The three dimensional inverse scattering problem for acoustic waves

We consider the inverse scattering problem for an acoustically soft obstacle in R³. By assuming a priori that the unknown scattering obstacle is starlike and has its boundary lying in a compact family of Hölder continuously differentiable surfaces, it is shown that an optimal solution can be constructed which depends continuously on the measured far field data. Remarks are made on the numerical approximation of the optimal solution.     

The inverse Fourier transform of the filtering function and its integral powers

The convex coordinates of a point, P,in a closed triangular region are defined as weights which must be placed at the vertices of the region to shift the balance point of the weight distribution to P. The vertices of the triangle are interpreted as energy states of a physical system, and the convex coordinates become probabilities. The Maxwell‐Boltzmann distribution function is derived with the aid of convex coordinates.     

The numerical solution of an inverse scattering problem for acoustic waves

In a previous paper, the authors presented a dual space methodfor the numerical solution of the two-dimensional inverse scatteringproblem for acoustic waves in an inhomogeneous medium. Here,by making major modifications to the dual space method, a dramaticimprovement in the numerical performance of this method is achievedfor solving the inverse scattering problem.     

Generation and dissipation of ocean surface waves

Ocean surface waves constitute one of the most important sources of external forces that act on ships and offshore structures. Most ocean waves are generated by wind, but various other effects such as currents, ground and coastal topology, breaking and wave–wave interaction have an influence on the growth and dissipation of wave energy at specific frequency ranges. These water waves are inherently random in nature and their exact shape is difficult to describe, even when confining the described area to a small range. While many different approaches exist to describe the spectral characteristics of ocean waves, some of the processes which affect the generation of waves are still poorly understood. This paper addresses some techniques which serve to describe seaway spectra with respect to the subsequent analysis of dynamic mechanical systems in the ocean such as ships, platforms and pipelines. Advantages and limits of the different approaches are discussed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The arithmetic fourier transform and the visual pathway

The Arithmetic Fourier Transform is an algorithm for the computation of Fourier coefficients. In this paper it is extended to the computation of double Fourier coefficients by a repeated sum. We discuss the relevance of the repeated sum algorithm to signal processing by neurons in the visual pathway.     

The analysis study on nonlinear iterative methods for inverse problems

In this paper, the nonlinear iterative methods, which are different from the classical algorithms, to solve inverse problems are presented. Our methods by denoting some parameters and some properties of the algorithm in both noise and noiseless cases are studied. Finally, the convergence of the sequence generated by the algorithm without noise is discussed.     

Solving Theodorsen's integral equation for conformal maps with the fast fourier transform and various nonlinear iterative methods

Summary We investigate several iterative methods for the numerical solution of Theodorsen's integral equation, the discretization of which is either based on trigonometric polynomials or function families with known attenuation factors. All our methods require simultaneous evaluations of a conjugate periodic function at each step and allow us to apply the fast Fourier transform for this. In particular, we discuss the nonlinear JOR iteration, the nonlinear SOR iteration, a nonlinear second order Euler iteration, the nonlinear Chebyshev semi-iterative method, and its cyclic variant. Under special symmetry conditions for the region to be mapped onto we establish local convergence in the case of discretization by trigonometric interpolation and give simple formulas for the optimal parameters (e.g., the underrelaxation factor) and the asymptotic convergence factor. Weaker related results for the general non-symmetric case are presented too. Practically, our methods extend the range of application of Theodorsen's method and improve its effectiveness strikingly.This work was partially supported by NRC (Canada) grant No. A8240 while, in 1976, the author was at the Dept. of Computer Science, University of British Columbia, Vancouver, B.C., Canada. It is part of a thesis submitted for Habilitation at ETH Zurich     

Regularized inner products of distorted plane waves and near-forward inverse scattering

Regularized inner products, r(s, e₁, e₂,) of the distorted plane waves fór the plasma wave equation u_u ? Δu + qu = 0 are introduced for potentials with compact support. The regularized inner product may be represented in terms of the far-field pattern. The use of the WKB approximation shows that the behaviour of r as e₂ → ? e₁ is closely related to the Radon transform of q. This observation indicates the possibility of finding the Radon transform of q in terms of r(s, e₁, e₂) and then of recovering q by means of the inverse Radon transform.     

