972 resultados para INTEGRAL-EQUATION THEORY
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We propose and investigate a method for the stable determination of a harmonic function from knowledge of its value and its normal derivative on a part of the boundary of the (bounded) solution domain (Cauchy problem). We reformulate the Cauchy problem as an operator equation on the boundary using the Dirichlet-to-Neumann map. To discretize the obtained operator, we modify and employ a method denoted as Classic II given in [J. Helsing, Faster convergence and higher accuracy for the Dirichlet–Neumann map, J. Comput. Phys. 228 (2009), pp. 2578–2576, Section 3], which is based on Fredholm integral equations and Nyström discretization schemes. Then, for stability reasons, to solve the discretized integral equation we use the method of smoothing projection introduced in [J. Helsing and B.T. Johansson, Fast reconstruction of harmonic functions from Cauchy data using integral equation techniques, Inverse Probl. Sci. Eng. 18 (2010), pp. 381–399, Section 7], which makes it possible to solve the discretized operator equation in a stable way with minor computational cost and high accuracy. With this approach, for sufficiently smooth Cauchy data, the normal derivative can also be accurately computed on the part of the boundary where no data is initially given.
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We investigate a mixed problem with variable lateral conditions for the heat equation that arises in modelling exocytosis, i.e. the opening of a cell boundary in specific biological species for the release of certain molecules to the exterior of the cell. The Dirichlet condition is imposed on a surface patch of the boundary and this patch is occupying a larger part of the boundary as time increases modelling where the cell is opening (the fusion pore), and on the remaining part, a zero Neumann condition is imposed (no molecules can cross this boundary). Uniform concentration is assumed at the initial time. We introduce a weak formulation of this problem and show that there is a unique weak solution. Moreover, we give an asymptotic expansion for the behaviour of the solution near the opening point and for small values in time. We also give an integral equation for the numerical construction of the leading term in this expansion.
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The paper is devoted to the study of the Cauchy problem for a nonlinear differential equation of complex order with the Caputo fractional derivative. The equivalence of this problem and a nonlinear Volterra integral equation in the space of continuously differentiable functions is established. On the basis of this result, the existence and uniqueness of the solution of the considered Cauchy problem is proved. The approximate-iterative method by Dzjadyk is used to obtain the approximate solution of this problem. Two numerical examples are given.
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Mathematics Subject Classification: 26A33; 70H03, 70H25, 70S05; 49S05
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2000 Mathematics Subject Classification: 45A05, 45B05, 45E05,45P05, 46E30
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Mathematics Subject Classification: 44A05, 44A35
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Mathematics Subject Classification 2010: 45DB05, 45E05, 78A45.
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In this work we study an Hammerstein generalized integral equation u(t)=∫_{-∞}^{+∞}k(t,s) f(s,u(s),u′(s),...,u^{(m)}(s))ds, where k:ℝ²→ℝ is a W^{m,∞}(ℝ²), m∈ℕ, kernel function and f:ℝ^{m+2}→ℝ is a L¹-Carathéodory function. To the best of our knowledge, this paper is the first one to consider discontinuous nonlinearities with derivatives dependence, without monotone or asymptotic assumptions, on the whole real line. Our method is applied to a fourth order nonlinear boundary value problem, which models moderately large deflections of infinite nonlinear beams resting on elastic foundations under localized external loads.
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In this thesis I show a triple new connection we found between quantum integrability, N=2 supersymmetric gauge theories and black holes perturbation theory. I use the approach of the ODE/IM correspondence between Ordinary Differential Equations (ODE) and Integrable Models (IM), first to connect basic integrability functions - the Baxter’s Q, T and Y functions - to the gauge theory periods. This fundamental identification allows several new results for both theories, for example: an exact non linear integral equation (Thermodynamic Bethe Ansatz, TBA) for the gauge periods; an interpretation of the integrability functional relations as new exact R-symmetry relations for the periods; new formulas for the local integrals of motion in terms of gauge periods. This I develop in all details at least for the SU(2) gauge theory with Nf=0,1,2 matter flavours. Still through to the ODE/IM correspondence, I connect the mathematically precise definition of quasinormal modes of black holes (having an important role in gravitational waves’ obervations) with quantization conditions on the Q, Y functions. In this way I also give a mathematical explanation of the recently found connection between quasinormal modes and N=2 supersymmetric gauge theories. Moreover, it follows a new simple and effective method to numerically compute the quasinormal modes - the TBA - which I compare with other standard methods. The spacetimes for which I show these in all details are in the simplest Nf=0 case the D3 brane in the Nf=1,2 case a generalization of extremal Reissner-Nordström (charged) black holes. Then I begin treating also the Nf=3,4 theories and argue on how our integrability-gauge-gravity correspondence can generalize to other types of black holes in either asymptotically flat (Nf=3) or Anti-de-Sitter (Nf=4) spacetime. Finally I begin to show the extension to a 4-fold correspondence with also Conformal Field Theory (CFT), through the renowned AdS/CFT correspondence.
