integrals in dual boundary integral equations have been solved by numerical and rigid-body motion methods. This paper then introduces two applications of the dual BEM to fracture mechanics. These research results include the stress intensity factor values of different cracks in the materials, some fracture mechanics properties of layered rocks in rock engineering.postprin

    Application of displacement and traction boundary integral equations for fracture mechanics analysis

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    A general formulation by dual boundary integral equations and a computational solution algorithm for the general mixed-mode crack in a linearly elastic, isotropic medium is presented. Traction boundary integral equations are collocated at the points on one crack surface while displacement boundary integral equations are collocated at the opposite points on the other surface to ensure a unique solution. The hypersingular and strongly singular integrals in the traction and displacement boundary integral equations are regularized before the numerical implementation. The singular integration elements on both crack surfaces are replaced by smooth curved auxiliary surfaces to avoid the direct integration over the singular elements. Usage of these detoured auxiliary contours is justified by certain identities of the fundamental solutions. Convergence tests for integration order and subdivision of the auxiliary surface elements were performed. To demonstrate the accuracy and efficiency of the present technique, the deformation and the stress intensity factors for two- and three-dimensional embedded and edge crack problems are given

    Exploring the mirror TBA

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    We apply the contour deformation trick to the Thermodynamic Bethe Ansatz equations for the AdS_5 \times S^5 mirror model, and obtain the integral equations determining the energy of two-particle excited states dual to N=4 SYM operators from the sl(2) sector. We show that each state/operator is described by its own set of TBA equations. Moreover, we provide evidence that for each state there are infinitely-many critical values of 't Hooft coupling constant \lambda, and the excited states integral equations have to be modified each time one crosses one of those. In particular, estimation based on the large L asymptotic solution gives \lambda \approx 774 for the first critical value corresponding to the Konishi operator. Our results indicate that the related calculations and conclusions of Gromov, Kazakov and Vieira should be interpreted with caution. The phenomenon we discuss might potentially explain the mismatch between their recent computation of the scaling dimension of the Konishi operator and the one done by Roiban and Tseytlin by using the string theory sigma model.Comment: 69 pages, v2: new "hybrid" equations for YQ-functions, figures and tables are added. Analyticity of Y-system is discussed, v3: published versio

    A dual reciprocal boundary element formulation for viscous flows

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    The advantages inherent in the boundary element method (BEM) for potential flows are exploited to solve viscous flow problems. The trick is the introduction of a so-called dual reciprocal technique in which the convective terms are represented by a global function whose unknown coefficients are determined by collocation. The approach, which is necessarily iterative, converts the governing partial differential equations into integral equations via the distribution of fictitious sources or dipoles of unknown strength on the boundary. These integral equations consist of two parts. The first is a boundary integral term, whose kernel is the unknown strength of the fictitious sources and the fundamental solution of a convection-free flow problem. The second part is a domain integral term whose kernel is the convective portion of the governing PDEs. The domain integration can be transformed to the boundary by using the dual reciprocal (DR) concept. The resulting formulation is a pure boundary integral computational process
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