The effect of surface topography on weakly nonlinear roll waves

The propagation of short waves in turbulent single layer flows forming on inclined surfaces has received considerable interest in the past. It is well known that such flows on flat surfaces are unstable if the Froude number of the unperturbed uniform state exceeds a critical value. In the initial linear stage disturbances grow exponentially with propagation distance but it has been shown that weakly nonlinear effects may limit the maximum wave amplitude under strictly periodic conditions leading in turn to a train of permanent roll waves. The present study investigates how the flow behaviour is affected if the slope of the bounding surface is no longer constant but changing slowly in the streamwise direction. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Projections of convex bodies and the fourier transform

The Fourier analytic approach to sections of convex bodies has recently been developed and has led to several results, including a complete analytic solution to the Busemann-Petty problem, characterizations of intersection bodies, extremal sections ofl _p-balls. In this article, we extend this approach to projections of convex bodies and show that the projection counterparts of the results mentioned above can be proved using similar methods. In particular, we present a Fourier analytic proof of the recent result of Barthe and Naor on extremal projections ofl _p-balls, and give a Fourier analytic solution to Shephard’s problem, originally solved by Petty and Schneider and asking whether symmetric convex bodies with smaller hyperplane projections necessarily have smaller volume. The proofs are based on a formula expressing the volume of hyperplane projections in terms of the Fourier transform of the curvature function.     

求鳞状因子循环矩阵的逆阵及广义逆阵的快速付氏变换法

借助快速付立叶变换(FFT),本文给出一种求n阶鳞状因子循环矩阵的逆阵、自反g-逆、群逆、Moore-Penrose逆的快速算法,该算法的计算复杂性为O(nlog2n),最后给出的两个数值算例表明了该算法的有效性.     

Bifurcations and exact solutions for a nonlinear surface wind waves equation

By using the method of dynamical systems, for the nonlinear surface wind waves equation, which is given by Manna, we study its dynamical behavior to determine all exact explicit traveling wave solutions. To guarantee the existence of the aforementioned solutions, all parameter conditions are determined. Our procedure shows that the nonlinear surface wind waves equation has no peakon solution. Copyright © 2015 John Wiley & Sons, Ltd.     

Three-dimensional simulation of the runup of nonlinear surface gravity waves

The runup of nonlinear surface gravity waves is numerically simulated in two and three dimensions on the basis of the Navier-Stokes equations. The three-dimensional problem is formulated, and the boundary and initial conditions are described. The splitting method over physical processes is used to construct a discrete model taking into account the cell occupation coefficient. The runup of nonlinear surface gravity waves is simulated in two dimensions for slopes of various geometries, and the numerical results are analyzed. The structural features of the simulated three-dimensional basin are described. Three-dimensional models for the staged runup of nonlinear surface gravity waves breaking on coastal slopes in shallow water areas are considered.     

Stabilization and error bounds for the inverse laplace transform

We present some theorems on the stabilization of the inverse Laplace transform. We assume the Laplace transform is measured at N points to within some error ?. We prove error bounds for the inverse Laplace transform in terms of ? and N, under suitable a-priori constraints. This is achieved by proving parallel stabilization results for a related Hausdorff moment problem.     

The linear sampling method for the inverse electromagnetic scattering problem for screens

We consider the inverse electromagnetic scattering problem of determining the shape of a screen from a knowledge of the electric far field pattern of the scattered wave at fixed frequency. We adapt the linear sampling method invented by Colton and Kirsch (Inverse Problems 12 (1996) 383-393) for the case of obstacles with nonempty interior. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)