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Inverse analysis is currently an important subject of study in several fields of science and engineering. The identification of physical and geometric parameters using experimental measurements is required in many applications. In this work a boundary element formulation to identify boundary and interface values as well as material properties is proposed. In particular the proposed formulation is dedicated to identifying material parameters when a cohesive crack model is assumed for 2D problems. A computer code is developed and implemented using the BEM multi-region technique and regularisation methods to perform the inverse analysis. Several examples are shown to demonstrate the efficiency of the proposed model. (C) 2010 Elsevier Ltd. All rights reserved,
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A new excitation model for the numerical solution of field integral equation (EFIE) applied to arbitrarily shaped monopole antennas fed by coaxial lines is presented. This model yields a stable solution for the input impedance of such antennas with very low numerical complexity and without the convergence and high parasitic capacitance problems associated with the usual delta gap excitation.
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The well-known modified Garabedian-Mcfadden (MGM) method is an attractive alternative for aerodynamic inverse design, for its simplicity and effectiveness (P. Garabedian and G. Mcfadden, Design of supercritical swept wings, AIAA J. 20(3) (1982), 289-291; J.B. Malone, J. Vadyak, and L.N. Sankar, Inverse aerodynamic design method for aircraft components, J. Aircraft 24(2) (1987), 8-9; Santos, A hybrid optimization method for aerodynamic design of lifting surfaces, PhD Thesis, Georgia Institute of Technology, 1993). Owing to these characteristics, the method has been the subject of several authors over the years (G.S. Dulikravich and D.P. Baker, Aerodynamic shape inverse design using a Fourier series method, in AIAA paper 99-0185, AIAA Aerospace Sciences Meeting, Reno, NV, January 1999; D.H. Silva and L.N. Sankar, An inverse method for the design of transonic wings, in 1992 Aerospace Design Conference, No. 92-1025 in proceedings, AIAA, Irvine, CA, February 1992, 1-11; W. Bartelheimer, An Improved Integral Equation Method for the Design of Transonic Airfoils and Wings, AIAA Inc., 1995). More recently, a hybrid formulation and a multi-point algorithm were developed on the basis of the original MGM. This article discusses applications of those latest developments for airfoil and wing design. The test cases focus on wing-body aerodynamic interference and shock wave removal applications. The DLR-F6 geometry is picked as the baseline for the analysis.
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A method for the accurate computation of the current densities produced in a wide-runged bi-planar radio-frequency coil is presented. The device has applications in magnetic resonance imaging. There is a set of opposing primary rungs, symmetrically placed on parallel planes and a similar arrangement of rungs on two parallel planes surrounding the primary serves as a shield. Current densities induced in these primary and shielding rungs are calculated to a high degree of accuracy using an integral-equation approach, combined with the inverse finite Hilbert transform. Once these densities are known, accurate electrical and magnetic fields are then computed without difficulty. Some test results are shown. The method is so rapid that it can be incorporated into optimization software. Some preliminary fields produced from optimized coils are presented.
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A scheme is presented to incorporate a mixed potential integral equation (MPIE) using Michalski's formulation C with the method of moments (MoM) for analyzing the scattering of a plane wave from conducting planar objects buried in a dielectric half-space. The robust complex image method with a two-level approximation is used for the calculation of the Green's functions for the half-space. To further speed up the computation, an interpolation technique for filling the matrix is employed. While the induced current distributions on the object's surface are obtained in the frequency domain, the corresponding time domain responses are calculated via the inverse fast Fourier transform (FFT), The complex natural resonances of targets are then extracted from the late time response using the generalized pencil-of-function (GPOF) method. We investigate the pole trajectories as we vary the distance between strips and the depth and orientation of single, buried strips, The variation from the pole position of a single strip in a homogeneous dielectric medium was only a few percent for most of these parameter variations.
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A mechanical electroscope based on a change in the resonant frequency of a cantilever one micron in size in the presence of charge has recently been fabricated. We derive the decoherence rate of a charge superposition during measurement with such a device using a master equation theory adapted from quantum optics. We also investigate the information produced by such a measurement, using a quantum trajectory approach. Such instruments could be used in mesoscopic electronic systems, and future solid-state quantum computers, so it is useful to know how they behave when used to measure quantum superpositions of charge.