By carefully analyzing the radial part of the wave-equation for a scalar field in AdSd+1, we show that for a particular range of boundary conditions on the scalar field, the radial spectrum contains a bound state. Using the AdS/CFT correspondence, we interpret this peculiar phenomenon as being dual to an unstable double trace deformation of the boundary conformal field theory. We thus show how ...

In this paper, we introduce a radial basis function collocation method for computing solutions to the time-dependent radiative transfer equation. For these computations, we use finite differences to discretize the time coordinate, a discrete ordinate method to discretize the directional variable, and an expansion in radial basis functions to approximate the spatial dependence of the solution. W...

In this paper, we are interested to determine the carbon dioxide pressure in the arterial blood through radial velocity difference. The blood was modeled as a two phase mixture (an aqueous carbon dioxide solution with carbon dioxide gas) by Drift flux model and the Young-Laplace equation. The distributions of mixture velocities determined from the considered model permitted the calculation of t...

In this paper‎, ‎we decide to select the best center nodes‎ ‎of radial basis functions by applying the Multiple Criteria Decision‎ ‎Making (MCDM) techniques‎. ‎Two methods based on radial basis‎ ‎functions to approximate the solution of partial differential‎ ‎equation by using collocation method are applied‎. ‎The first is based‎ ‎on the Kansa's approach‎, ‎and the second is based on the Hermit...

We prove a Liouville type theorem for sign-changing radial solutions of a subcritical semilinear heat equation ut = ∆u + |u|p−1u. We use this theorem to derive a priori bounds, decay estimates, and initial and final blow-up rates for radial solutions of rather general semilinear parabolic equations whose nonlinearities have a subcritical polynomial growth. Further consequences on the existence ...

This paper presents a new neural network based controller design for multivariable systems. The proposed controller is designed using radial basis function (RBF) neural network. Weight update equation using classical least mean square principle is derived for the RBF network. The controller generates optimal control signals abiding by constraints, if any, on the control signals. Simulation resu...

The light quark-antiquark scattering Green's function is considered near a meson resonance peak. The Bethe-Salpeter equation is used to write formal expressions for the resonance width/mass ratio. Arguments are made concerning to what extent this ratio can be calculated perturbatively, and an upper bound is placed on the growth of this ratio as a function of radial excitation. Certain mesons an...

In this article, we consider the discretization of the time-dependent Schrödinger equation using radial basis functions (RBFs). We formulate the discretized problem over an unbounded domain without imposing explicit boundary conditions. Since we can show that time stability of the discretization is not guaranteed for an RBF-collocation method, we propose to employ a Galerkin ansatz instead. For...

A meshless method for the solution of 2D Helmholtz equation has been developed by using the Boundary Integral Equation (BIE) combined with Radial Basis Function (RBF) interpolations. BIE is applied by using the fundamental solution of the Helmholtz equation, therefore domain integrals are not encountered in the method. The method exploits the advantage of placing the source point always in the ...

In this study, the non-linear creep behaviour of a thick-walled cylinder made of stainless steel 316 is investigated using a semi-analytical method. The thick-walled cylinder is under a uniform internal pressure and a non-axisymmetric thermal field as a function of the radial and circumferential coordinates. For the high temperature and stress levels, creep phenomena play a major role in stress...